-------
     It is reasonable to assume that the segments of
duration DT of the rainfall hyetograph are straight lines.
The accuracy of this assumption is greater when the
increments of time DT become smaller.

     Two conditions have to be satisfied at the point of
the intersection A:

     (a) rainfall intensity at A = infiltration rate at A

     (b) accumulated mass precipitated until A = accumu-
         lated mass infiltrated until A.

     From the condition  (a):
or
so
      -Kt
             i(I) +
                       [id + i)
     t = - i in
                id) +
                        fo - fc
                          [id + i) - id)] - f
                             fo - fc
if and only if the argument of the logarithm is between
0.0 and 1.0.

     From the condition (b):
f£,^
60 T
      60K
           (l-e"Kt) =
 x
60
                                                         (3)
                                                         (4)
where mi(I) = mass precipitated until a time (I-DT)

and i(I) = ordinates of the rainfall intensity curve.

     Each time increment DT can be divided in as many n
increments as desired.  Therefore x = DT/n where n = 1,2,..

     The computer will solve equation (3) for 1=1 and

                    2DT       „ = (n-1)  DT. fQr M and
x = 0  x =
x   u, x
            n
                X=
                x
           DT
x = 0 , x = — ,
                     n
                        fn—
                    x = -
                              x
                              DT
                                     n

                                 ;  and so on .   The time t
which will be found for each combination of I and x will
be substituted (together with the corresponding values of
I and x) into equation (4) .
                             238

-------
     When equation (4) is satisfied, then the computation
will stop and the values of t, I, and x will be stored.
The computation of the actual infiltration curve will
follow, and the stored value of t will be used to start
the calculation of the surface retention.
                              239

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                  5.  SURFACE RETENTION


     Surface retention includes interception, depression
storage, and evaporation during a storm.

     Interception by vegetation may range from 0.01 to 0.5
inches in forest areas, but is not usually significant in
urban drainage.

     Evaporation is of little significance for the short
rainfall duration encountered in urban storm drainage
design.

     Therefore, for simplicity of the model, interception
and evaporation will be assumed negligible for an urban
area.

     Some investigators have assumed that all depressions
must be filled before overland flow begins.  The real
situation is that almost immediately after the beginning
of the rainfall excess, the smallest depressions become
filled and overland flow begins.  Most of this water in
turn fills larger depressions, but some of it follows an
unobstructed path to the collecting gutters.

     Linsley, Kohler, and Paulhus [14] recommended an
exponential relationship
                V
1 - e
                              -N(P - F)
(5)
where V  = volume of water in depression storage at any
           time throughout a storm, in inches

      S, = total depression storage capacity of the basin,
           in inches

      P  = accumulated volume of water precipitated in
           inches

      F  =  accumulated volume of water infiltrated in
            inches

      N  =  storage constant
                            240

-------
     Assuming that the initial  increment  of  rainfall
excess is completely retained by depressions:
             dV
           d(p - F)
                    = 1   when  (P  -  F)  is  near  zero.
Then by differentiation can be found that

     N _  1
     ^\j _ --^---i-------"
                                                        (6)
     If the depression storage  supply  is  s  (in/hr),  then:
            •t
              s dt = V
           0
where t is time in hours from the beginning of  the rainfall
excess .
     Then
     or
                   s =
                   s =
                   d
                  dt
__d
dt
                                          P - F
     Sd
                       (P - F) e
                                       P  - F
     but
     therefore
                   dt
                (P - F) =  (i - f)
                      (in/hr)
                                   P  -  F
              s =  (i - -f) e
                                 (7)
     Of course on impervious  areas  where infiltration is
zero and also accumulated volume  of water infiltrated does
not exist, equations  (5) and  (7)  become
                             241

-------
                    V
                           3d
1 - e
                    s = i e

     Horton  [15] stated that the depression storage
"commonly ranges from 0.125 to 0.75 inches for flat areas
and from 0 .-5 to 1.5 inches for cultivated fields and for
natural grass lands or forests".  On moderate or gentle
slopes he estimated that pervious surface depressions
"can commonly hold the equivalent of 0.25 to 0.5 inch depth
of water and even more on natural meadow and forest land".

     Hicks  [16] has used depression storage losses of 0.20
inch for sand, 0.15 inch for loam, and 0.10 inch for clay,
considering high rates of rainfall and runoff.

     Recent gagings show depression storage to be about
0.3 inch in forest litter, 0.2 inch in good pasture, and
0.05 to 0.10 inch in smooth cultivated land [17].

     If there are no data available, the overall de-
pression storage capacity can be assumed equal to 0.25
inch on pervious urban areas which usually present
individual depressions with depths from 0 to 0.5 inches.
The overall depression storage on impervious urban areas
can be assumed equal to 0.0625 inch with the depth of de-
pressions ranging from 0 to 0.125 inches.  These assump-
tions, when there is lack of data about the basin under
consideration, seem reasonable from observations made
during rainfalls [4], [9] , [18] .

     A typical computer output of the developed computer
program (Appendix III) simulating infiltration and
depression storage supply is presented graphically in
Figure 138.

     Subtracting the calculated values of infiltration
and depression storage supply from the rainfall intensity
at any time, the rainfall excess which produces the over-
land flow is obtained.
                            242

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O


CM
              O
O
 *

o
       243

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                     6.  OVERLAND FLOW
     En route to a channel or gutter/ the water is desig-
nated as overland flow.

     Because of the complex nature of flow, models are
generally simplified to two dimensions.  This was the
approach used by Keulegan  (1944) who first worked on the
spatially varied unsteady flow problem.

     Horton  [19] and Izzard [3] studied unsteady flow
across sloping plane surfaces.  However, Horton's equation
for overland flow has limited experimental support, and
Izzard^s dimensionless hydrograph is limited to situations
where iL < 500, where i is the rainfall intensity in in/hr
and L is the length of overland flow in ft.

     In the following the build up of the flow over a
sloping plane is treated starting with the partial differ-
ential equations of momentum and continuity governing the
two-dimensional overland flow on a plane surface  with
vertical inflow (rainfall excess).

     Subtracting retention and infiltration from the rain-
fall intensity, the overland flow supply is obtained.  As
this supply increases,  a sheet of water builds up over the
surface and the water starts to flow toward the collecting
gutter.   This movement of water is overland flow  and the
volume of water on the surface is the surface detention

Continuity Equation

     Considering flow of unit  width on a surface  with
small bottom slope (sin B = 0)  and uniform velocity dis-
tribution,  the continuity equation can be written:
                   J II  I  Id)
                   mi
^
                 Figure 139.   OVERLAND FLOW
                           244

-------
~Sx
              .
                  9A
                  £Ft
                         =  i  Ax  -  f  Ax  -  s  Ax
or
         la
         9x
                   9t
           =   i-f-s
because Area A = y  • 1, where y  is the depth of  flow  in  ft,
g is the discharge  in cfs/ft of  width, and  (i  -  f  - s) is
the inflow or supply rate in cfs/sq.ft.

Momentum Equation

     The momentum equation can be written in the following
form, neglecting the raindrop momentum due to  the  impact of
the raindrops on the surface
 9V
Tt
          9V
        8y _
                  9x
                     =  (i-f-s)
                                           PY
                                    + g sinO   (9)
where V is the velocity of flow
       r  is the shear stress at the bottom
        o

       p  is the water density


       b  is the width of flow perpendicular to the direc-

          tion of flow. For overland flow b» y, so £ = 0.
     In comparison with gravity, the rainfall-infiltration
process has a negligible effect upon the flow dynamics  [20]
Therefore the term (i-f-s) can be omitted from the
momentum equation.

     An order of magnitude analysis for overland flow can
lead to the conclusion that free surface slope and inertia
terms in equation (9) are negligible in comparison with
those of bottom slope and friction.
                            245

-------
      Equation  (9) then reduces to the well-known relation
for steady uniform flow in a wide channel:
                     TQ =  Y y sine                    (10)

where y  is the .specific weight of water.
Laminar Flow
      For laminar flow Newton's law of viscosity applies:
                             dv
                             dy'
relating the dynamic viscosity y and the shear  stress  T
at a distance y' from the bottom.  Equation  (10) can be
written for any laminar layer:
                                      (11)
       = Y
                               ~ y1 ) sin9
                 or
T =-^~ (y - y') sine
where v  is the kinematic viscosity in  (ft /sec)
      Then from equations  (11) and  (12):
                     dv = g
                            sin9
                        _
                              V

                        _ gsinB
                  (y - y1 )
                                  (yy. -
                             v    %-*J     2 '
      Therefore the average velocity V will be:
                     V  =
so  q  =
          1  P
          7
             Jo
             Vdy-  =
                                      (12)
                            3v
                                                       (13)
                            246

-------
Turbulent Flow

     For turbulent flow, Manning's equation can be used,
considering the hydraulic radius R equal to the depth y.
          q = 1..49
                      n
                      (14)
          with q  (cfs/ft width) and y  (ft).

     Equations (13) and  (14) are of the general form

          q = K ym                                    (15)
           (a) for laminar flow!


          m = 3  and  K =
-[— i
 [sec.
                                     _
                                     ft
                           2.              2
          with g in  (ft/sec ) and V in  (ft /sec)
          (b) for turbulent flow:
          m =    and  K = 1.49
                                 Vsine
                                  n
                                         sec
     Equation (15) is a good approximation for discharge
of surface flow for practical purposes, supported by
Keulegan  [21], Chow [22], and Eagleson  [20].

Criteria of Flow Regime

     Horton [23] believed that the Reynolds criterion is
not satisfactory for sheet flow over relatively rough
surfaces.  He found that the point of equal velocities
represents the minimum amount of energy capable of main-
taining turbulent flow.

     Equating the velocities for laminar and turbulent
flow, the following relationship is obtained:
          gsin9
            v    3
1.49   2/3
  n   y
     or
           2/3
                         32.17 n y
   VsinG
                                  2/3
                            247

-------
Substituting the above in Manning's equation.we get:

                     v
          V  =
                4.83 n2 y2/3
                                                      (16)
     The flow cannot be turbulent if the velocity is less
than that given by equation (16) .

     Therefore because q = Vy, turbulent flow occurs if:
          q <
               v
                  1/3
                                                      (17)
              4.83 n

otherwise the flow is laminar .

     Izzard  (1946) believed the overland flow to be
turbulent for:

          i L > 500

     where i = supply rate  (in/hr)

           L = length of overland flow  (ft)

     But the experimental data of Izzard and Augustine and
of Ekern  (1950) support the hypothesis  that rainfall
causes the flow to be turbulent even when  i L «: 500.

     Field investigations have shown that  overland  flow  in
thin sheets may be entirely turbulent,  or  partly turbulent
and partly laminar.  For smooth surfaces,  it appears that
laminar flow exists with the  possibility of changing from
laminar to turbulent, and vice versa, within a  short
distance,.  For subdivided flow through  grass, most  of the
experimental data indicate  that the flow is laminar to
some extent  and may be represented by a condition of 75%
turbulent flow, in which case the profile  of overland^
flow can be  assumed parabolic [24] with an equation like
 (15), having an m = 2.

     Also experimental measurements of  surface  detention
show that high intensity rainfalls often yield  Reynolds
numbers that indicate turbulent flows.

     However, because the division between the  laminar  and
turbulent ranges  is difficult to  establish and  because  of
the nature of urban areas,  the turbulent range  equations
have been finally selected  in the development of  the
                            248

-------
 Cincinnati  Urban Runoff Model.

 Overland Flow Equations

      Overland flow can be defined by the system:
            9t
                  ax
                                                        (8)
             =  Ky11
                                                       (15)
     These  equations  constitute  a  Kinematic  wave  problem
which has been  solved by  Eagleson  [20]  for s =  0,  i  and  f
constants in  time  and space,  using the  method of
characteristics.

     Here,  an attempt has been made to  solve equations  (8)
and  (15) considering  rainfall intensity,  infiltration, and
depression  storage supply as  variables  of time.

     The only rigorous general methods  for simulating un-
steady overland flow  are  finite  difference techniques for
the numerical solution of the governing partial
differential  equations.  However,  the accuracy to  be
gained by using so laborious  methods for  overland  flow is
still subject to question because  of the  limited accuracy
of the basic  field data.            •

     Therefore  an analytical  method based finally  on an
empirical relationship between outflow  depth  and detention
storage [8]  has been  chosen in connection with a routing
equation.

     From the continuity equation  (8),  at equilibrium:
           ay _
           Tt ~
                0
          and q = rx
                                                       (18)
where r = (i -
       2
                      is the overland flow supply rate in
(cfs/ftz) and q is the discharge at equilibrium in cfs/ft of
width at any section x on the flow plane.  Therefore the
outflow at equilibrium is q  = rL.
                            249

-------
     Also as Wolf  [25] stated, the change  in  discharge as
a function of x on a uniformly sloping plane  must  be zero,
before local equilibrium is reached.  Therefore  the depth
at any point on the plane prior to local equilibrium
(Figure 140) is
          y = rt
                     (19)
           Figure 140.  OVERLAND FLOW ON A UNIFORMLY
                            SLOPING PLANE
     Between time t =  0  and  t  =  t   (where t  = time to
                                 s          s
equilibrium in sec), the total inflow will be equal to the
total runoff  (outflow) plus  the  surface detention (storage)

in units ft /ft of width.

     The total inflow  during this time will be:
          I = r L t
                      (20)
     The surface detention  will  be:
                   ydx
but equation  (15) gives  y  =    -)/    and also the discharge

at equilibrium from  equation  (18)  is q = rx
     SO
/'
Jo
dx
                            250

-------

                                                       (21)
      Accepting that the total runoff is some fraction  (a)
of the total inflow:
           R = arLt
but also   R
 _r
 ~4>
qdt
      From equation  (19), from t
at x = L should be:
           v =  (—-) v
                V  *
      Then equation  (15) becomes:

               _, m   T,  / t»m   m
           q = Ky  = K  (^—)  y
                         e

Therefore equating  (22) and  (23):
                          m
           arLt  = K
(22)


(23)
                       0 to t = te/ the depth
                    e tmdt
                     m
from where arL =
                  m + 1
but
qe »  rL =
                          m
so
                  m + 1
      Then the total runoff will  be  R =

                                                       (24)
                                           (25)
      The necessary  time  to  reach  equilibrium now can be
found from the equation:   I  =  D  + R substituting the ex-
pressions of equations  (20) ,  (21) , (25).   Therefore:
                             251

-------
     rLt  =
     rje
                           K
from where
                     K
                      1/m
                                                       rLt
                                                       (26)
                                          5             I/IT
      For turbulent flow has been found m=j and K-1.486 n


where S is the slope in ft/ft equal to the sine for small

slopes.
      Then from equation  (24):  a = 0.375
From equation (21): Dg =






From equation (26): t  =
                               0.493  r
                                 °'6
                                                  1 ' 6
                               0.01315 L°'6  n°'6
Where:  D  = detention storage at equilibrium  in  ft /ft  of

         e   width


        t  = time to reach  equilibrium  in minutes
         e

                                                2
         r = overland flow  supply rate  in cfs/ft


         S = slope of the plane  in  ft/ft


         L = length of overland  flow in ft


         n = Manning's roughness coefficient


       Detention  storage  in  inches depth per unit  area and

overland flow  supply rates  in inches per hour _ are more easy

to visualize.  Therefore changing in these  units:
            De =
           0.009792
                                n° - 6 L° ' 6
                 0.94 L
                         S


                       0.6
                    0.3
                                                       (27)
                   0.4  C0.3
                  JT     O
                             252

-------
where now DQ  (in/unit area),  tQ  (min),  r  (in/hr), L  (ft),
S  (ft/ft).      ,

     The rate of discharge  from  overland  flow based  on
Manning's equation is:

          a = 1'486 v5/3 S1/2
          ^         y    to
where q in cubic feet per second per foot of width and y
the depth in feet at the lower edge of the  flow plane.

     Rewriting Manning's equation with q in inches per
hour per unit area, y in inches, and L in ft:
          q .
                           l/2
                                        (28)
     The most satisfactory empirical relationship found
between outflow depth and detention storage for repro-
ducing experimental hydrographs  [8] is:
          y =
D  1.0
+ •0.6 (5)
        e
                                          (29)
where y is the outflow depth in inches
     DS is the detention storage required at equilibrium
        for the current rate of inflow in inches per unit
        area, calculated from equation (27)

      D is the current detention storage in inches per
        unit area

     During recession flow, when D  is less than D, the
                                  ti
ratio D/Dg in equation (29) is assumed to be one .
     Then equation (28) becomes

          q
= 1020.7 sl/2 D5/3 r
     with units q (in/hr/unit area)
                        0.6
                                   5/3
                                   (30)
                L (ft) and D, D  (in/unit area)
                            253

-------
     To determine the overland flow runoff hydrograph, a
storage routing procedure is used.

     The storage equation can be written:
where r is the inflow  (overland flow supply, known from
the infiltration model), q is the outflow, dD is the change
in detention storage, and dt is the time increment in
minutes.

     This equation can be written in an incremental form
form [26]
            :1 + r2 _ ql + q2 _
                               60
               D2 - D]
                  At
     or
                                           D
                                        60
                                            AT
                                   (31)
where the subscripts 1 and 2 indicate values at the begin-
ning and the end of the routing increment  At.

     Combining equation  (31) with equation  (30) we get:
             D.
	 —
At
nL
                                        D
                                              ,5/3
                                                   D.
                                                + 60-
                                 At
                                      (32)
where D  can be found  for each corresponding r  from
       e
equation  (27).

     Now all the known values are at the  left-hand side of
equation  (32).  Starting at the  first  time  increment with
q_ =0, D, =0 the value of D« is found from equation  (32)

and then q2 is found from equation  (30).  Then  the calcu-
lated values of q2, D2 become q^ and DI for the subsequent

period and the above process is  repeated  giving the hydro-
graph of the overland  flow in inches per  hour which can be
directly compared to the rainfall rates.
                            254

-------
     However, in order to calculate the discharge entering
into the gutters due to the overland flow supply, it is
easier to have available the overland flow in cubic feet
per second per foot of width.  This can be done by
multiplying the values of q found from the routing pro-
cedure by a factor, i. e.
cfs
                                     in/hr
ft width
         43200
                                   unit area
Where L is the length of the overland flow.

     This method has the advantage in using the Manning ' s
roughness coefficient for which there are, a lot of experi-
mental data available for different ground covers (see
Appendix I) .

     This method agreed satisfactorily with the well known
Izzard's method [3], [27].  An example output is presented
in Figure 141.  Overland flow rates by using Izzard's
method are less during the beginning of the rainfall excess
and higher near the peak than these calculated by using the
Urban Runoff Model.  But finally the volume of water which
ran off is approximately the same  (areas under the overland
flow curves) .  The differences can occur due to the fact
that Manning's n =0.35 may not well correspond to Izzard's
C = 0.06.

     Several computer runs have shoxvn that the Cincinnati
Urban Runoff Model simulating the overland flow, finally
comes out with a volume of water ^ which ran off, approxi-
mately equal to the total volume of water which was
available for overland flow.  Differences of less than 5%
proved that the model follows adequately the continuity
principle.

     A brief sensitivity analysis has been done for the
overland flow model which proved ever more its accuracy.
An example is presented in Figure 142.  For bigger
Manning's roughness coefficients, the peaks of overland
flow hydrographs tend to be higher and to occur at earlier
times.  For bigger lengths of overland flow the peaks tend
to be lower and to occur at a later time, resulting in a
flatter overland flow hydrograph.

     The described overland flow model offers simplicity
and calculating speed compared with other more exact
methods, while attempting to maintain a reasonable
approximation to physical behavior.
                             255

-------
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    256

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                                             257

-------
                      7.  GUTTER FLOW

     Gutters will gather overland flow in a continuous
fashion along their lengths, to feed the catchment's inlets
and catch basins.

     Experiments by W. I. Hicks, introducing equal
increments of flow at regular intervals along the length of
a gutter, showed the difference between the water-surface
slope and the construction grade.  The upstream water slope
was much flatter. ;

     The type of flow in roadside gutters is spatially
varied unsteady flow with increasing discharge.

     In this type of flow, the energy loss is of relatively
high magnitude and uncertainty, and is due to the turbulent
mixing of the added water and the water flowing in the
channel  [26].  The momentum equation will be found more
correct than the energy equation in solving this problem.

     Considering the x component of the Velocity of the
lateral inflow negligible, the general differential
equation for spatially varied unsteady flow, based on the
momentum principle, is:
         _iY_ + Y-
          3x   g  3x
                                4. _Y- _iQ + I  8V
                                  gA  9x   g  at
(33)
where     S  = slope of the gutter bottom


          Sf = slope of total head line

          Q,V,y are the discharge, velocity and depth at a
               certain cross section of the gutter

           g = acceleration of gravity

     The total head line slope Sf will be computed from
Manning's equation, i. e.:
where
          Sf =
                  C
    2.22 A2 R4/3
                                           (34)
n = Manning's roughness coefficient

A = area of gutter cross section
                            258

-------
Also
           R = hydraulic radius of gutter cross section

                           / Qx_ _Q   3Q    Q2  3A
V  3V = J2  3
g  3x   gA  3x
                                ..
                               gA
                                 __  .
                                 2  3x
therefore  ^ _3V = _Q^ _3Q _ Q^T
           d  ,} %r     v  ^ *v      <
           y  O-'i   x-rA ^  °X   — •» J
                                           3  3x
                                                       (35)
where
           T = width of the water surface.
            V  JQ = _Q	3C2
               3x   _,2  3x
Also:
     By using equations  (35) and  (36), equation  (33)
becomes:
                                                       (36)
           S  - S  -  -    n -
            °    f "  3X      gA3
                                   + 2
                                        Q   9Q
                                               (37)
     The continuity equation for unsteady flow with lateral
inflow gT , is:
       '
                                                        (38)
     The lateral inflow qT , available from the overland

flow, will be constant along the length of the gutter for
a time interval.  So qT is a function of t but not of x.
     Because only the discharge entering the sewer catch
basins at the downstream end of the gutters is required,
equation (37) can be discarded and the Q at the end of the
gutters can be obtained by using only equation (38).

     For an urban area the lengths of the gutters are
relatively small.  Also the overland flow supply in cfs/ft
is small.  Therefore, in a time increment, the change of
the depth in the gutter will be very small in comparison
with the other terms of equation (38) (see Appendix I).
Omitting the term
                      T equation  (38) becomes:
                            259

-------
            3Q
               =
     and integrating:  Q = q   • L + Q
(39)
where QQ is the discharge entering the gutter from an up-

stream gutter, otherwise zero  (Figure 143)
            q =q
                ^
                        Figure ]k3.  GUTTER FLOW

     Once the hydrpgraph of  the  discharge  entering  into  an
inlet  (inflow hydrograph)  is obtained  from equation (39)
it will be routed through  the  sewer  until  the  next  inlet
downstream, where a new inflow hydrograph  will be added  to
the routed one and the summation will  be routed downstream,
and so on.
                             260

-------
      8.  ROUTING THROUGH LATERAL AND MAIN SEWERS
     In Chicago, Tholin and Keifer  [4] used a time-offset
method for conduit routing because of its simplicity com-
pared with other routing methods and because more refined
procedures (storage routing) had not led to significantly
different results.

     Storage routing can be applied if satisfactory dis-
charge-storage relationships are available.  This makes
necessary the computation of instantaneous backwater
curves.  Since only the rate of change in storage is
necessary to solve the storage equation, it is considered
expedient to assume a uniform flow condition for each dis-
charge rate  [22] and compute the conduit volume occupied
by the flow.

     Other methods used in Europe, like the semigraphical
method of Hauff and the Italian storage method, are
relatively easy to use, but are based on broader
assumptions  [28].

     Generally there are many points of entry (inlets)
into a lateral sewer.  As points of entry for a main sewer
are considered the junctions with the lateral sewers.

     Considering a lateral sewer of uniform flow and
cross-section, for each inlet a hydrograph of the inflow
is available from the gutter flow.  It seems more
reasonable to use a hydrograph simplified as constant
discharge rates for each time increment, rather than a
smooth curve discharge-time relationship (Figure 144).


       Q
               DT
              Figure 144.  TRANSFORMED HYDROGRAPH
                           261

-------
     Assuming a uniform flow condition for each discharge
rate, Manning's equation can be used to find the depth and
the velocity of flow into the sewer for each discharge.
So the velocity with which each water volume element is
moving downstream will be known.

     The average velocity with which the total inflow
volume (represented by the area under the hydrograph curve)
moves downstream is considered to be the weighted average
of all the partial velocities with respect to the
corresponding volumes, i. e. multiply each volume element
by its velocity, sum the products and divide the sum by
the total volume of the water which moves downstream.

     Once the average velocity of flow is found and knowing
the length of the conduit between inlets, the time needed
for the inflow water volume to travel this distance can be
found.

     Each inflow hydrograph is shifted in time without
changing in shape.  This has been found satisfactory and
convenient, producing only a slightly higher peak rate of
flow occurring at a somewhat later time than other more
exact methods.

     Therefore, for a lateral sewer of uniform slope and
cross-section, the computer shifts the first inflow hydro-
graph the time required  to reach the  second inlet.  ;Then,
it adds the new inlet hydrograph and  the  shifted one and
shifts the summation hydrograph until the next inlet,  and
so on until it reaches a critical point.

      Changes  in slope or changes in cross-section are  con-
sidered as critical points.  After a  critical point,_the
procedure is  repeated from the  beginning, with the_first
inflow hydrograph the one found at the critical point.
This  continues until the junction of  the  lateral sewer
under consideration with a main sewer.

      The routing through the lateral  sewers  is done first,
in order to  find the hydrographs entering into  the  main
sewer at the  junctions.  These  hydrographs  are  used as
inflow hydrographs  for  the main sewer and the  same  method
is followed  to find  the  hydrographs  at selected points of
the  main  sewer.

      Overflow of  the  sewer  system  is  not  allowed.   The
                             262

-------
 computer compares continuously the maximum capacity of the
 conduits and the routed discharges.  If the capacity of a
 conduit is not sufficient, the computer indicates that in
 the output.  This justifies the purpose of the present
 "Model" to design a sewer system or improve an existing
 one.  In case of:.overflow, the cross-section of the in-
 sufficient conduit or its slope or both have to be changed
 and the computer program rerun.

  ; •   It is assumed that the Manning's roughness coefficient
 remains constant as the depth changes (actually the rough-
 ness coefficient decreases as the depth of flow increases).

      For practical purposes also, it can. be assumed that
 the  maximum discharge of a circular conduit does occur at
 the  full depth,  because the depth for maximum discharge is
 sp.close to the  top that there is always a possibility of
 slight backwater to increase this depth closer or equal to
 the  full depth [22.3 .

      Time steps,  for  the computer solution,  may be chosen
 to coincide with the  spacing of the.ordinates of the
 inflow hydrographs for convenience.   However, 1 minute
 intervals will facilitate the addition of the hydrographs.

      Let us suppose now that the discharge entering into
 the  sewer during a time increment At is  Q,  taken from the
 inflow hydrograph.  In order to find the velocity with
 which the volume  (Q .  At)  is traveling downstream,  Manning's
 equation is used:                                ,  .    .    .
                       R2/3  sl/2
                                          (40)
where
Q
discharge in' cf s
           n = roughness coefficient of the conduit  (see
               Appendix I)

           A = cross-sectional area of flow in ft2

           R = hydraulic radius in ft

           S - slope of the invert of the conduit in ft/ft

     The present method is used for sewers of circular and
rectangular cross section.  Other shapes can be transformed
•into these basic two cross sections.
                            263

-------
     (A) Circular  shape:
                                   A =
                           (x -  sinx)   (41)
                                                  sinx
                                   "   P   4       x

                                   where x in radians and

                                   0 ^. x  =^ 2-rr
     The maximum capacity of the pipe is  (full  flow):
                  0.46417 n8/3  1/2
           Q    =     ' '   L)    D
           ~max      n
For partially full flow conditions  equation  (40)  becomes:
              - sinx)
                     5/3
              x
            13.566 Q n
          ~ rs8/3 . ci/:
(42)
     The riaht hand part  of  equation (42)  is known,  so
equation  (42) can  be  solved  by trial to find the angle x.
Knowing x, the area of  flow  A is  obtained from equation
 (41) and the velocity of  flow V is obtained from the
equation:
           V
| (ft/sec)
      (B)  Rectangular shape
H
I

5 (A)
L PI 	 — -4
                                                        (43)
                                       A = Dy


                                       P = D + 2y


                                       R = Dy/(D + 2y)
                             264

-------
     The maximum discharge passing through  the  conduit
 (full flow, y = H) is:
           Q.
                  0.9361  (D H)
                              5/3
                                     a/2
            max
                    n
                          (D + H)
                                2/3
     For partially full flow, equation  (40) becomes
               5/3
                               Q n
            (D + 2y)
                   2/3
                         1.486 S1/2 D5/3
                                                       (44)
     The right hand part of equation  (44)  is known,  so  can
be solved by trial to find the depth of flow y  (in  ft).
Then the velocity of flow will be
           V =
                   (ft/sec)
(45)
     If an inflow hydrograph consists of N time  increments
 At with the corresponding discharges Q,  , Q«  ,  .. ., Q,,  ,
then the average velocity with which the total inflow
volume travels downstream until the next inlet is:
Vav=(VlQl At+V2Q
                                      At+Q2 At+...+QN At)
or
       =  (V1Q1
where V, , V~ ,  ... are the velocities with which the
volumes Q, At, Q2 At,  ... travel downstream.  'These
velocities are given from equations  (43) or  (45) ..
                            265

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  9.  FIRST CASE STUDY ON SIMULATION OF URBAN STORM WATER

     RUNOFF BY USING THE CINCINNATI URBAN RUNOFF.MODEL


     A catchment of 10 acres in,Chicago, Illinois, has been
selected to verify the Cincinnati Urban Runoff Model be-
cause detailed data were available and because it is
typical of the Chicago street pattern and may be typical of
some other cities.

     The catchment has been divided into six basic types of
subcatchments:
     Type
                  Length         Manning's
Description        (ft)*  Slope*     n	
       I   Dense blue grass turf,
           pervious

      II   Dense blue grass turf,
           pervious

     III   Dense blue grass turf,
           pervious

      IV   Street pavement,
           impervious

       V   Alley pavement,
           impervious
      VI   Common composition
           roofing, impervious
                    16
                    40
                    70
                    17
                     8
                    12
                                     0.0100   0.350
                                     0.0100   0.350
                                     0.0100   0.350
                                     0.0200   0.013
                                     0.0375   0.013
                                     0.6670   0.012


*Parallel to the direction of overland flow
     The 10 acres catchment constitutes 5.37 acres (53.7%)
of pervious areas and 4.63 acres (46.3%) of impervious
areas.

     Building roofs are not discharging through the down-
spouts on the lawn areas, but are connected directly to the
underground sewers.  To reduce the amount of computations,
six roofs were considered directly connected with each
catch basin.

     The garage roofs, because they discharge onto backyard
lawns, were considered a part of the pervious areas.
                            266

-------
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     The lateral sewer was of circular cross section with
a diameter of 3 ft, a slope of 0.0045 ft/ft, and a
Manning's roughness coefficient of 0.013.

     The subdivision of the catchment into subcatchments,
the sewerage, and the directions of overland flow and
gutter flow are shown in Figure 145.

     Figure 146 represents the catchment as a system of
geometric elements, the types of overland flow, gutters,
catch basins, and sewer system.  The way of numbering the
gutters, the points of entry into the sewer system, and the
numbering of the pipes is shown on Figure 146.

     The computer program for the Cincinnati Urban Runoff
Model is inserted in Appendix III.  Complete information
for the preparation of the data cards is in Appendix IV,
and the data cards for the Chicago 10-acre catchment are
presented in Appendix V.

     A 181-minute design storm was applied to the drainage
basin and the computations were made at 5-minute
intervals.  A detailed computer output for the present
case study is available at the Division of Water Resources,
Department of Civil Engineering, University of Cincinnati.

     For the purpose of comparison, the runoff hydrograph
at the outlet of the Chicago 10-acre catchment was calcu-
lated by three methods:  the Cincinnati Urban Runoff Model,
the EPA Storm Water Management Model, and the Chicago
Method.  The resulted hydrographs are plotted in Figure
147 together with the 181-minute design storm hyetograph
which was applied to the drainage basin.
Comments on the Results of the First Case Study

     1.  The Chicago Method, the EPA Storm Water Manage-
ment Model, and the Cincinnati Urban Runoff Model, calcu-
lated that the peak would occur at about the same time,
i.e., 75 minutes from the start of the rainfall as shown
in Figure 147.

     2.  The Chicago Method and the EPA Storm Water Manage-
ment Model calculated a peak of 18.2 and 22.6 cfs respec-
tively.  The Cincinnati Urban Runoff Model calculated a
peak of 23.0 cfs, which agreed satisfactorily with the EPA
Storm Water Management Model.  However, the latter divided
the Chicago 10-acre catchment into 80 subcatchments, 40
gutters, and 4 pipes, while the Cincinnati Urban Runoff
                           269
-------
                                                           CHICAGO,  10-ACRE TRACT
                                                                DESIGN STORM
                                          80       100
                                          TIME (MINUTES)
                                                                                         ISO  190
   22

   20

   18

   16

? 14
o

S 12

S 10
O
     8

     6

     it

     2

     0
                       CINCINNATI
                  URBAN RUNOFF MODEL
                        EPA STORM WATER
                        MANAGEMENT MODEL
                                     CHICAGO METHOD
               20
                                 60
           80         100

            TIME  (MINUTES)
                                                                                        IfaO  190
                   Figure
RAINFALL HYETOGRAPH AND CALCULATED RUNOFF HYDROGRAPHS
                 CHICAGO,  10-ACRE TRACT
                     DESIGN  STORM
                                             270
-------
Model used repeatedly 6 basic types of subeatchments, 40
gutters, and 8 pipes, therefore reducing the computer time
to about 5.5 minutes using the IBM 360/65 computer of the
University of Cincinnati.

     Comparing the peaks obtained by the three above
methods with the Rational Formula Q = ciA , the following
is obtained:

          c = coefficient of runoff equal to 0.40 for
              relatively flat residential areas, 30%
              impervious [29]

          A = catchment area, 10 acres

          i = average rainfall intensity in inches per hour
              for a duration equal to the time of concen-
              tration of the catchment
          Q = peak flow rate, in cfs

     During the rainfall used in the previously presented
study case/ 2.50 inches of water precipitated on the
catchment.  The duration of the rainfall was 181 minutes.
This rainfall has a return period of 10 years for the
Chicago area [30].  Then the average rainfall intensity,
for a time of concentration equal to 15 minutes and a re-
turn period of 10 years, is i = 5 inches per hour [31].
Therefore, Q=0.4x5xlO=20 cfs, which agrees
satisfactorily with the peaks in Figure 147.

     3.  The three methods gave a comparable rising limb.
However, the Chicago Method and the Cincinnati Urban Runoff
Model calculated a lower recession than that obtained from
the EPA Storm Water Management Model.  This can only be
accounted for by a larger infiltration loss.  Actually the
Chicago Method and the Cincinnati Urban Runoff Model com-
pute the mass curve for infiltration loss.  Thus, the
infiltration rate tends to be satisfied at any given time
even though there is not sufficient rainfall at that
moment, under the condition that the accumulated mass
precipitated is bigger than the accumulated mass infil-
trated.

     4.  The EPA Storm Water Management Model maintained
the mass continuity within 0.1% of the rainfall.  No such
information was available on the Chicago Method for com-
parison.  The Cincinnati Urban Runoff Mathematical Model
maintained the mass continuity within an acceptable 2% of
the rainfall as has been shown by a series of case studies
performed at the University of Cincinnati.  Manpower and
computer time did not justify an effort for more accuracy.
                            271
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  10. SECOND CASE STUDY ON SIMULATION OF URBAN STORM WATER

      RUNOFF BY USING THE CINCINNATI URBAN RUNOFF MODEL


     The Oakdale Avenue drainage basin in Chicago, Illinois,
has been selected to verify the Cincinnati Urban Runoff
Model because rainfall and runoff have been periodically
measured and recorded since 1959 by the Chicago Department
of Public Works, Bureau of Engineering [32].

     The Oakdale Avenue catchment is an urban drainage area
12.9 acres in size (approximately 2 1/2 blocks long by one
block wide) and consists entirely of residential dwellings.
The catchment has been divided into six basic types of
subcatchments:
     Type     Description

       I   Grassed, pervious

      II   Grassed, pervious
        \

     III   Grassed, pervious

           Grassed, pervious
IV

 V


VI
           Street pavement,
           impervious

           Common composition
           roofing, impervious
Length
 (ft)*

  35

  35

  50

  23

  15


  11
Slope*
0.010
0.010
0.010
0.010
0.020
Manning ' s
n
0.350
0.300
0.350
0.350
0.013
0.667
0.012
     *Parallel to the direction of overland flow

     The 12.9 acres catchment constitutes 7.05 acres
 (54.7%) of pervious areas and 5.85 acres (45.3%) of im-
pervious areas.

     Building roofs and garage roofs are draining directly
into the underground sewers.

     The existing 30-inch diameter combined sewer was in-
stalled in 1958 and replaced a smaller combined sewer of
inadequate storm water capacity.  The slopes of the 30-inch
lateral sewer vary from 0.0045 upstream to 0.0030 down-
stream, and the Manning's roughness coefficient is
considered to be 0.013.

     The plan of the 12.9-acre Oakdale Avenue drainage
                            272
-------
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                           273
-------
 basin is  presented in Figure  148.   In order  to  use  the
 Cincinnati Urban Runoff Model,  the  Oakdale Avenue drainage
 basin has been divided into 6 basic types of subcatchments,
 52  gutters and 9 sewer pipes.

      Two  storms were  applied  to the Oakdale  Avenue  drainage
 basin,  the second storm of  July 2,  1960  having  a duration
 of  66 minutes  and the storm of  July 7, 1964  having  a
 duration  of 86 minutes.   The  computations were  made at
 1-minute  intervals.   A detailed computer output for this
 case  study is  available at  the  Division  of Water Resources,
 Department of  Civil Engineering, University  of  Cincinnati.

      For  the storm of July  2, 1960  the runoff hydrograph
 at  the  outlet  of the  Oakdale  Avenue drainage basin  was
 calculated by  three methods:  the Cincinnati  Urban Runoff
 Model,  the EPA Storm  Water  Management Model  and the RRL
 Method.   The resulting hydrographs  are plotted  in Figure
 149 together with the recorded  hydrograph and the 66-
 minute  storm hyetograph.

      For  the storm of July  7, 1964,  the  runoff  hydrograph
 at  the  outlet  of the  Oakdale  Avenue drainage basin  was
 calculated by  three methods:  the Cincinnati  Urban Runoff
 Model,  the RRL Method and the Chicago Method.   The
 resulted  hydrographs  are plotted in Figure 150  together
 with  the  recorded hydrograph  and the 86-minute  storm hye-
 tograph .

 Comments  on  the  Results of  the  Second Case Study

 (a) Second Storm of July 2, 1960:

      1.   The  two  peaks calculated  by the three methods
 occurred  at  about  the same  time, i.e. around 38 and 62
minutes from the  beginning  of the rainfall.  The recorded
 first peak,  however occurred  sometime earlier,  32 minutes
 from the  beginning of  the rainfall.   The second peak was
not recorded.

      2.   The Cincinnati Urban Runoff Model, the RRL Method
and the EPA  Storm Water Management Model calculated a first
peak of 18.13 cfs, 14.30 cfs  and 15.60 cfs respectively
and a second peak of  10.58  cfs,  6.90 cfs and 12.50 cfs
respectively.  The first peak calculated by the Cincinnati
Urban Runoff Model (18.13 cfs) was closer to the recorded
peak^  (17.40 cfs) because it considered a reduced infil-
tration capacity due to the wet antecedent condition of
the soil caused by the previous  rain which occured earlier
                            274
-------
           u
                  I       J     1
                                                                     OAKDALE AVENUE. BASIN

                                                                 SECOND STORM OF JULY 2. I960
              10        20         30       kO        50       60


                                            TIME  (MINUTES)
                                                                      70
                                                                               80
                                                                                        90
                                                                                                 100
   19




   18




   17



   16



   15




   \k




   13




   12




*-. 11
«/i
u.

ii 10

LU


I  9

5
w>

o



    7




    6
RECORDED
                         CINCINNATI  URBAN


                           RUNOFF MODEL
                                               EPA STORM WATER

                                                IAGEMENT MODEL
             10
                       20
           30
                                                   50       60



                                             TIME  (MINUTES)
                                                 70
                                                                              80
                                                                   90
                                                                                                100
              Figure  H9.   RAINFALL  HYETOGRAPH.  CALCULATED AND OBSERVED RUNOFF HYDROGRAPHS


                                              OAKOALE  AVENUE  BASIN, CHICAGO ,



                                              SECOND STORM OF JULY 2,  I960
                                              275
-------
i   3
§  0
 OAKDALE  AVENUE BASIN
STORM OF  JULY 7.  196U
                                          40       50
                                        TIKE  (MINUTES)
                                                                              80
                                                                                      90
                                                                                      90
                                        TIME  (MINUTES)



         Figure  '50.  RAINFALL HYETOGRAPH,  CLACULATED AND OBSERVED RUNOFF HYDROGRAPHS.

                                     OAKDALE  AVENUE BASIN, CHICAGO

                                          STORM OF JULY 7, 196*4
                                        276
-------
the same day.  Therefore, some overland flow was generated
from the pervious areas and contributed to the first peak.
In comparison, the RRL Method without taking into con-
sideration flow from pervious surfaces calculated lower
peaks.

     3.   The three methods gave a comparable first rising
limb.  However, the RRL Method calculated a lower re-
cession than that obtained by the other two methods,
producing a smaller total runoff than that recorded.

(b)  Storm of July 7, 1964:

    •1.   The two peaks predicted by the Cincinnati Urban
Runoff  Model and the Chicago Method occurred at'about the
same time, i.e. around 17 and 36 minutes after the begin-
ning of the storm.  The two peaks predicted by the RRL
Method  both delayed for about 3 minutes.  The recorded
peaks occurred 20 and 37 minutes after the beginning of
the storm.  Therefore the three methods agreed quite satis-
factorily in the timing of the peaks.

     2.   The Cincinnati Urban Runoff Model, the RRL Method
and the Chicago Method calculated a first peak of 3.95 cfs,
6.00 cfs and 6.00 cfs respectively, and a second peak of
8.83 cfs, 11.40 cfs and 12.13 cfs respectively.  Again the
peaks predicted by the Cincinnati Urban Runoff Model
(3.95 cfs and 8.83 cfs) were closer to the recorded peaks
(4.2 cfs and 9.6 cfs).  By using the Cincinnati Urban
Runoff  Model, the storm under consideration generated a
very small amount of overland flow from pervious areas 30
minutes after the beginning of the rainfall and for 10
minutes only.  Since the RRL Method does not take into con-
sideration flow from pervious areas and since the overland
flow from pervious areas predicted by the Cincinnati Urban
Runoff  Model was very small, a better agreement between
these two methods was expected.

     3.   The three methods calculated comparable rising
limbs for both peaks.  However the two recessions calcu-
lated by the Cincinnati Urban Runoff Model were consider-
ably lower than the recessions predicted by the other two
methods.
                            277
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    11. CONCLUSIONS AND SUGGESTIONS FOR FURTHER STUDY


     The Cincinnati Urban Runoff Model consists of five
sub-models:

     1.  The Infiltration Model uses Horton's equation to
find the shape of the proper infiltration capacity curve.
If data from the urban basin under study are not available,
the use of Jens' Infiltration Capacity Curves is recom-
mended.  A method has been developed for the computer to
shift the infiltration capacity curve in time, so Horton's
equation can be used when i  < f  .

     2.  The Depression Storage Model uses an equation
proposed by Linsley, Kohler, and Paulhus, and a new
equation has been developed from it relating rates of de-
pression storage versus time.

     3.  The Overland Flow Model has been developed using
the continuity equation, the momentum equation, and an
equation by Crawford relating the depth of flow at the
downstream end of the overland flow plane with the surface
detention.  Several computer runs showed a satisfactory
degree of sensitivity of this model to changes of ground
slope, ground cover, and length of overland flow.

     4.  The Gutter Flow Model used the continuity
equation for steady flow since the change in depth with
respect to time was found negligible.  The validity; of
this simplification is shown in Appendix I.

     5.  The Routing Model routes the flow through the
lateral and main sewer by shifting an inflow hydrograph
from one inlet to the next, adds the shifted hydrograph
with the new one, and proceeds downstream.  This solution
does not reduce the peak flows, but it has been proved to
compare sufficiently close to the solution obtained from
more rigorous methods  (i.e., backwater curves computation).

     A computer program has been developed and combines
the five mentioned sub-models in the sequence with which
they appear above.

     It is believed that although a great deal of time
has been spent in the development of the presented Mathe-
matical Model, each step can and should be improved when
more field data are available for verification.

     Since depression storage reduces significantly the
                           278
-------
 overland  flow,  especially  from  pervious  areas, more  re-
 search  is needed  to  determine the proper depression  storage
 to  be used in  the Model.

     Other factors reducing  the overland flow which  can be
 considered in  the future are:   evaporation,  interception,
 and wetting of surfaces.

     More exact storage routing procedures can be  de-
 veloped to route  the flow  through the  gutters and  the
;lateral and main  sewers.   However,  each  improvement  of the
 Mathematical Model has to  be justified by manpower and
 computer  time  needed.

     Further research is recommended concerning  the
 capacity  of the storm-water  gutter  inlets, because during
 hea\sy rainstorms  there exists a carry-over flow  (i.e., the
 portion of the gutter flow that does not go  into an  inlet).

     If the water table of an urban basin is high, then
 groundwater infiltration or  seepage through  pipe joints,
 broken  pipes,  cracks, or openings in manholes and  similar
 faults, should be taken into account.  Research  can  be
 oriented  to find  a relation  between pipe material, age of
 the sewer system, and groundwater infiltration or  seepage.

     The  Cincinnati  Urban  Runoff Model as presented  is
 considered to  be  preliminary and will  be improved  as
 additional testing is accomplished  with  actual field data.
                            279
-------
                       APPENDIX I

          DIMENSIONAL ANALYSIS  OF  GUTTER FLOW
     Gutters are usually  triangular channels with the one
side approximately vertical  (this  depends on the shape of
the curb).  As can be  seen in Figure 151, a typical
battered  curb has a  height of 5.5  inches and if the water
is flowing with this depth then it is covering the corres-
ponding half of the  roadway.
<*>

"• i
£..
• .7'
-t -- -p
1 wax
6
lr-s*

"
	 ou —

p.
- — ( 	
"'Concrete Povt..




.1

17' i
3% Slops !^.5SSlc35'|
' ,' *
6% Slops •••'
5" One course .concJ
walk.-
                -
     Curb grade-?^ -fr-
t
                 X
                     0
        BATTERED  CURB
    Figure 151.

CONCRETE ROADWAY WITH
BATTERED CURB DETAIL
     The Rational  formula gives:

                 .  A
          q =  c  i  E


where     q is the discharge in cfs/ft width

          A is the contributing area in acres

          b is the width of overland flow  (ft)

          c is runoff factor < 1

          i is average rainfall intensity  in inches per
            hour for a storm duration equal to the time  of
            concentration of the area which provides  the
            overland flow.  Usually i is not less than 1
            nor  more than 3 inches per hour for urban
            areas.
                            280
-------
     Through the assumption of orders of magnitude/  it  is

possible to show that the term  [T-^] in equation  (38) on
page 259 can be neglected.

     It seems reasonable to assume: [the symbols " =  ORD ( )"
mean "is of the order ( )"]


          T = ORD (10°) ft


         Ay = ORDUO"1)  ft
         At =' ORD(10) sec


          c = ORD (10"1)


          i = ORD (10°) in/hr


          A = ORD (10°) acres
          b = ORD(10 ) ft

then the ratio
      t AZ
       At = 1. Ay/At
      q     c   i
                             = ORD(10 2)
Therefore the term  [T--j can be neglected from equation
(38) as being small in comparison with the rest of the
terms of this equation.

     As an illustration, for a certain rain, two values of
overland flow have been considered in a 5 minute inverval,
namely q.^ = 0.00069 cfs/ft and q2 = 0.00115 cfs/ft at the
beginning and the end of the interval.  The length of the
gutter was 100 ft with a slope 0.03 ft/ft and a Manning's
coefficient 0.017.  The slope of the street pavement was
1:27.

     The corresponding depths of flow have been found by
Manning's equation to be y1 = 0.0774 ft and y_ = 0.0852 ft,

The average surface width of the flow was T = 2.195 ft.
Then T-IT T = 0.000057-
                              which is a 6% of the average
inflow q.
                           281
-------
                        APPENDIX II

              MANNING'S ROUGHNESS COEFFICIENT

1.  For Overland Flow

      Manning's n for overland flow can be estimated from
the table below [8], or from other more detailed sources •
[22].
           Watershed
             Cover
      Smooth asphalt
      Asphalt or concrete paving
        Packed clay
        Light turf
        Dense turf
      Dense shrubbery & forest
      litter
                      Manning's n For
                       Overland Flow

                           0.012
                           0.014
                           0.030
                           0.200
                           0.350

                           0.400
      When there is a mixture of ground cover in a sub-
catchment of area A, then a harmonic mean Manning's rough-
ness coefficient n can be obtained from the expression:
           A
           n
B_
n.
(A -  B)

  n2
where B is a part of the subcatchment area having a
Manning's roughness coefficient n, and the rest of the

subcatchment area (A - B) has a roughness coefficient equal
to n2  [8] .

      The same procedure can be used if an area has more
than two different kinds of ground cover.


2.  For Pipe Flow

      For a combined sewer system, the same coating of
slimes form on the inside of all materials used for the con-
struction of the sewers.  This means that all materials used
in the construction of combined sewers will have the same
hydraulic roughness coefficient  [31].  In Manning's formula
that coefficient is n =  0.013.  Proof of this was demon-
strated by extensive tests at the Ohio State University
 [33].
                             282
-------
                        APPENDIX  III
  COMPUTER PROGRAM FOR THE CINCINNATI URBAN RUNOFF MODEL
      The volume of computations required by the Cincinnati
Urban Runoff Model would have been too formidable without
the use of an electronic computer.  A digital computer IBM
1130 with an available storage of 16K was used to run parts
of the present program.  Because usually more storage is
required, the whole program was run on the digital computer
IBM 360/65, of the University of Cincinnati, which has a
maximum storage capacity of 512K.  The computer program is
written in FORTRAN IV language.
      The differences in programming for the IBM 1130 and
the IBM 360/65 are only:
1
2
3
4
    IBM 1130
job cards
READ (-2 , . . .)
WRITE (3, ...)
Only arithmetic IF
statements
     IBM 360/65
job cards
READ (5, ...)
WRITE (6, ...)
Both logical and arith-
metic IF statements
      The program presented here consists of three parts,
the main program and two subroutines, namely:
I/ MAIN program:

2/ GUTFL subroutine:
3/ PIROU subroutine:
           for infiltration, depression storage,
           and overland flow
           for the gutter flow
           for the routing through the lateral
           and main sewers
                            283
-------
C
c
C
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
    21
              "CINCINNATI  URBAN  RUNOFF  MODEL"

                       COMPUTER PROGRAM
 *********************** ************ *******************
 INFILTRATION AND  DEPRESSION  STORAGE  IK PERVIOUS AREAS
 *«#*»****##*##*******#*************«*************#***

 DIVIDE  THE  TOTAL  RAINFALL  TIME IN N  EQUAL SMALL INCREMENTS
 READ  N+l  VALUES OF AVAILABLE RAINFALL HYDROGRAPH ( I M/HR )
 EACH  TIME INCREMENT DT  IS  IN MINUTES
 AT  TIME ZERO 1=0.  AT THE  END OF THE  TIME PERIOD I=N
 RAINFALL  INTENSITY AT TIME ZERO IS R01FOR 1=0)                   .^
 RAINFALL  INTENSITY AT A TIME T=DT*I  IS RItl)
 AT  A  TIME T=DT*I . INFILTRATION CAPACITY IS F(I) AND ACTUAL
 INFILTRATION IS AFU) IN  (IN/HR)
 THE CONSTANT RATE AT WHICH F(I) APPROACHES ASYMPTOTICALLY
 AS  TIME CONTINUES»IS FC
 THE RATE  OF INFILTRATION  CAPACITY WHEN TIME=0(I.E.  1=0)  IS FO
 CK  IS A POSSITIVE CONSTANT
 DIFFERENCE BETWEEN RAINFALL AND ACTUAL INFILTRATION  S(I)
 ACCUMULATED MASS  PRECIPITATED UNTIL A TIME DT*I IS RMII) INCHES
 ACCUM^MASS ACTUALLY INFILTRATED UNTIL A TIME DT*I  IS AFM(I) INCHES
 WHERE RMtl) OR AFM1I) INDICATE THE MASS FROM TIME  DT*(I-1) UNTIL
 TIME  DT*I »PLUS  THE PREVIOUS MASS
 DIFFERENCE BETWEEN MASSES UNTIL A TIME DT*I IS P(I) IN  INCHES
 VOLUME OF WATER  IN DEPRESSION STORAGE IS VS ( I ) INCHES
 TOTAL DEPRESSION  STORAGE CAPACITY SD  INCHES
 DEPRESSION STORAGE SUPPLY IS Dfl)  INCH/HOUR
 SS(I) IS THE RATE OF ( RA IN-I NF I LTR-DEPRESS ION STORAGE)
 PPU) IS THE ACCUMULATED MASS OF ( RA I N- INF I LTR-DEPRESS ION STORAGE)
 COMMON    RK70) ,AF(70) iS<70> »RMt70) tAFM(70> ,P ( 70 ) , D < 70 ) , VS I 70 ) ,SS
1(70) tPP(70) ISSIM170) tPPIM(70) iVSIMt70) .DIM (70) .DATE(S) »DC(70) »OE(7
20) »OVQ(250i 30) »OVQW(70) »NEW( 30) «Q!NL( 70.20) .QINLOI20) t IW(250 1 »V(25
30) «QLEAV<250) »N,DT,NN«N INLtQINP ( 250 »20 )
 WR1TE16.1)
 FORMAT ( ' 1 ' )
 READ! 5*21) (DATE (I) »I=1«8>»DT.N
 FORMAT(8A4»F5t2«I5)
 READ (5»4)  RO
 FORMAT (F5. 2)
 READ(5»5)  (RI(I)tI=l»N)
 FORMAT (12F5t2)
 READ (5»6)  FC.FO.CK.SD.SDIM
 FORMATOF1045.2F8.4)
 READ(5t20)AN
 FORMAT (F5. 2)
 WRITEC6*501)
 FORMAT ( 5X » ' *******************************************************
l****«*i,/,5X. "SIMULATION  OF  INFILTR.AND  DEPRESSION STOKAGE IN  PERV
2 IOUS AREA" »/»5X.'*** **********************************************
    20
   501
       WRITE (6.221 (DATE! 11,1=1.5)
    22  FORMAT (5X. "RAIN OF ' , 6X « 5 A4 , // )
       WRITE(6.23)(DATEII)»I=6t8)
    23  FORMAT(5X» "TIME OF RAIN  START • i3X ,3A4 •// I
                                 284
-------
    WRITE (6t605)
605 FORMAT!1IX.•FC'»8X»•FO1»9X»'CK')
    WRITE(6»606)FC»FO»CK
606 FORMAT(10X,F4.2»6X,F4.2«6X«F6.4,//)
    WRITE(6«607)  SD
607 FORMAT<5X«'TOTAL DEPRESSION STORAGE CAPACITY OF THE'»/»5X*'SUBCATC
   1HMENT IS   (IN INCHES)  ='t15X.F8.4t//)
    IF (RO-FO) 10»7»7
  7 DO 8 I=liN
  8 AF(I)=FC-M (FO-FC)*(2.718**(-CK*DT*I)>>
    SO=RO~FO-
    DO 9 I«=1»N
  9 S(1)=RI(I)-AF+RI < I-U ) /2.0)*OT/60.0
    DO 13 1=1iN   •
 13 AFMfI)=((FC/60.0)*DT*I) + ((< FO-FC ) / (60.0*CK.))*(1tO-(2.718**<-CK*DT*
   II))))
    DO 14 I=1»N
 14 PU )=RMf I )-AFM< I )
    OD=SO
    SSO=0.000
    NCON=0.0
    DO 800 I=1*N -
    IFIRKI)-AF(I))  900.900»799
900 0(11=0.000
    NCON=1«0
    VS(
    SS(
    PP(
    GO
     )=SD
     )=S(I)
     )=P(I1-SD
    TO 800
799
798
 IF(NCON) 798*798*900
800

 15
 16
 17
 18

805

806
 DU =S( I)*(2.718**(-P( I )/SD) )
 VS( )=SD*(1.0-12.718**t-PtI1/SD)))
 SSI )=S(I)-D  TT«RI( I)*AF(I)»D(I 1*SS!I )
 FORMAT!5X«F8.2.6XjF6.3»8X.F6.3»8X«F6.3*8X*F6.3)
 WRITE(6,805)
 FORMAT('1')
 WRITE(6»S06)
 FORMAT(5X*'TIME FROM        MASS           MASS      DEPRESSION
   1DIFFERENCE'»/.5X,'KAIM START   PRECIPITATED
                                                INFILTRATED
STORA
                                  285
-------
     2GE     (MR-MI-DS)'»/*5X.'(MINUTES)         (IN)           (IN)
     3    (IN)         (IN)    '»/)
      00 807 1*1»N
      TT«DT*I
  807 WRITEt6»808) TT.RM(I)»AFM(I)»VS(I)»PP(1/
  808 FORMAT(5X«F8,2.8XiF6.3»9X,F6.3»7X.F6.4»7X»F6.3i
      GO TO 118
C     IF INFILTRATION CAPACITY GREATER  THAN  RAINFALL  INTENSITY
C     AT THE BEGINNING OF  THE  RAINFALL  (WHERE  TIKE=0  AND  1=0) THEN
C     INFILTRATION CAPACITY CURVE STARTS AFTER A  TIME ( I*DT-t-X*L) FROM
C     THE BEGINNING OF THE RAINFALL
C     WE HAVE DIVIDED DT IN (NN+1) EQUAL INCREMENTS X(L FROM  1 TO NN)
c     THE SHIFTED  INFILTRATION CAPACITY  CURVE  WILL  INTERSECT  THE
C     RAINFALL  INTENSITY CURVE AFTER  A  TIME  TJ=J*DT+Y AFTER THE
C     BEGINNING OF THE INFILTRATION CAPACITY CURVE.OR AFTER A TIME
C     (I*DT+X#L) FROM THE  BEGINNING OF  THE  RAINFALL
C     THE I AFTER WHICH  THE SECTION OF  THE  CURVES TAKES PLACE IS(ISEC)
   19 XsDT/AN
9999
 299
      00 299 L=1«NN
      ALLL=< (RI ( I )+*(X*L/60.0)
      B2*(FC*TJ/60.0)-K ( FO-FC )*( 1. 0- (2.718** t-CK.*TJ ) ) ) / ( 60.0*CK.»
9998
 300
 301
 100
      LSEC=L
      B12T=ABS(B1-B2)
      IF(B12T-0.01)  301»301i299
      CONTINUE
      DO 300  I=2.N
      DO 300  L=1»NN
      RMl I )=RM( I-1) + {(RI(I)+RHI-1> > /2 .0 )*DT/60.0
      ALLL=((RI(I)+(X*L*(RI(I-H)-RI < I )) /DT 1-FC) /( FO-FC) )
      IFIALLL.GT.O.ANDtALLL.LT.l. )  GO  TO  9998
      GO TO 300
      TJ*-tl.O/CK>*ALOGt (R I ( I >-KX*L*< RI t 1 + 1 1-RI t I) 1 /DT )-FC )/( FO-FC ))
      B1=RM+-RI (I ))/(2.0*DT) ) )*tX*L/60. 0)
      B2-(FC*TJ/60.0)-M (FO-FC ) * 1 1. 0-1 2.718**(-CK.*T J ) ) )/ ( 60. 0*CK.) )
      ISEC=I
      USEC=L
      B12T>=ABS(B1-B2)
      IF(B12T-0.01)  301»301»300
      CONTINUE
      BEFORE  THE SECTION
      AFO=RO
      S0=0»0
      00-0.000
      550=0.000
      DO 100  I=1»ISEC
      AF(1)=RI(I)
      S(I)=0«0
      D(I)=0.000
      ssm=o.ooo
                                   286
-------
    AT THE SECTION
    IISEC=ISEC-H
    RISEC=(LSEC*X*(RI( II.SEO-RH I SEC) J/DTl+RK I SEC)
    AFSEC=RISEC
    SSEC=0.0
    DSEC=0.000
    SSSEC=0.000
    AFTER THE SECTION
    IISEC=ISEC-H
    DO 101 I=IISEC»N
    AFU) = FC+()))
101 sm=RI(I )-AF(I)
    BEFORE THE SECTION
    DO 102 I=2»ISEC
102 RM(I)=RM( I-l) + «Rim+RI(l-l))/2.0)*DT/60.0
    DO 103 I*1«ISEC
    AFM(I)=RM(I)
    VSU>=0.0000
    PPU)=0.000
103 P(I)=AFM+RI < 1-1 ) )/2 .0 )*DT/60«0
    DO 105 I=IISEC«N
105 AFM(1) = {FC/60.0)*{(I-1SEC)*OT-X*LSEC+TJ) -K (FO-FC)/(60«0*CK))*(
   1(2»718«*(-C<*((I-ISEC)*DT-X*LSEC+TJ))11
    DO 205 1=1 ISEC»N
205 P(I)=RM(I)-AFM(I)
    NCON=0.0
    DO 810 I=IISEC»N
    IFIRIfI)-AF(I)) 901»901»795
901 D(I!=0.000
    NCON=1«0
    VS(
    sst
    pp(
    GO
        )=SD
        )=StI)
        )=P(I1-SD
        0 810
795
794
    VS(
    SS<
    IF1NCON) 794t794i901
        =St I)*(2.718**(-P(
        )=SD*<1.0-<2.718**<-P(I 1/SD)))
        )=S(I)-DfI)
    PPII)=P(1)-VStI)
810 CONTINUE
    T«=DT*I SEC+X*LSEC-TJ
    WRITE(6»106) T
106 FORMAT(5X»'INFILTRATION CAPACITY CURVE
   1INNING OF THE  RAINFALL (IN MINUTES)
    WTT = DT*ISEC-i-X*LSEC
    WRITE(6»108)WTT
                                            STARTS AFTER -THE1t/»5Xf'BEG
                                           ••»5X»F8.2.//)
                                287
-------
r
                   c
                   c
                   c
                   c
                   c
                   c
                   c
                   c
                   c
                   c
                   c
108 FORMATI5X."INFILTRATION CAPACITY CURVE  INTERSECTS  THE'«/.5X,'RAIN
   1FALL INTENSITY CURVE AFTER THE BEGINNING*»/»5X."OF THE  RAINFALL
   2  (IN MINUTES)  ='»12X»F8«2«//)
    WRITE (6.110)
110 FORMAT!5X»'TIME FROM    RAINFALL        ACTUAL      DEPRESSION
   10VERLAND  «»/.5X.*RAIN START    INTENSITY    INFILTRATION   STOR.SUPP
   2LY   FLOWSUPPLY'./»5X,'(MINUTES)      (IN/HRJ       UN/HR)         (
   31N/HR)       (IN/HR)  '«/>
    W=0«00
    WRITE(6»111)W.RO«AFO»OD»SSO
111 FORMATt5XtF8.2»6X»F6.3»8X»F6t3.8X.F6.3»8X»F6.3)
    DO 112 I*1»ISEC
    WW"=DT*I                   .
112 WRITE(6»113)WW»RI(I)»AF(I)»D(I)»SS(I)
    FORMAT(5X»FS.2 »6X.F6.3 » 8X *F6•3i8X•F6 4 3»8 X »F6•3)
    WRITE(6»114)WTT»RISEC»AF5EC»DSEC.SSSEC
    FORMAT(5X»FS.2.6X»F6.3»8XtF6.3tSX.F6.3«8X.F6.3)
    DO 115 I=IISEC»N
    WWW»DT*I
    WRITE(6»116)  WWW.RItI)»AF(I)»DtI)»SS(I)
    FORMAT!5X.F8.2»6X»F6.3»8XtF6.3i>8X»F6.3»8X»F6.3)
    WRITE(6»120)
    FORMAT!'!')
    WRITE!6»121)
    FORMAT!5X,'TIME FROM         MASS            MASS      DEPRESSION
   1D!FFERENCE',/»5X»'RAIN START    PRECIPITATED   INFILTRATED     STORA
   2GE  *   tMR-MI-DS)'»/.5X,'(MINUTES)         (IN)            (IN)
   3     (IN)          (IN)    './)
    DO 122 I=1»ISEC
    WW=DT*I
    KRITE(6*123)  WW»RM(I).AFM!I)»VS(I)»PP!I)
    FORMAT!5X»F8.2«8X«F6.3»9X.F6.3.7X.F6.4»7X»F6.3)
    WRITE(6.124)WTT»RMSEC«AFMSE.VSSEC»PPSEC
    FORMAT!5X»F8.2»8X.F6.3»9X»F6.3»7X»F6«4.7X.F6t3)
    DO 125 I=IISEC.N
    WWW«DT*I
    WRITE(6. 126)  WWW.RM!I)»AFMtI)»VS(I)»PP(I)
    FORMAT(5X»F8.2.eXtF6.3»9X,F6.3.7X,F6.4,7X.F6t3)
    WRITE (6.119)
    FORMAT  ('1')

    ********#**********************************************
    INFILTRATION AND  DEPRESSION STORAGE IN IMPERVIOUS AREAS
    **#********************************#*******«***********

    INFILTRATION CAPACITY  IS  ZERO
    VOLUME OF WATER  IN  DEPRESSION STORAGE IS VSIM(I)  INCHES
    TOTAL DEPRESSION  STORAGE  CAPACITY IS SDIM (INCH)
    DEPRESSION  STORAGE  SUPPLY IS DIM!I) INCH/HOUR
    SSIM(I)  IS  THE RATE OF  IRAINFALL-DEPR.STORAGE)
    PPIM(I)  IS  THE ACCUMULATED  MASS OF (HAIN-DEPR.STORAGE)
    WRITE(6»500)
 500 FORMAT < 5Xt'*********#***********«*******•********»*****************
    1*#******« ,/,5X.'SIMULATION  OF INFILTR.AND DEPRESSION STORAGE IN  IM
    2PERVIOUS AREA1 t/«5Xt '#**********#********•**#***#*#*******•»********
                        t//)
                    113

                    114
                    115
                    116

                    120

                    121
                     122
                     123
                     125
                     126
                     118
                     119
                                                       288
-------
                              CAPACITY IS ZERO'.//)
   WRITE<6»25>
25 FORMAT(5X«'INFILTRATION

26 FORMAT!5X.'TOTAL DEPRESSION STORAGE CAPACITY  OF  THE••/»5X«'SUSCATC
  1HMENT IS   (IN INCHES)  =*»15X»F8.4 . //)
   DO 28 1=1»N
   DIM
   SSIM(I)=RI(I1-DIM1I I
   PPIMt I )=RMC I J-VSIMU)
   CONTINUE        .                                  '
   WRITE(6.29)
   FORMAT(5X»'TIME FROM    RAINFALL    DEPRESSION   OVERL.FLOW't/,5X
                  INTENSITY   STOR.SUPPLY      SUPPLY1•/i5X»'(MINUTES)
                      (IN/HR)        
-------
    READ(5i649)IA»INDW«ALW«ARW»SW
649 FORMAT(2I2t3F7.4)
    WRITE(6.652>
652 FORMAT ( /»5X» ' **•*****#*****#*********#***********#**#****#****»»*##
   1**' I
    IFUNDW-1)  653»654»653
653 WRITE(6«655)IA
655 FORMAT(5X»'OVERLAND FLOW SIMULATION OF IMPERVIOUS AREA NUMBER  «»I2
   1)
    GO TO 657
654 WRITE(6i656)IA
656 FORMAT(5Xi'OVERLAND FLOW SIMULATION OF  PERVIOUS AREA NUMBER  '»I2)
657 WRITEI6.658)
658 FORMAT 15X »'**»*******»*»******•******»*****#*#**********************
   !«*//)
    WRITE(6»659)ALW
659 FORMAT(5X»'LENGTH OF OVERLAND FLOW IN FEET        «««F7.2>
    WRITE(6»690) SW
690 FORMATOX.'SLOPE AT THE DIRECTION OF FLOW  (FT/FT) ='»F7.4)
    WRITE<6»691) ARW
691 FORMAT(5Xt'MANNINGS  ROUGHNESS  COEFFICIENT
    AAA=510.35*(SW**0.5)/
-------
     IF851»852,852
 851 CONTINUE
 852 DC(I)=G
     OVQW( I )=(2.0*AAA)*(DC( I >**1.6666>*( ! 1.0+ < AA* ( DC t I)**3.0) J )** 1.6666
    1)
     OVQ( I »IA) =ALW*OVQW( I ) /43200.0
 829 TIME=DT*I
     WRITE (6 ,85 3) TIME,OVOW( I ) ,OVQ( I , I A ) »DE ( I I • DC < I ) »SS t I >
 853 FORM AT { 7X.F6.2 » 11X»F7 .4 » 14X »F8 .6 » 10X ,F8. 5 » 10X»F8.5»10X,F6.3)
     NWN=N+8
     NSTAR=N+1
     DO 661 I=NSTAR»NWN
     ssm=ss
     IF(STB-STA)  664,665,665
     CONTINUE
     DO 679  10=1,20000,1
     WD=ID
     G«=WD/100000.0
     STB«( ( (BA*G)-t-(ABA*(G**4.0) ) ) **1 .6666 l-t- 1 ABB*G )
     IF(STB-STA)  679,665,665
     CONTINUE
                                  291
-------
1650 DO 646 IDnl«2000»l
                                ) **1»6666 )+ ( ABB*G >
     G=WD/1000.0
     STB» ( ( (BA*G)+{ ABA*(G**4.0)
     IF(STB-STA) 646»665i665
     CONTINUE
     DC(K)=G
     1F(DE(K)-DC«) )  666.667,667
     IF(INOW-l) 5060.1651.5060
     IFtSW-0.5) 5027.5026*5026
     DO 668 10=1.20000.1
     WD=ID
     G*WD/10000.0
     STB- ( AAA* t G**l . 6666 ) *AB ) + ( ABB*G )
     IF/43200.0
                                  292
-------
      SUBROUTINE GUTFL
C
c     »#*********#***»******
C     GUTTER  FLOW  PROGRAMM
C     *#*##»***•****#********
C
C     NINL IS THE NUMBER OF INLETS
C     N IS THE NUMBER OF TIME  INCREMENTS
C     NW IS THE NUMBER OF SUBCATCHMENTS
C     THE PROGRAM WILL TREAT  INLETS ACCEPTING  A  NUMBER OF
C     NBRAN  SYSTEMS OF GUTTERSiAND DIRECT CONNECTIONS
C     Nl IS THE NUMBER OF THE  FIRST UPSTREAM GUTTER OF
C     EACH GUTTER SYSTEM
C     N2 IS THE NUMBER OF THE  LAST DOWNSTREAM  GUTTER OF
C     EACH GUTTER SYSTEM
C     ITYPL IS THE NUMBER OF  SUBCATCHMENT FEEDING  A  GUTTER
C     FROM THE LEFT SIDE
C     ITYPR IS THE NUMBER OF  THE SUBCATCHMENT  FEEDING  A  GUTTER
C     FROM THE RIGHT SIDE
C     GLEN IS THE LENGTH OF THE GUTTER
C     IROOF IS THE NUMBER OF  HOUSE 'ROOFS DIRECTLY  CONNECTED WITH  AN  INLET
C     IWRF IS THE NUMBER OF THE TYPICAL HOUSE  ROOF SUBCATCHMENT
C     ROOFL IS THE WIDTH OF A  ROOF IN FEET
      COMMON    RIt70).AF(70>,S<70),RM(70) »AFM<70) tP ( 70 ) .0(70 ) »VS t 70 ) »SS
     1 (70) »PP{70) »SSIM(70) tPP!M(70) »VSIM(70) »DlM<70) i DATE (8 ) .DC ( 70 ) ,DE ( 7
     20) »OVQ(250»30) iOVQW(70> .NEW (30) »QINL( 70.20) «OINLO(20) »IW(250).V(25
     30) »OLEAV(250) tN.DT.NN.N INL ,G INP < 250»20 )
     READt5«?000) NINL
3000 FORMAT I 15)
     DO 3004 I IN = ltNINL
     DO 3004 1=1 «N
3004 QINL( I » I IN 1=0.0
     DO 4001 I !N=1»NINL
     READ<5»3009) NBRAN
3009 FORMAT f 15)
     DO 4010 11=1, NBRAN
     READ(5,3010) N1»N2
3010 FORMAT (215)
     DO 4002 J=N1»N2
     READ(5»3011) ITYPL.ITYPR.GLEN
3011' FORMAT(2I5.F10.2)
     DO 4002 I=1.N
     QGUT=(OVO( I«ITYPL)+OVQ< I .ITYPR) )*GLEN
4002 QINL( I »IIN)=OINL( I. I IN1+QGUT
4010 CONTINUE
     READI5.3013) IROOF, IWRF .ROOFL
3013 FORMAT (215. F5. 2)
     GTIMO=0.00
     QINL01 II,M)=0. 00000
     DO 4005 1=1 .N
     HERE QGUT  SHOUS FLOW ENTERING  THE  INLET
     OGUT*IROOF*2.0*ROOFL*OVQ( I , IWRF)
     QlNLt I . IIN)=QINL( I »I INI+QGUT
4005 CONTINUE
4001 CONTINUE
     DO 5890 NINI=1»6
     WRITE(6.5500)
5500 FORMAT t ' 1 ' )
     N15=5*NINI-4
     N16*5*NINI
                                               FROM  DIRECT  CONNECTIONS
                                   293
-------
     WRITE(6,5555)(I,I=N15,N16)
5555 FORMAT(5X,1TIME FROM   DISCHARGE
    1 DISCHARGE',/.5X,'RAIN START
    2ERING   ENTERING'»/,5X.'     IN
    3INLET ',12,'   INLET '.12,'   INLET
    4    IN  CFS    IN  CFS     IN  CFS
     IFIN16-NINL) 5800,5800.5810
     N16=NINL
     WRITEI6.3014) GTI MO,IQINLOt1 IN),IIN = N15»N16>
     FORMAT(6X»F7.2i4X«F8.5»4(3X»F8.5))
     DO 5850 1=1.N
     GTIMSI*DT
     WRITE(6.5820) GTIM.tQINL
5810
5800
3014
5820
5850
     THIS  IN ORDER  TO  FACILITATE  THE  ADDITION  OF THE  HYDROGRAPHS
     DURING THE  ROUTING  THROUGH  THE LATERAL  AND MAIN  SEWERS
     KK=DT/DDD
     NN=KK*N
     DO  6901  IIN=1.NINL
     DO  6901   1=1.N
     JJ=N+2-I
     JJJ=N+1-I
     QINL(JJ,HN)=QINLUJJ»IIN>
 6901 CONTINUE
     DO  6900  I IN = 1.NINL
 6900 QINLU »I IN)=OtOOOOO
     DO  6912  I IN=1,NINL
      11*0
     00  6911  1=1,N
     DO  6911  K=1,KK
      11=11+1
     QINPdltllNl
     1NL(I,IIN)1)
 6911  CONTINUE
 6912  CONTINUE
      DO  6922  NINI=1»6
      WRITE(6,6916)
 6916  FORMAT('!')
      N15*5*NINI-4
      N16=5*NINI
      WRITE(6,6917) { I , I=N15.N16)
 6917  FORMAT(5X,«TIME FROM   DISCHARGE  DISCHARGE   DISCHARGE  DISCHARGE
     1  DISCHARGE',/,5X,'RAIN START  ENTERING    ENTERING   ENTERING   ENT
              ENTERING' ,/,5X, «
                                   IN
12
                     INLET  '.12.'
                     IN  CFS     IN
                   6918.6918.6919
                                     INLET
                                     CFS
 6919
 6918
 6921
 6920

 6922
 6923
2ERING
3INLET '
4    IN  CFS
 IF(N16-NINL)
 N16=NINL
 DO 6920 1=1. NN
 TRTIM=DDD*( 1-1)
 WRITE(6.6921) TRTIM. (QlNPt I »J> »J=N15.N16)
 FORMAT (6X«F7»2«4XiF8»5»4J3X«F8»5) )
 CONT 1MUE
 IFIN16-NINL) 6922.6923.6923
 CONTINUE
 RETUR'N
 END
INLET '.12.'    INLET '.12.'
',I2./.6X.'MINUTES     IN  CFS
 IN  CFS'.//)
                                    294
-------
      SUBROUTINE PIROU
C     **#*»»******#*****'***#****#**#**********
C     ROUTING THROUGH LATERAL AND MAIN  SEWERS
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
  909
  917
  907
  905
  912
  913
  925

  906
      USE OF MANNING'S EQUATION  TO  FIND  THE  AVERAGE  TIME NEEDED
      FOR A DISCHARGE HYDROGRAPH TO TRAVEL DOWNSTREAM UNTIL  A
      POINT ( INLET tMANHOLE ) WHERE  A SECOND DISCHARGE HYDROGRAPH
      ENTERS THE  SEWER SYSTEM. ADD THE  SHIFFTED  AND THE NEW
      HYDROGRAPH  AND CONTINUE UNTIL THE  POINT FOR WHICH WE SEEK
      THE OUTFLOW HYDROGRAPH
      «AREA' IS THE AREA OF FLOW IN SQUARE FEET
      'SLOP' IS THE SLOPE OF THE INVERT  IN FT/FT
      «ALEN' IS THE- LENGTH BETWEEN  TWO CRITICAL POINTS ( INLETS »
      MANHOLES* CHANGE IN SLOPE OR DIAMETER OR SHAPE)
      (WHEN THERE IS A CHANGE  IN SLOPE OR DIAMETER OR SHAPE  WE
      CONSIDER THERE AN HYPOTHETICAL MANHOLE WITH ZERO  INFLOW)
      «PIPN' IS THE MANNING'S ROUGHNESS  COEFFICIENT  OF THE PIPE
      'Y1 IS THE  DEPTH OF FLOW  IN THE  CONDUIT  IN FEET
      •HR'  IS THE HYDRAULIC RADIUS  IN  FEET
      «DIA' IS THE DIAMETER OF  THE  SEWER PIPE  IN FEET OR  ITS WIDTH
      IF  IT IS RECTANGULAR
      «H«   IS THE HEIGHT OF RECTANGULAR  SEWER  IN FEET
      14=1  INDICATES CIRCULAR PIPE*I4=2  RECTANGULAR  CONDUIT
      NINL=NUMBER OF INLETS. MANHOLES AND CHANGES IN  SLOPE AND DIAMETER
      NPIPE=NUMBER OF PIPES
      COMMON    RI (70) »AF(70) »S(70) »RM<70) «AFM(70) tP(70)«D(70) iVS(70) »SS
     1(70) «'PP(70) .SSly,(70) .PPIM(70) »VSIM(70) .DIM I 70) .DATE(8) *DC(70) »DE(7
     20) iOVQ( 250.30! iOVQW(70 ) »NEW( 30) .01 NL( 70.20) »QiNLO(20) .IW(250)»V(25
     30) *QLEAV(250) »N »DT »NN »N INL»Q I NP (250*20 1
      READ<5*909) NPIPE
      FORMAT (15)
      NIN=NINL-1
      DO  1050  1IN=1*NIN
      J=IIN
      WRITE(6»917)
      FORMAT ( '!« )
      READ (5*907) 14 .SLOP.P IPN «DI A.H* ALEN
      FORMAT! I 5 »F10.6 *F 10.4.2F5.3 »F10«3 >
      KK=DT/1.0
      NN«=KK*N
      IFU4-1) 950*905*950
      QMAX=(0.46417*
-------
    SA-K
    X*SA/1000.0
    BB"=nx-SIN(X> )**1.6666)/(X»*0.6666>
    IF ) 955*951*951
955 IW(I)«=1
    GO TO 960
951 IWU)«0
    B«(QINP(IiIIN>*PIPN)/U.486*CSLOP**0«5)*JDIA**l»6666) )
    M«=H*1COO«0
    DO 959  K=1.M
    SA=K
    Y=SA/1000.0
    BB«=(Y**1« 66661/1 ( DIA-H 2.0*Y) )«*0.6666)
    IF(B-BB) 953»953«959
959 CONTINUE
953 V(I )=OINP( I«I IN!/(DIA*Y)
960 CONTINUE
970 SUK«:0.0
     DO 1000 I=1«NN
     SUM=SUM-f-tV( I )*QINP( I • UN) )
     SE=SE+QINP( I»IIN).
1000 CONTINUE
     AVERV=SUM/SE
     AVT=ALEN/(AVERV*60«0)
     1AVT=AVT
     DIF=AVT-IAVT
     IF(DIK-0«5) 991.992*992
     AVERT=IAVT
     GO TO 993
     AVERT=IAVT+1
     IAVET=AVERT
     DO 994  I=1.IAVET
     OLEAVt I 1=0.000
     IIAVT=IAVET+1
     NNEW=NN-KAVET
 991

 992
 993

 994
     DO 995  I=IIAVTtNNEW
     KL-I-IAVET
     OLEAVt H=OINP(KL« I IN)
     DO 996  I=NEEWiNNEW
     OINPtI »IIN)=0.000
 995
 996 VU)=0»00
                                   296
-------
997
     WRITE16.997) J
     FORM AT t 28X» '•»*************#*« »/»28X» 'PIPE
                                                NUMBER  '»I2i/.28X»'**»
                                      INVERT  IN FT/FT   IS
                                     PIPE   IN   FEET   IS
                                          COEFFICIENT   IS
      IF(I4-1) 968,969,968
 969 WRITE16.967) DIA
 967 FORMAT15X»'CIRCULAR CONDUIT   OF  DIAMETER   
     WRITE<6»964) ALEN
 964 FORMAT(5X,'THE LENGTH    OF   THE
    l',F7.2)
     WRITE(6»963) PIPN
 963 FORMAT(5X,'THE  MANNINGS ROUGHNESS
    l'.F7.5)
     WRITE(6»998)OMAX
 998 FORMAT(5X,'MAXIMUM CAPACITY  OF  THE  CONDUIT IS (CU.FEET/SEC)
    1 «»F6.2)
     WRITEI6.999) AVERV
 999 FORMAT(5X.'AVERAGE VELOCITY  OF  ENTERING DISCHARGES (FT/SEC)
    1  '.F5.2)
     WRITE(6,1001) AVERT
1001 FORMAT<5Xt=0.000
1070 Vtl)=0«00
     DO 1074 I=1,NNEW
1074 OLEAVfI)=QLEAV(I)+QINP(I»NINLI
1069 DO 1003 I=1.NNEW
     TIMP=(1-1)*1.0
     IF(lWtl)-l)  1072.1080,1072
1072 WRITE(6.1004) TIMP.OINP
-------
Comments on the Developed Computer Program
                        i
      1.  The Program does not take into account the dry
weather flow.  If information and measurements are avail-
able from the urban area under consideration, the dry
weather flow simply can be taken as an additional input for
the routing through the sewers.

      2.  The SUBROUTINE subprogram "PIROU" has been written
based on the assumption that only one lateral sewer drains
the catchment under consideration.  This is usually true
for catchments of about 10 acres area.

          If a broader subdivision of the whole basin will
be preferred, then the catchments probably will be drained
from a network of lateral sewers.  In cases like this the
SUBROUTINE "PIROU" has to be replaced by the program pro-
posed on the next page, which deals with a pipe network.
This program will use SUBROUTINE "PIROU" in the place of the
statements 6, 9, 12, and 15.  In Figure 152 a complex pipe
network is presented with constant inflows at the inlets.
Figure 152 shows the way of numbering the inlets and the
pipes, necessary for the computer input.
                            298
-------
Computer Program Dealing with a Pipe Network
       DIMENSION QINL(100)«IPIPS(100)»I PIPE(100)»PIPQ(100)
C
C
C
    50
    51
   150
    11

   100

    20
    21
     7
    10
     8
    12
   102

    13
NUMB.OF DOWNSTREAM LAST POINT  OF
N NUMBER OF INLETS OR CHANGES  IN.
NN  NUMBER OF PIPES
READ(5»50)N»NN»MAIN
FORMAT(315)
READ(5»51) (QINLU) »I = 1»N)
FORMATt12F5.2)
READ(5»3) dPIPS(J)»IPIPE(J)»J»ltNN)
FORMAT(2I5>                 ......
WRITE(6»150)
FORMAT(10X.'DISCHARGE AT PIPE  NUMBER&
TOTQ=0.0
TEMPQ=0«0
00 1 I=1»MAIN
DO 2 J*1»NN
IFdPIPE(J)-I) 2»5»2
K=IPIPS(J)
PIPQ(J)=OINL(K)
TEMPQ=PIPQ(J)
TOTQ=TOTQ+TEMPQ
WRITE<6»100)TOTQ»J
FORMAT(10X»F9.2»10XiI3)
GO TO 21
TOTQ=TOTQ+TEMPQ
TEMPQ=0.0
IPIPS(J)=1
GO TO 2
IDUM=J
IFdPIPS(J)-l) 6>6»7
IFdPIPSl IDUM)'-1J  9»9»10
JK=IDUM
DO 8 JJ=1»NN
IDUM=JJ
IF(IPIPEtJJ}-IPIPS(JK))8»7»8
CONTINUE
GO TO 12
K=IPIPS(JK)
PIPQ(JK)=QINL(KJ
TEMPQ=TEMPQ+PIPQ(JK>
IPIPS(JK)=1
IFMPIPEI JKJ-I )10»11»10
K=IPIPS(JK)
PIPQ(JK)=QINL(K)
TEMPQ=TEMPQ+PIPQ ( JK)
WRITE(6»102)TEMPO*JK
FORMAT(10X,F9.2»10X»13)
IF(IPIPE
-------
      IP(IPIPSUJ)-IPIPEUK) )
   15  K=IPIPS(JJ)
      PIPQfJJ)=QINL(K)
      TEMPQ=TEMPQ+PIPO(JJ)
      WRITE(6»103)TEMPQ»JJ
 103  FORMATUOX»F9.2»10X,I3)
      JKSJJ
      IFUPIPE(JK)-I) 13*20,13
   14  CONTINUE
   2  CONTINUE
   1  CONTINUE
      CALL EXIT
      END
II
 I
             113
             13
13
i
                     114
                               115
   (<)
           C2)
19
             112 --
\k
!
i.
        no
         \
     (S)
         -V
              C?)
                                          — 116
                                           117
                               5  C5)
                                   16
                                               17
                                               I
                                               i
                                               t
                                                       K
                                                       tu

                                                       ui
                                                       M
                                                  (7)  6
                                                         Z

                                                         s:
            Figure 152.  COMPLEX PIPE NETWORK WITH
                   CONSTANT INFLOWS AT THE INLETS
                        300
-------
                       APPENDIX IV

                  DATA CARDS PREPARATION

A. Rainfall Data Cards
  I. card  1  (8A4, F5.2, 15)
                                       Variable   Example
                                         Names    Values
     col.  1-20 Date of storm
                (day, month, year)

     col. 21-32 Hour of start of storm
                (hours, min.,AM or PM)   DATE
     col. 33-37 Time interval between
                intensity values
DATE  24 SEPT 1970


        5:35 AM


 DT       5.00
     col. 38-42 Number of time steps
                to be calculated           N

 II. card 2   (F5.2)

     col.  1-5  First value of rainfall
                intensity                 RO

III. Rainfall intensity cards, each  (12F5.2)

                Intensity,in in/hr      •  RI

B. Infiltration Data Cards

  I. card 1 (3F10.5, 2F8.4)

     col.  1-10 Const, infiltr. rate
                (in/hr)         _           FC :
     col. 11-20 Initial infiltr. rate
                (in/hr)'                    FO
     col. 21-30 Decay rate of infil.
                (1/min)                    CK
     col. 31-38 Retention storage of
                pervious areas (in)       SD
     col. 39-46 Retention storage of
                impervious areas (in)    SDIM
            36
          0.20
          0.53


          3.00


         0.0697


         0.250


         0.0625
                           301
-------
   II. card 2 (F5.2)
                                         Variable
                                           Names
         Example
         Values
       col.  1-5 A number to divide DT
                 in smaller intervals
                 (see statement 19. If
                 DT = 5.0 min, a logical
                 value of AN is 20.0 or
                 30.0. Then the new
                 intervals will be of
                 0.17 min. each)

C. Overland Flow Data Cards

    I. card 1 (15)

       col.  1-5 Number of subcatchments
                 to be simulated

   II. One card for each subcatchment
       (212,  3F7.4)

       col.  1-2 Number of the subcatch-
                 ment
       col.  3-4 Indication number (1 for
                 pervious, 2 for imper-
                 vious)
       col. 5-11 Length of area at the
                 direction of flow (feet)

       col.12-18 Manning's roughness coef.

       col.19-25 Slope of the area at the
                 direction of flow (ft/ft)

D. Gutters Data Cards

    I. card 1 (15)

       col. 1-5  Number of entry points
                 into the sewer system

    (Data cards of type II, III, IV, V to
     be repeated for each entry point)
 AN
 NW
 IA



INDW


 ALW

 ARW


 SW
NINL
30.0
16.0

0.35


0.01
                             302
-------
 II. card 2 (15)
                                       Variable
                                         Names
     col.  1-5
Number of gutter
branches leading into
the entry point
 (Data cards of type III, IV to be
  repeated for each gutter branch)

III. card 3 (215)

     col.  1-5  Number of the first up-
                stream gutter segment
                of the gutter branch

     col.  6-10 Number of the last down-
                stream gutter segment
                of the gutter branch

 (Data cards of type IV to be repeated
  for each gutter segment)

IV.  card 4 (215,  F10.2)

     col.  1-5  Number of the subcatch-
                ment providing flow to
                the gutter segment from
                the left

     col.  6^-10 Number of the subcatch-
                ment providing flow to
                the gutter segment from
                the right

     col. 11-20 Length of the gutter
                segment in feet

 V.  card 5 (215,  F5.2)
                                  Example
                                  Values
                                         NBRAN
                          Nl
                          N2
                         ITYPL
                         ITYPR
                          GLEN
   5


297.0
     col.   1-5  Number of roofs directly
                connected with entry
                point                    IROOF
     col.   6-10 Number of subcatchment
                corresponding to the  -
                roof type                 IWRF

     col.  11-15 Length of the roofs (ft)  ROOFL
                                     6

                                   30.0
                           303
-------
E.  Pipes Data Cards

    I. card 1 (15)

       col.  1-5  Number of pipes

   II. one card for each pipe
       (15, F10.6, F10.4, 2F5.3, F10.3)

       col.  1-5  Indication number, 1
                  for circular pipe, 2
                  for rectangular

       col.  6-15 Slope, of the pipe
                  invert

       col. 16-25 Manning's roughness
                  coefficient

       col. 26-30 Diameter of circular
                  pipe or width of rec-
                  tangular pipe (ft)

       ^col. 31-35 Height of rectangular
                  pipe (0.0 for circular)
                  (ft)

       col. 36-45 Length of pipe (ft)
Variable
 Names


 NPIPE
   DIA



    H

  ALEN
Example
Values
14
SLOP
PIPN
1
0.0045
0.013
  3.0



  0.0

120.0
                           304
-------
             APPENDIX V




DATA CARDS FOR THE FIRST CASE  STUDY
24
0.20
0.20
5.30
0.35

30.0
6
1 1
2 1
3 1
If 2
$ 2
6 2
9
2
1
3
1
3
5
If
0
if
5
2
6
If
7
ii
8
2
12
If
9
2
10
It
11
if
12
2
12
if
13
2
1ft
It
15
if
16
2
12
ft
17
SEPTFMBER 1,970 5 35 AM 5.0 36,

0.20
5.25
0.25
0.53


16.
I»0.
70.
17.
8.
12.


2
5
\i
if
3
1
6

5
If
6
2
7
2
8
it
6

9
ft
10
2
11
2
12
ft
6

13
It
1ft
2
15
2
16
ti
6

18

O.?0 0.20 0.20 0.20 0.42 0.42 0.50 0.62 0.87 1.63
2.80 1.75 1.25 0.88 0.80 0.67 0.50 0.47 0.47 0.47
0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25
3.00 0.0697 0.2500 0.0625


0 0.35 0.01
0 0.35 0.01
0 0.35 0.01
0 0.013 0.02
0 0.013 0.0375
0 0.012 0.667



297.0
IftO.O

297.0
IftO.O
30.0


105.0

105.0

105.0

105.0
30.0


105.0

105.0

105.0

105.0
30.0


105.0

105.0

105.0

105.0
30.0


                  305
-------
5
19
3
1
21
3
1
23
5
0
It
25
2
26
E}
27
1}
28
2
12
29
2
30
It
31
It
32
2
12
L
1
33
2
3J
35

36
2
12
2
37
5
k
39
3
1
0
8
1
1
1
1
1
1
1
1
3 297.0
20
5 297.0
I* 140.0
22
5 - 297.0
k 140.0
21*
3 297.0
6 30.0

25
l» 10 5-. 0
26
2 105.0
27
2 105.0
28
I* 105.0
6 30.0
29
U 105.0
30
2 105.0
31
2 105.0
32
I* 105.0
6 30.0
33
l» 105.0
2 105.0
35
2 105.0
36
it 105.0
6 30.0

38
3 297.0
1 11*0.0
1(0
5 297.0
4 11*0. 0
6 30.0

0.001*5 0.013 3.0 0.0
0.001*5 0.013 3.0 0.0
0.001*5 0.015 3.0 0.0
O.OOU5 0.013 3.0 0.0
O.OOU5 0.013 3.0 0.0
0.001*5 0.013 3.0 0.0
0.001*5 0.013 3.0 0.0
0.001*5 0.013 3.0 0.0



















-


























120.0
210.0
210.0
120.0
120.0
210.0
210.0
120.0
306
-------
                        SECTION  VII

           MATHEMATICAL  MODEL FOR  SIMULATION  OF

          RUNOFF  QUALITY FROM AN URBAN  WATERSHED

                      1.  INTRODUCTION

     This  study  is devoted  to the development of  a mathe-
matical  formula  for  the concentration  of pollutants at  any
location within  a combined  sewer  system of an urban water-
shed.  A stochastic  process  is  used to describe the removal
of surface pollutants by the runoff water and inertial
effects  of solids during motion are taken into account.  The
pollutants are routed from  the  inlets  through the lateral
and main sewers.
                     2. PREVIOUS WORK
     A lot of information concerning urban runoff pollution
is available, but only a few studies have included data on
both runoff quantity and quality in sufficient detail so
that the quality of direct surface runoff can be evaluated
as a function of runoff intensities.      .

     A recent study under the sponsorship of the Environ-
mental Protection Agency, Water Quality Office by a con-
sortium of contractors—Metcalf & Eddy, Inc., the University
of Florida, and Water Resources Engineers, Inc.  [9] --
provides probably.the most comprehensive runoff quality
model currently available.  The model presented here, as
developed at the University of Cincinnati, has similarities
with the above referenced model; however, a major difference
is that an integral solution has been developed instead of
a stepwise solution.
        3. DEVELOPMENT OF THE MATHEMATICAL MODEL

                FOR URBAN RUNOFF QUALITY
     Wastewater, surface dust and dirt, catch basin trap-
pings, and air pollutant residues are the major sources of
storm runoff pollution.

     The pollutants in this study are classified as soluble
and non-soluble.  The following are soluble: BOD, COD,
                             307
-------
total hydrolyzable phosphates, various forms of nitrogen,
and various forms of coliforms; while suspended solids  are
recognized as non-soluble.

3.1 Mathematical Formula for Surface Pollutant Removal

     Surface pollutants consist of street litter and
dustfalls that appear on the surface at the start of an
oncoming storm.

     The following assumptions are made as the basis for
the development of the mathematical formulation:

     a. Decaying effects of pollutants due to chemical
changes or biochemical degradation during the running-off
period are neglected.

     b. The amounts of pollutants percolating into the
soil by infiltration are neglected.

     c. The rate of removal of pollutants by runoff water
is assumed to be proportional to the amount of pollutant
remaining, and to the runoff intensity.

     d. Because the distribution of air pollutants in the
atmosphere is non-uniform, spatially and unsteady, varying
from time to time, it is difficult to formulate the amount
which runs off in rainfall; therefore, this source has  not
been evaluated separately but is considered to be included
in the overall runoff constituents.

     The amount of a pollutant remaining on a runoff
surface at a particular time, the rate of runoff at that
time, and the general characteristics of the watershed  can
be related in a simplified form as follows:
           -dP
            dt
        KqP
(D
Rearranging,
            -dP
Integrating,
               = Kqdt
 rp
 I   dP
J   "*"'
•'•n
                       Kqdt =
                             308
-------
            In ^ = - K
                o
                qdt = - K V.
 where
Vt =  J  qdt
             P    -KV
            — = 6
            P  =
                                                        (2)
      In  equations  (1)  and  (2) ,       '

           PQ  =  amount of  pollutant  on  the  surface  drainage
                 area at  the  start  of an oncoming  storm

            P  =  amount of  pollutant  remaining  on  the  surface
                 at time  t

            g  =  runoff intensity at  time t

           Vt  =  accumulated  runoff water volume up  to  time t
            e = the base of natural logarithms

            K = a constant characterizing the drainage area.

     Thus, the remaining amount of pollutant at any instant
on the surface is assumed to be decreasing exponentially as
a function of the accumulated runoff volume.

     Probabilistically, P/PQ = e~KVt can be considered as

the probability that a polluting particle on the surface
will still remain at its original position when .storm runoff
water volume has accumulated to V.  at time t.
     Consequently,
                                                       (3)
where 0 is the probability that a polluting particle will
be removed from its original position after time t.  Differ-
entiating equation (3) with respect to V:
                              309
-------
            *-  f(V) =
                                                        (4)
where  f (V) is the probability density function for 4>. The
integral of  f(V) over all possible values of V is unity:
          1
               f (V) dV =
Ke~KV dV
       -too
= -e-KVl   = 1
       Jn
It is assumed that the function  f(V) is nowhere negative,
and is single-valued.

     Therefore the probability that a particle is removed
from its original position during the time from ^ to t2/.
with corresponding accumulated volume of runoff from ^
V«, is
                                                         to
Pr (V, -£ V ^ V,) =
    •*•    •«.   ^*
                           -KV     -KV
                         Ke KVdV=-e KV
                                           =-KVi_e-KV2
                                        V-
     Assuming  that  once  a  soluble pollutant is picked up by
runoff water it will  flow  into  an inlet ,the amount of
pollutants  which  are  flushed into a sewer inlet is :
 Figure  153  schematically represents the removal of soluble
 surface pollutants by runoff water.

      For the transport of s'olids by runoff water, the drag
 force exerted by flowing water on a particle varies as the
 square  of the flowing velocity, i.e.
      Hence, the portion of the solids that are removed from
 their original positions and flushed into a sewer inlet is
 assumed to be proportional to the square of the runoff
 intensity.
            r = X q'
                                                           (6)
                              310
-------
  LU
>-
h-

-------
In equation (6),  r is the fraction of the removed solids
that is carried off into a sewer inlet at the instant when
the runoff intensity is q;  X  is a proportionality factor.
     Thus, the amount of solids that are flushed into a
sewer inlet during the same time interval from t, to t0
                                                JL     £
with mean runoff intensity


           -   ql + q2
           q = 	^	 , 'is
           P0 X q
 (e
                     -KVl
e-KV2)
(7)
Thus, with the previous assumptions and this formula, it is
obvious that the closer a particle is to the inlet, the
smaller the runoff rate necessary to wash it into the inlet,
and the larger the particle, the greater the runoff rate
required.,

     Metcalf & Eddy, Inc., et al,  [9] found that a rainfall
rate of 0.14 in/hr would begin to move 20 micron material,
and a rate of 0.65 in/hr would begin to move 40 micron
material.  Also a runoff rate of 0.01 in/hr would transport
20 micron material and a rate of 0.03 in/hr would transport
40 micron material.

     If the sewer inlet is a catch basin, then the retention
of solids in the trap should be taken into consideration.
In its relation to sedimentation, the size-weight
composition of a suspension can be expressed by the
frequency distribution of the settling velocities of constit-
uent particles  [35].

     A hypothetical cumulative distribution of settling
velocities of a suspension carried into a sewer inlet is
presented in Figure 154.

     Thus, with the size distribution of the flushed-in
suspension and the flowing rate of runoff,  u  , the portion
of the flushed—in suspension that is retained in the catch
basin can be estimated at any instant during the running-
off period.

     The proportion 1-9   of particles settling with
velocities u
is retained in its entirety.   The remainder
                             312
-------
   100
CtL
o
r  6o-
O
o
o
U-
o
                                                         - 20
                                                           10
              0.02      0.04       0.06      0.08

                SETTLING VELOCITY  V  (CM/SEC)
0. 10
 Figure 154. HYPOTHETICAL FREQUENCY DISTRIBUTION AND CUMULATIVE

           DISTRIBUTION OF SETTLING VELOCITIES OF A SUSPENSION
                              313
-------
                      de
reaches the bottom, and the overall retention portion be-
comes
                   - eo)

                                  U
                                  u
                                      de
(8)
     Since the catch basin is generally short in the
direction of flow, hence 1 - 6  is the portion of the
suspension that is retained, and 9  is that portion which
is carried by runoff water into a sewer.  Consequently,
during the time interval from t.. to t2 the amount of solids
that are flushed into a sewer is
           Po X q2  (e

while the amount that is retained in a catch basin is
                                                        (9)
                                                       (10)
3.2  Significance of K Value

     In all these derivations K is a very important para-
meter presumably characterizing the drainage area.

     Suppose that a continuous random variable x has a
probability density function  f (x) .

     The expectation  E (x) of the random variable x is de
fined as  [36] :
            E
              (x) =   f x f(x) dx
                    •J —00
which may be interpreted as the center of gravity of the
probability density function  f (x) .

     In this study, the probability density  function is

            f (V) = Ke~KVt
                             314
-------
           E(V) =
           V f (V) dV =
V K e~KV dV
d(VKe KV) = KVde~KV + e KV d(KV) = -K2 Ve~KV dV + Ke~KV dV
           KVe~KV dV = i |Ke~KV dV - d(KVe~KV)
E(V) =
                  i\
                      KVe •   dV
             I
-------
                  = 0.1
           K = 4.6

     The factors that will affect the K value presumably
are;
        (a)  size and shape of a drainage area,

        (b)  slope of gutters,

        (c)  types of storm water inlets,

        (d)  time of concentration of a drainage area,

        (e)  kind of pollutant to be transported.

3.3 Removal of Pollutant from Catchbasins

     Catchbasins historically have been constructed on in-
lets to combined sewers and storm drains for the purpose of
removing heavy grit and detritus which might otherwise
settle out in the piping system and providing a water seal
to confine sewer gas.

     The trapped pocket of liquid and solids in which
organic materials undergo decomposition between storms con-
tributes a substantial amount of pollutants to urban runoff
water.

     The American Public Works Association  [37] determined
the way the soluble pollutants in a catchbasin at the start
of a storm are flushed into the sewer.  They experimented
by adding 15 to 45 pounds of sodium chloride dissolved in
water to a catchbasin containing 353 gallons.  Water from a
hydrant was discharged through a hose and water meter to
the gutter near the catchbasin.  Samples were taken from
the effluent when various quantities of water up to 1685
gallons had been added to and passed through the catchbasin,

     Figure 155 presents the cumulative percent of salt dis-
charged as a function of gallons of liquid added.

     A formula regressioned by Metcalf and Eddy, Inc. [9]
to fit the'curve in Figure 155 came out to be
           R =
1.0 - e
100
(12)
                            316
-------
  100
   80
o
o:
o
-  60
O
o
Q_

1-

LU
O
o:'
LU
Q.
   20
                                        e
                                   Theoretical values with
                                   perfect mixing
                                   Observed values at
                                   flow rate of
                             1 cu. ft./min. O
                             4 cu. ft./min. 4-
                             7 cu. ft./min. 9
                  353
             706

GALLONS OF LIQUID ADDED
                                                               1059
             Figure 155.RELATIONSHIP OF FLOW  INTO CATCHBASIN AND

                        REDUCTION OF CONCENTRATION ON SALT  (NaCl)
                                    317
-------
 In equation (12),

            R = percent of salt removed,

            V = cumulative inflow volume  to the catchbasin,
                and

            G = trapped volume of liquid  in a catchbasin.

      A scrutiny of equation (12)  reveals the similarity of
 this  empirical equation and the equation derived  previously

 for soluble pollutant removal in the  form of  =  1  -e~KVt  ,
 equation (3).   Hence,  it might be inferred that K value is
 inversely  proportional to the size of a  drainage,  area.

      If Y  is the amount of soluble pollutants in  a  catch-
 basin at the start of a storm,  then
               R = Y
                                 V,
                       1.0 - e
                                 1.6G
will be the amount of  soluble pollutant in the catchbasin
to be flushed out into the  sewer when the runoff volume
                        During the time interval when the

                                               , the per-
centage of removal during that time interval is
has accumulated to V  .

volume of runoff has accumulated from V, to V
                                       •!•
                    V,
           R =
                   1.6G
                                                     (13)
     For solids removal from a catchbasin, the portion of
the solids flushed out into the sewer by the incoming
runoff could be estimated from Figure 154.  Assuming that
an amount of solids Z is retained in a catchbasin at the
instant the flushing velocity is UQ , the amount of solids
to be flushed out into the sewer is Z
Z (1
       9Q)
           is to be retained.
                                      &  while the amount
                                       o
3.4 Routing of Soluble Pollutants through Lateral and Main
Sewers

     For simplicity in routing soluble pollutants through
sewer systems, it is assumed that the decaying effects due
to chemical and biochemical changes are negligible.
                             318
-------
     The soluble pollutant is assumed to travel at current
velocities along the distance from where it enters the
inlet to any point downstream in the sewer system.

     Routing takes account of the volume of runoff 'water
and amount of pollutant removed into an inlet from the
farthest inlet area upstream.

     At the next inlet point, the contributions from the
next inlet area are added to the previously routed
pollutant from upstream.  This process is continued at
successive points.

     The total amount of soluble pollutant at the outlet
end of the lateral sewer at the mean time, from t^ to t^

can be expressed mathematically as
          n
                   n
W =
                       01
                       -KV,
                                          -KV,
                                       - e
 n
5>i
                      1.6G
                      - e
                             1*6G
                                                        (14)
     The concentration of the routed soluble pollutant at
the outlet end of the lateral sewer is
          c =
                          W
           r
           /
          Jt
                    Qdt-f
                                               (15)
In equations  (14) and (15)
          n
              x.
               """
              estimated amount of pollutant due to
              rainfall contamination in the air, and
              n is the number of inlet contributions
              routed.
          n
         z
          oi
                    -KV
                  tl~tr
                             -KV
                          - e
                            t2~tr
                            319
-------
total amount of surface soluble pollutant flushed into in-
lets by runoff water, and P .  denotes the amount of soluble

pollutant on the surface drainage area served by the i-th
inlet, and t  is the travel time from the i-th inlet to the

outlet end.
           n
               Y
                      v
       tl-tr
       1.6G
                    V
                               - e
t0-t
 2  r
1.6G
total amount of soluble pollutant flushed out from catch
basins.
           r
           AI
                c q dt = total amount of pollutants in dry
                         weather flow from tn to t9,  and c
                                            -L     «£       S
                         is the concentration of the pollu-
                         tant in dry weather flow, and q
                                                        S
                         is the dry weather flow rate.
q dt  = dry weather flow volume monitored
        at the outlet end from t, to t~.
                Q dt  = runoff volume at the outlet end
                        during the routing period from
                           to t  .
     Routing of soluble pollutants through the main sewer
follows the same method as that used for the lateral sewers
by taking the outlet pollutants of the laterals as the
individual contributions to the main sewer.

     Diagrammatical representation of the routing of sol-
uble pollutants through a sewer system is shown in Figure
156.

3.5 Routing of Settleable Solids in Sewer Systems

     Heavy solids in sanitary sewage water and in runoff
water are swept down the sewer invert like the bed load of
streams.  Light materials float on the water surface.
                             320
-------
 Latera
 Sewer
              i-th
              inlet
Mai n
Sewer
\
Outlet end
of lateral
sewer
                                                   V. Cumulat i ve
                                                  I   runoff  volume
                                     Time
                            Lateral  Sewer     ,
                            Outlet Hydrograph]
             Figure 1 56. D1AGRAMMAT1C REPRESENTATION OF
                           SOLUBLE  POLLUTANT  ROUTING
                              321
-------
When the velocity in the conduit falls, the heavy solids
are left behind as bottom deposits; when velocities rise
again, gritty substances are picked up once more and moved
along in heavy concentrations.

     This section of the study is devoted to the estimation
of the amount of sediments in sewers to be scoured from the
sewer bottom or to be deposited on the sewer bottom with
respect to the varying velocities involved in the water
transport in sewers.

     The channel velocity [35] initiating scour of parti-
cles deposited in sewers is defined as
           V =
               1.486
                 n
           R'
            1/6
B (ss - 1)
              1/2
(16)
In equation (16)
         n = Manning's n roughness coefficient

         R = hydraulic radius of the conduit

         d = particle diameter

         B = shield magnitude of sediment
             characteristics
        s  = specific gravity of particles
         s
Manning's formula for flow velocity is

                       ,2/3 -1/2
V =
                 n
                      R
                         (17)
After equating equations  (16) and  (17) and solving for d:
           d =
               B  (ss - 1)
                                           (18)
     In equation  (18), S is the slope of the invert of the
sewer; B varies from 0.04 for unigranular sand to 0.06 or
more for nonuniform sticky materials; and s  is taken as
                                           s
2.70.  Equation (18) is used to find the critical diameter
of sediments to be deposited or scoured up.

     Case I.  Sediment Uptake:  that portion of sewer sedi-
ments that has particle sizes greater than or equal to the
critical diameter found from equation  (18) will remain at
the bottom of the sewer.  Those particles with diameters
smaller than the critical diameter will be scoured up and
transported downstream.
                             322
-------
     Case II.  Sediment Deposition:  that portion of the
suspension in the incoming flows with particle diameters
greater than or equal to the critical diameter found from
equation (18) will settle to the bottom of the sewer. Those
particles with diameters smaller than the critical diameter
will be transported farther.

     The sewer sediment characteristic is approximated by a
plot prepared by Metcalf and Eddy, Inc. [9] and shown in
Figure 157.

     Routing of solids in sewer systems can be accomplished
by applying the continuity equation of mass transport,
starting from the farthermost upstream point of the sewer
and moving downstream.

     Routing procedures for settleable solids take the
following steps:                      ,

     (a) Calculate the average velocity in each conduit.

     (b) Calculate the hydraulic radius in the conduit of
         concern.

    -- (c) Determine the critical diameter of particles by
         equation (18).

     (d) Determine the fraction of particles with diameters
         greater than that calculated in step (c).

     (e) Determine sediment scour and deposition by con-
         sidering the mass balance in the sewer conduit
         considered.

     Figure 158 shows the contributing settleable suspen-
sion flow sources in a sewer conduit considered for
routing of solids.

         M, = amount of sediments at the sewer bottom at
              time t, ,

         x, = fraction of M, with particle diameters greater
              than or equal to the critical diameter calcu-
              lated in equation (18),

         M9 = amount sediments at the sewer bottom at time

              fc2  '
                             323
-------
            1.00


            0.80
          lo.60
          E 0.40
          o
          <
          u-0.20


            0.00
                                      5.0
                            PARTICLE DIAMETER (mm)
10.0
               Figure 157.SIEVE ANALYSIS PLOT FOR SEWER SEDIMENT

                               (AFTER METCALF & EDDY,  INC.)
      Settleable Suspension Flow
      Rate  F_  From Runof
Settleable Sus-  m
pension Flow Rate
F| From Upstream
                                     Settleable Suspension Flow Rate
                                     F_  From Incoming Sewage
                  Figure 158.MASS FLOW IN A SEWER CONDUIT
                                  324
-------
            At = t2 - t1


            Fl = settleable suspension flow rate from sewer
                 conduit immediately upstream,

            F2 = settleable suspension flow rate of incoming
                 sewage,

            F3 = settleable suspension flow rate of incoming
                 runoff,

            x2 = fraction of settleable suspension flows with
                 particle diameters greater than the critical
                 diameter calculated in equation (18),

            VQ = current volume of wastewater in the sewer
                 conduit under consideration,

            QQ = incoming flow rate at the sewer conduit con-
                 sidered.

      Then the total amount of sediment at the sewer conduit
 under consideration at time t0 is
           M2 = Ml
     X
                                        At
                                                            (19.).
      The  concentration of the suspension which will  flow
 into  the  next  sewer  conduit is
Concentration =
(1.0 - x,) M
- - - -
     V
                               +
                                 (1.0  -  x,)  (F,  +  F0  +  F_)
                                         2     1.2     3
                                           Q
                                            o
                 4. APPLICATION OF THE MODEL
     At the present stage, equation  (15) is tested by con-
sidering the drainage area as a whole, instead of being made
up- of a number of individual inlet drainage areas with
individual inlet hydrographs which are routed through the
system and combined with other inlet areas as the routing
proceeds downstream.  Contribution of the pollutants from
the air was neglected, and catchbasin,contributions were
included in surface loadings.  Dry weather flow was assumed
,to have a constant rate and a constant level of quality
during the whole period of storm runoff.  Furthermore, in
                             325
-------
these tests the K value is chosen as 4.6, based upon the
assumption that after a runoff of 1/2 inch, 90% of the
surface pollutants are removed from the whole drainage
area.

     The Laguna Street combined sewer draining a steep
drainage area of 370 acres in San Francisco  [9] was se-
lected as a demonstration site for the verification of the
model.  One storm occurred there on March 10, 1967 yielding
a total runoff of 0.22 inch, and another storm occurred 5
days later with a total runoff of 0.33 inch.  Both storms
were analyzed assuming a dry weather flow of 1.5 cfs with
a 250 mg/1 BOD concentration.  The surface loading of BOD
at the start of the storm was estimated to be 3.85
pounds/acre.  Tables 65 and 66 tabulate the computations,
and Figures 159 and 160 show the computed results and the
measured values.  The results reveal a good agreement of
the trends of the variation of BOD concentrations during
the whole period of runoff.

     The "Bloody Run" combined sewer watershed of approxi-
mately 2380 acres in Cincinnati, Ohio, was also selected
to test the model.  A storm occurred there on April 1, 1970
with a total runoff of 0.10 inch.  The dry weather flow
was at 1.5 cfs with BOD at a level of 300 mg/1.  The
surface BOD loading was estimated to be 5.65 pounds/acre.
The results of computations and trends of variations of
BOD concentrations are shown in Table 67 and Figure 161.
                            326
-------
San Francisco  Lagunn  Street
    'March 10,  1967 Storm

           TABLE 65
Time
20:35

21:05

21:20

21:35

21:50

22:05

22:35

22:50

23:05

23:20

23:35

23:50

24:05

24:25
q
in/hr
Av
in
V
in
^V,^.^-
Po'D
^V*83.8
Di luted
• Sewage
BOD
Result
BOO
mg/1
0.0
0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

,02

,02

03

045

055

02

025

03

13

21

13

08

04

0

0

0

0

0

0

0

0

.01

.005

.0075

.01125

.014

.01

.00625

.0075

0.0449&
0.
,01


0.02172
0.
015


0.03165
0.

0.

0.

0.

0.

0.
0225

03375

04775

05775

064

0715
0.0325


0.
1040
0.0525


0.
1560
0.0325


0.
1890
0.02


0.
2090
0.013


0.
2190

0.

0.

o.

o.

0.

0.

0.

0.

0.

0.


04547

05340

03609

02173

02526

09994

13297

0676

03685

01719

76.1

74.0

72.0

68.5

64.8

61.5

59.0

57.3

52.3

43.0

37.4

31.4

22.5

41.6

41.6

29.4

20.4

17.0

41.6

29.4

7.5

4.7

7.5

4.7

11.9

22.7

117.7

115.6

101.4

88.9

81.8

103.1

88.4

64.8

57.0

50.0

42.1

43.3

45.2

                327
-------
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m
    50
                                    Reported BOD




                                    Computed BOD
r
                                    TIME
           Figure 159. SAN  FRANCISCO  LAGUNA STREET COMBINED  SEWER


                                 March 10, 196?  Storm
                                    328
-------
San Francisco Laguna Street
    March  15, 1967 Storm

          TABLE  66
Time
20:15

20:30

20:45

21:00

21:15

21:30

21:45

22:00

22:15

22:30

22:45

23:00

23:15

23:30

23:45

24:00
q
in/hr

0

0

0

0

0

0
'
0

0

0

0

0

0

0

0

0


.02

.03

.025

.015

.01

.005

.0

.06

.205

.21

.08

.12

.19

.18

.15

Av
in

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0


.005

.0075

.00625

.00375

.0025

.00125

.0

.015

.05125

.0525

.02

.03

.0475

.045

.0375

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0
V
In
.0

.005

.0125

.01875

.0225

.025

.02625

.02625

.04125

.0925

.1450

.1650

.1950

.2425

.2875

.3250
D
e-KVe-' t

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.


02274

03314

02676

01569

01031

00511

0

05909

17372

14020

04511

0&034

08004

06128

04222

Po.D
1^*83.8

77.4

75.0

73.0

71.2

70.0

69.5

0,0

67.2

57.5

45.5

38.4

34.2

28.7

23.1

19.2

Di luted
- Sewage
BOD"

41.6

29.4

34.5

52.6

71.4

ni.o

250.0

1.5.6

4.8

4.7

11.9

8.05

5.15

5.43

6.5

Result
EGD
mg/1

119.0

104.4

107.5

123.8

141.4

180.5

250.0

82.8

62.3

50.2

50.3

42.3

33.9

28.5

25.7

                329
-------
  0.00
Q
O
CO
 0.10



 0.20



  200



  150



1 100



   50
      o
      o
      o
      CM
                                                 Reported BOD


                                                 Computed BOD
            o
            CM
                   O
                   o
                    CM
o


CM
 O
 O
 CM
 CM
TIME
                                          o
CM
CM
       O
       O
O
CO
               CM
         Figure 160. SAN  FRANCISCO  LACUNA STREET COMBINED SEWER

                             Storm  of March 15, 196?
                                330
-------
Cincinnati  Bloody  Sewer
 ' April  1,  1970  Storm

        TABLE 6?
Time
5:05
X • *' «^
5:12.5

5:20

5:27.5

5:30

5:37.5

5:50

5:57.5

6:05

6:12.5

6:20

6:27.5
q £
in

0.

0.

0.

0,

0.

0.

0.

0.

0.

0.

0.


06

107

123

118

102

087

074

056

03*1

026

022


0

0

0

0

0

'0

0

0

0

0

0

^v
in

.0075

.013375

.015375

.01*475

.01275

.010875

.009375

.007

.00*125

.00325

.00275


0

0

0

0

0

0

0

0

0

0

0

0
V
in
.0

.0075

.020875

.036250

.05100

.06375

.07*»625

.084

.091

.09525

.09850

.10125
-KV
e

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

D
U-KV2

03391

057&5

06203

05552

0*f505

03639

02994

02153

0127**

00957

00799

P .D
o
£V*57.0

113.0

108.0

101.0

94.0

88.5

83.7

80.0

77.0

75.0

7*i.O

72.6

Di luted
Sewage
BOD

62.6

35.0

30.5

31.8

36.8

42.2

50.8

67.2

110.0

I*t5.0

170.0

RGSLI] t
BOD
ir.g/ 1

175.6

1*O.O

131.5

125.8

125.3

125.9

130.8

144.2

185.0

219.0

242.6

              331
-------
u.
u.
o
 0.00



 0.02



 0.0k



'0.06



 0.08



 0.10


 0.12







  300
   200
o

§  100
                                 Reported  BOD


                                 Computed  BOD
               LA
               O
               r-
                                          o
                                          LA
                                                    o
                                                    oo
o
CS
oo
                                  TIME
                 Figure  161-CINCINNATI BLOODY  RUN  SEWER

                               Storm of Apr!1 1 ,  1970
                                  332
-------
               5. CONCLUSIONS AND SUGGESTIONS

                     FOR FURTHER STUDY
 Conclusions

      1. The quality of urban runoff can be modeled from
 .urban runoff hydrographs and pollutant contributions from
 the associated environments.

      2. The amount of surface pollutants in an inlet
 drainage area removed during the time that the volume of
 runoff water increases from V.  '   "
       to V» is expressed by
                 -KV.,
                      - e
-KV2
and correspondingly the amount of soluble pollutants in a
catchbasin is indicated by

                   v,        v.  \
                  1.6G
              \
                       - e
   1.6G
     3. The concentration of soluble pollutants at any moni-
toring station in the drainage area can be found from
equation (15) after finding W from equation (14).  Equation
(15) is repeated below.
            c =
                X!
                         W
Suggestions for Further Study

     The present study is confined to theoretical consider-
ations of pollutant, removal and transport in the drainage
system.  Verification or modification is anticipated as
field data become available.

     A determination of the surface pollutant removal con-
stant K as a function of the physical characteristics of
various drainage areas would be worthwhile research.

     Experimental determination on the proportionality
factor A in equation (7) for the removal of solids into .an
inlet by runoff water would make the formula for solid
removal more reliable.
                            333
-------
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                         SECTION VIII      ;

                       ACKNOWLEDGMENTS

     A  list  is given below of various people  in the Division
of Water  Resources  at  the University of Cincinnati who have
contributed  significantly to this research project.
     Dr. Herbert C. Preul   •
     Associate Professor of
     Civil Engineering

     Dr. Louis M. Laushey,
     Head, Civil Engineering
     Department

     Constantine Papadakis
     Research Assistant
     A. S. Rashidi
     Research Assistant

     T. C. Wu
     Research Assistant

     J. S. Chien
     Research Assistant
     D. D. Dasnurkar
     Research Assistant

     Paul F. Carlson
     Research Assistant

     David L. Maase
     Research Assistant

     R. T. Kuo
     Research Assistant

     John B. Malouf
     Research Assistant
Principal Investigator
and Project Director
Acting Project Director,
Summer period, 1970
Project Engineer and Co-
ordinator  (also contrib-
uted M.S.  thesis on "Cin-
cinnati Urban Runoff Model")

Project Engineer
Spring, 1970

Laboratory Analyst
and Field Assistant

Laboratory Analyst (also
contributed M.S. thesis on
"Mathematical Model for
Urban Runoff Quality")

Laboratory Analyst,
Civil Engineer

Field & Office Engineer
Field & Equipment Engineer
Laboratory Analyst,
Civil Engineer

Laboratory Analyst,
Civil Engineer
     Appreciation is extended to the following officials of
,the Water Quality Office of the Environmental Protection
Agency for their assistance and cooperation during the
                             335
-------
course of the Project:

     Mr. Darwin R. Wright, Project Manager, Storm and Com-
                           bined Sewer Pollution Control
                           Branch

     Mr. Robert L. Feder, Director of Regional Research and
                           Development Office

     Mr. William A. Rosenkranz, Chief, Storm and Combined
                           Sewer Pollution Control Branch
                             336
-------
                         SECTION IX

                         REFERENCES

 1.  Gregory, R. L. and C. E. Arnold
     "Runoff - Rational Runoff Formulas"
     Trans. Amer. Soc. Civil Eng., Vol. 96, 1932.

 2.  Hicks, W. I.
     "A Method of Computing Urban Runoff"
     Trans. ASCE, Vol. 109, 1944.

 3.  Izzard, C. F.
     "Hydraulics of Runoff from Developed Surfaces"
     Proceedings, 26th Annual Meeting, Highway Research
     Board, Vol. 26, 1946.

 4.  Tholin, A. E. and C. J. Keifer
     "The Hydrology of Urban Runoff"
     Trans. ASCE, Vol. 125, 1960.

 5.  Kaltenbach, A. B.
     "Storm Sewer Design by the Inlet Method"
     Public Works, Vol. 94, 1963.

 6.  Eagleson, P. S.
     "Unit Hydrograph Characteristics for Sewered Areas"
     Journal of the Hydraulic Division, ASCE, Vol. 88,
     No. HY2, March, 1962.

 7.  Terstriep, M. L. and J. B. Stall
     "Urban Runoff by Road Research Laboratory Method"
     Jour, of Hydraulic Division, ASCE, Vol. 95,
     No. HY6, November, 1969.

 8.  Crawford, N. H. and R. K.  Linsley
     "Digital Simulation in Hydrology:  Stanford  Watershed
     Model IV", July 1966, Tech.  Rep. 39,  Stanford Univer-
     sity.

 9.  Metcalf and Eddy, Inc.; University of Florida',1 Water
     Resources Engineers, Inc.
     "Storm Water Management Model"
     Draft Report; Environmental  Protection Agency, Water
     Quality Office; September, 1970.

10.  Horton, Robert E.
     "An Approach Toward a Physical Interpretation of In-
     filtration Capacity"
     Soil Science Society Proceedings, Vol. 5, 1940.
                             337
-------
11.  ASCE - Manual of Engineering Practice 28
     "Hydrology Handbook".
     1949

12.  Jens, Stifel W.
     "Drainage of Airport Surfaces - Some Basic Design
     Considerations", ASCE Transactions, Vol. 113,  1948.

13.  U. S. Soil Conservation Service
     "National Engineering Handbook"  Section 4,
     Hydrology, Supplement A

14.  Linsley, R. K., M. A. Kohler, and J. L. H. Paulhus
     "Applied Hydrology"

15.  Horton, R. E.
     "Surface Runoff Phenomena. Part I, Analysis of the
     Hydrograph", Horton Hydrol. Lab. Pub. 101,1935.

16.  Hicks, W. I.
     "A Method of Computing Urban Runoff"
     Tfans. ASCE, Vol. 109, 1944.

17.  ASCE Manual of Practice No. 9
     "Design and Construction of Sanitary and Storm Sewers"
     1969.

18.  Keifer, C. J. and H. Hsien Chu
     "Synthetic Storm Pattern for Drainage Design"
     ASCE Proceedings, HY4, August 1957.

19.  Horton, R. E.
     "The Interpretation and Application of Runoff  Plot
     Experiments, with Reference to Soil Erosion Problems"
     Proc. Soil Sci. Soc. Amer., Vol. 3, 1938.

20.  Eagleson, P. S.
     "Dynamic Hydrology"
     McGraw-Hill, 1970.

21.  Keulegan, G. H.
     "Spatially Variable Discharge over a Sloping Plane"
     Trans. Amer. Geophysical Union, Pt. VI, 1944.

22.  Chow, Ven Te
     "Open Channel Hydraulics"
     McGraw-Hill 1959.

23.  Horton, R. E., H. R. Leach, and R. Van Wiet
     "Laminar Sheet Flow"                          '
     Trans. Amer. Geophysical Union, Vol. 15, 1934.
                            338
-------
24.  Horner, W.  W.  and S.  W.  Jens
     "Surface Runoff Determination from Rainfall without
     Using Coefficients"
     Trans. ASCE, Vol. 107,  1942.

25.  Wolf, P. O.
     "The Influence of Flood Peak Discharges of Some Meteo-
     rological,  Topographical, and Hydraulic Factors"
     In srnational Assoc.  of Scientific Hydrology,  General
     Assembly of Toronto,  Tome III, 1958, pp 26-34.

26.  Henderson,  F.  M.
     "Open Channel Flow"
     1969.
27
28
29
30
31
Izzard, C. F.
"The Surface Profiles of Overland Flow"
Trans. Amer. Geophysical Union, Part VI, 1944.
Papadakis, C.
"Sewer Systems Design"  p,
Athens, Greece, 1969.
                                45 and 96
Horner, W. W. and F. L. Flynt
"Relation between Rainfall and Runoff from Small Urban
Areas", Trans. ASCE, Vol. 101, p. 140, 1936.

U. S. Weather Bureau Technical Paper No. 40
Chart 26, p. 59, May, 1961.

American Concrete Pipe Association
"Concrete Pipe Field Manual"
1966
32.  Tucker, L. S.
     "Oakdale Gaging Installation, Chicago-Instrumentation
     and Data"
     ASCE Urban Water Resources Research Program, Technical
     Memorandum No. 2, August 15, 1968.

33.  Cosens, K. W.
     "Sewer Pipe Roughness Coefficients"
     Sewage and Industrial Wastes Journal, January, 1954.

34.  Yarnell, D. L.
     "Rainfall Intensity-Frequency Data"
     Miscellaneous Publication No. 204, U.S.D.A., Washing-
     ton, 1935.
                              339
-------
35.  Pair, G. M.,  J. C. Geyer, and D.  A.  Okun
     "Water and Wastewater Engineering" Vol.  I
     John Wiley and Sons,  New York  1966

36.  Gutman, Irwin and S.  S. Wilks
     "Introductory Engineering Statistics"
     John Wiley &  Sons, Inc., 1965

37.  Federal Water Pollution Control Administration
     "Water Pollution Aspects of Urban Runoff"
     by the American Public Works Association, 1969
                            340
-------
     Accession Nt.mihor
                             Subject /*"io/r/&-. Group
                                                 SELECTED WATER  RESOURCES ABSTRACTS
                                                        INPUT TRANSACTION  FORM
     Organization
                University of Cincinnati;  Division of Water  Resources;
                Department of Civil  Engineering; Cincinnati,  Ohio 45221
     Title
                URBAN RUNOFF CHARACTERISTICS
10

22
Author(s)
Preul , Herbert C.
and
Papadakis, Constantine
•IJL Project Designation
EPA Rebearcli Grant No. 11024 DQU
2] Note ^ 	

Citation
 23
Descriptors (Starred First)

 *Storm Water,  *Runoff,  "'Overflows, ''-Watershed  Characteristics, *Hydrographs,
 *Pollutographs, "'Management Model, Theoretical  Models, Computer  Program,
 Sequential Sampling,  Pollution Analyses.
 25
Identifiers (Starred First)

    Storm V/ater Management,  Model Testing
 •yj  Abstract
     This  i s  an  interim report on  investigations for the  development of a comprehensive
     storm  water management model

     Detailed information on the watershed characteristics  and data on runoff  quantity
     and quality have been compiled  from a one year study of a combined sewer  watershed
     of approximately 2380 acres  in  Cincinnati, Ohio.   Collection of these data  is
     planned  to  continue over a several  year period.   The information collected  will  be
     used  to  test and develop practical  storm water management models.
Abstractor
         Herbert C. Preul
                               Institution
                                 Un 5 ve r s 5 ty  of Cin.c i_nn_a_tj ;_Dj_yJ sion  of Water Resources
 WR:I02 (REV JULY 1969)
 WHSIC
                                           SEND TO: 'YVATEIR RESOURCES SCICNTIFIC INFORMATION
                                                   U.S. DECP ARTMENLT OF THE INTERIOR
                                                   WASHINGTON. D. C. 20140
                                    U. S. GOVERNMENT PRINTING OFFICE: 1979 — 657-060/5335
-------
-------
Continued from inside front cover.
11022
11023
11020
11023
— 08/67
	 09/67
	 12/67
	 05/68
11031 	 08/68
11030 DNS 01/69
11020 DIH 06/69
11020 DES 06/69
11020 	 06/69
11020 EXV 07/69

11020 DIG 08/69
11023 DPI 08/69
11020 DGZ 10/69
11020 EKO 10/69
11020 	 10/69
11024 FKN 11/69

11020 DWF 12/69
11000 	 01/70

11020 FKI 01/70

11024 DDK 02/70
11023 FDD 03/70

11024 DMS 05/70

11023 EVO 06/70
11024 	 06/70
11034 FKL 07/70
 11022 DMU 07/70
 11024 EJC 07/70

 11020  	 08/70
 11022  DMU 08/70

 11023  	  08/70
 11023  FIX 08/70
 11024  EXF 08/70
Phase I - Feasibility of a Periodic Flushing System for
Combined Sewer Cleaning
Demonstrate Feasibility of the Use of Ultrasonic Filtration
in Treating the Overflows from Combined and/or Storm Sewers
Problems of Combined Sewer Facilities and Overflows, 1967
(WP-20-11)
Feasibility of a Stabilization-Retention Basin in Lake Erie
at Cleveland, Ohio
The Beneficial Use of Storm Water
Water Pollution Aspects of Urban Runoff, (WP-20-15)
Improved Sealants for Infiltration Control, (WP-20-18)
Selected Urban Storm Water Runoff Abstracts, (WP-20-21)
Sewer Infiltration Reduction by Zone Pumping,  (DAST-9)
Strainer/Filter Treatment of Combined Sewer Overflows,
(WP-20-16)
Polymers for Sewer Flow Control, (WP-20-22)
Rapid-Flow Filter for Sewer Overflows
Design of a Combined Sewer Fluidic Regulator,  (DAST-13)
Combined Sewer Separation Using Pressure Sewers,  (ORD-4)
Crazed Resin Filtration of Combined Sewer Overflows,  (DAST-4)
Stream Pollution and Abatement from Combined Sewer  Overflows •
Bucyrus, Ohio, (DAST-32)
Control of Pollution by Underwater Storage
Storm and Combined Sewer Demonstration  Projects -
January 1970
Dissolved Air Flotation Treatment of Combined  Sewer
Overflows,  (WP-20-17)
Proposed  Combined Sewer Control by Electrode Potential
Rotary Vibratory Fine Screening of Combined Sewer Overflows,
 (DAST-5)
Engineering  Investigation of Sewer Overflow Problem -
Roanoke,  Virginia
Microstraining and Disinfection of Combined Sewer Overflows
 Combined  Sewer Overflow Abatement Technology
 Storm Water  Pollution  from Urban Land Activity
 Combined  Sewer Regulator Overflow Facilities
 Selected  Urban Storm Water Abstracts, July  1968  -
 June 1970
 Combined  Sewer Overflow  Seminar Papers
 Combined  Sewer Regulation  and  Management - A Manual of
 Practice
 Retention Basin  Control  of  Combined  Sewer Overflows
 Conceptual Engineering Report  - Kingman Lake Project
 Combined Sewer Overflow Abatement Alternatives -
 Washington,  D.C.
-------
•it.
-------