WATER POLLUTION CONTROL RESEARCH SERIES 11034 FLU 06/71
Hydraulics of Long Vertical
Conduits and Associated
Cavitation
ENVIRONMENTAL PROTECTION AGENCY RESEARCH AND MONITORING
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WATER POLLUTION CONTROL RESEARCH SERIES
The Water Pollution Control Research Reports describe the results and progress
in the control and abatement of pollution of our Nation's waters. They provide
a central source of information on the research, development and demonstration
activities of the Water Quality Office of the Environmental Protection Agency,
through in-house research and grants and contracts with the Federal, State
and local agencies, research institutions, and industrial organizations.
Previously issued reports on the Storm and Combined Sewer Pollution Control
Program:
11023 FOB 09/70
11024 FKJ 10/70
11023 12/70
11023 DZF 06/70
11020 FAQ 03/71
11022 EFF 12/70
11022 EFF 01/71
11022 DPP 10/70
11024 EQG 03/71
11020 FAL 03/71
11024 DOC 07/71
11024 DOC 08/71
11024 DOC 09/71
11024 DOC 10/71
11040 GKK 06/70
11024 DQU 10/70
11024 EQE 06/71
11024 EJC 10/70
11024 EJC 01/71
11024 FJE 04/71
11024 FJE 07/71
11023 FDD 07/71
11024 FLY 06/71
Chemical Treatment of Combined Sewer Overflows
In-Sewer Fixed Screening of Combined Sewer Overflows
Urban Storm Runoff and Combined Sewer Overflow Pollution
Ultrasonic Filtration of Combined Sewer Overflows
Dispatching System for Control of Combined Sewer Losses
Prevention and Correction of Excessive Infiltration and
Inflow into Sewer Systems - A Manual of Practice
Control of Infiltration and Inflow into Sewer Systems
Combined Sewer Temporary Underwater Storage Facility
Storm Water Problems and Control in Sanitary Sewers -
Oakland and Berkeley, California
Evaluation of Storm Standby Tanks - Columbus, Ohio
Storm Water Management Model, Volume 1 - Final Report
Storm Water Management Model, Volume II - Verification
and Testing
Storm Water Management Model, Volume III -
User's Manual
Storm Water Management Model, Volume IV - Program Listing
Environmental Impact of Highway Deicing
Urban Runoff Characteristics
Impregnation of Concrete Pipe
Selected Urban Storm Water Runoff Abstracts, First Quarterly
Issue
Selected Urban Storm Water Runoff Abstracts, Second Quarterly
Issue
Selected Urban Storm Water Runoff Abstracts, Third Quarterly
Issue
Selected Urban Storm Water Runoff Abstracts, July 1971 -
June 1971
Demonstration of Rotary Screening for Combined Sewer
Overflows
Heat Shrinkable Tubing as Sewer Pipe Joints
To be continued on inside back cover....
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HYDRAULICS OP LONG VERTICAL CONDUITS
AND ASSOCIATED CAYITATION
St. Anthony Palls Hydraulic Laboratory
University of Minnesota
Minneapolis, Minnesota 55455
for the
ENVIRONMENTAL PROTECTION AGENCY
Project #1.10314. FLU
Contract # li|-12-86l
June 1971
For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402 - Price 60 cents
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EPA Review Notice
This report has been reviewed by the Water
Quality Office, EPA, and approved for publication.
Approval does not signify that the contents
necessarily reflect the views and policies of
the Environmental Protection Agency, nor does
mention of trade names or commercial products
constitute endorsement or recommendation for
use.
11
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ABSTRACT
Experimental studies have been undertaken to examine the flow in long
vertical conduits with particular reference to the design, of storm
water drop shafts. A distinguishing characteristic of such flow is the
potential cavitation regime. Its existence depends upon the design of
the structure. The cavitation regime will develop when the conduit is
sufficiently long and the head sufficiently large. It can also be
generated at a lower head if a control valve is installed in the supply
line so that the net head can be negative. The cavitation region con-
sists of a rather finely divided mixture of water and water vapor at a
constant cavitation pressure of about -32.0 ft of water throughout the
region and for all discharges. The cavitation region terminates with
a shock front whose location is also a function of the discharge. The
concentration of vapor, while relatively constant throughout the cavi-
tation region, decreases with increasing discharge.
If a small amount of air is introduced into the system, the cavitation
region is eliminated, the pressure gradient is more uniform, and the
flow consists of a uniform mixture of air and water.
This report was submitted in fulfillment of Project Number 1103l| FLU,
Contract EPA llj.-12-86l, under the sponsorship of the Water Quality
Office, Environmental Protection Agency.
111
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CONTENTS
Section
I Conclusions 1
II Recommendations 3
III Introduction 5
IV Experimental Apparatus 7
V Experimental Results 11
Cavitation Studies 11
Air Injection 19
VI Analysis of Data 27
VTI Head Discharge Rating Curves , 37
Transitional Plow 37
Cavitation Plow 38
Full Plow 42
Plow Behavior Patterns 42
VIII Acknowledgments 45
IX References 47
X Glossary of Symbols 49
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FIGURES
PAGE
1 GEOMETRY OF DROP SHAFT 8
2 INLET TO VERTICAL CONDUIT SHOWING DISCHARGE MEASURING
ORIFICE AND CONTROL VALVE 9
3 TRANSPARENT EXPERIMENTAL VERTICAL CONDUIT SHOWING PRESSURE
GAGES AND INSTRUMENT PORTS 9
4 DETAIL OF INSTRUMENT PORTS FOR VAPOR CONCENTRATION
MEASUREMENTS 10
5 TWO TYPES OF VAPOR-CONCENTRATION SENSORS: (a) PARALLEL
PLATE PROBE; (b) NEEDLE PROBE 10
6 PRESSURE TTKAT) VARIATION ALONG SHAFT 12-13
7 PIEZOMETRIC HEAD ALONG SHAFT 14-15
8 VAPOR CONCENTRATIONS 16-17
9 SHOCK-FRONT ELEVATION vs DISCHARGE 18
10 VAPOR CONCENTRATION vs DISCHARGE 20
11 PIEZOMETRIC HEAD ALONG SHAFT WITH AIR INJECTION 21-22
12 AIR CONCENTRATIONS ALONG SHAFT 23
13 EFFECT OF AIR INJECTION ON WATER DISCHARGE 24
14 EFFECT OF AIR INJECTION ON SHAFT PRESSURE 25
15 SKETCH SHOWING FLOW REGIMES 28
16 SONIC VELOCITY vs AIR CONCENTRATION 29
17 COMPUTED AND OBSERVED SHOCK FRONT ELEVATIONS 33
18 COMPUTED AND OBSERVED VAPOR CONCENTRATIONS ABOVE
SHOCK FRONT 35
19 THEORETICAL CURVES SHOWING SHOCK FRONT ELEVATION FOR
VARYING PIPE LENGTHS 36
20 DISCHARGE RATING CURVES - Dia. = 5.0 in. 39
21 DISCHARGE RATING CURVES - Dia. = 1.0 ft 40
22 DISCHARGE RATING CURVES - Dia. = 2.0 ft 41
VI
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SECTION I
CONCLUSIONS
1. The cavitation regime in a long vertical conduit is a part of the
complete head-discharge relationship. It will occur only if the head
is large enough to prevent the insufflation of air or if there is a
control valve in the inlet line. Its occurrence also depends on the
size of the conduit.
2. The pattern for cavitating flow appears to be well defined and con-
sists of the inlet region and an outlet full flow section connected by
a relatively homogeneous mixture of water and water vapor flowing at a
constant pressure of -31.75 ft of water for all discharges.
3. A shock front occurs at the downstream end of the cavitating region
and causes an abrupt pressure increase.
1;. The concentration of vapor in the cavitating region decreases with
increasing discharge, and the shock front generated by the cavitating
flow rises in elevation with increasing discharge, until the entire
conduit runs full.
5. Small quantities of air injected into the system have very little
effect on discharge and are very effective in eliminating the cavita-*
tion and the shock front. The mixture of air and water flows smoothly
through the conduit.
6. It appears from the study that in terms of the complete discharge
rating curve, the existence and the exploitation of a cavitation regime
depend on design decisions. The present results can be used as a
basis for preliminary design and for engineering feasibility studies.
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SECTION II
RECOMMENDATIONS
This program was limited to a laboratory study of the cavitating phe-
nomenon in a relatively short transparent vertical conduit. The equip-
ment allowed the examination of many aspects of the cavitation process,
such as pressure and vapor concentration distribution and the existence
of the shock front, but the conduit was not long enough for an investi-
gation of the effect of larger length-diameter ratios.
It is recommended that further measurements be made in a conduit both
longer and of larger diameter under conditions approximating field in-
stallations .
In light of the present results it is recommended that additional labo-
ratory measurements be made on a model equipped to transport larger
discharges. These would include additional measurements on a similar
model of greater length and smaller diameter.
Examination of the head-discharge rating curves indicates a wide range
of possible transitional flow relationships depending upon the inlet
geometry. It is recommended that this aspect be investigated in detail
in order to define the head-discharge relationship more clearly for all
practical design geometries.
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SECTION III
INTRODUCTION
In large urban areas, pollutional considerations more and more require
that surface runoff be treated before being discharged into streams.
To facilitate the efficient and economical treatment of this polluted
water it would be desirable to store the runoff temporarily so that the
treatment process could operate over a period considerably longer in
duration than the storm event and at a much lower rate of speed than
that of the peak runoff. In some cases storage in large tunnels con-
structed in the rock some distance below the ground surface seems ap-
propriate, and the surface water must be transported to these tunnels
through vertical drop shafts which may be quite long. To minimize the
size of the drop shaft, it obviously must run full when the discharge
is maximal. Given this requirement, the size and spacing of the drop
shafts for drainage of a particular area can be optimized by consider-
ing the local hydrology as well as the construction cost and the func-
tion of the drainage system. In some cases, the spacing of drop shafts
may be governed by the requirement of minimum surface storage, as on a
depressed roadway.
Drop shafts can be categorized as either atmospheric or subatmospheric
pressure systems. In an atmospheric pressure system, the water simply
falls down the shaft without completely filling the conduit, and the
pressure is atmospheric throughout. In a subatmospheric pressure sys-
tem the conduit flows full and the pressure thus decreases with increas-
ing elevation. Since the conduit is flowing full, with a greater
effective head, the velocities are greater than in an atmospheric
pressure system, and hence the same discharge can be transported through
a smaller conduit. However, since the velocities are larger and the
pressure in certain sections is reduced to the cavitation pressure,
special consideration must be given to the flow characteristics so
that efficient operation can be obtained. With a knowledge of the flow
pattern characteristics, the use Qf such drop shafts is governed by
economics.
The purpose of the experimental program described herein was to examine
and describe the hydraulic characteristics of flow in long vertical
conduits with particular reference to the application of this phenom-
enon to storm water drop shafts. It was thought that the relationships
developed through this research would provide a basis for the design of
prototype structures. Because the vertical conduit was quite long, it
was expected that the usual hydraulic relationships for conduit flow
would not be directly applicable, since according to hydraulic theory,
the pressure continually decreases as the elevation above the conduit
outlet is increased with the conduit running full. For a conduit of
sufficient length this pressure would decrease to the vapor pressure,
and it was expected that cavitation in some form would occur. Therefore
the first objective after the experimental apparatus had been fabricated
was to visually examine the flow characteristics for various discharges
and describe the phenomenon qualitatively. As was expected, when
the discharge was sufficiently large to seal the lower portion of the
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conduit, the flow in the upper part of the pipe where the pressure was
at a minimum began to cavitate and appeared to be a milky mixture of
water bubbles and water vapor flowing rapidly down the conduit. A
crackling noise could be heard in the region immediately downstream of
the control valve. At some elevation below the conduit inlet a shock
front was created. The mixture was transformed back into solid water
which filled the pipe and flowed at a much lower velocity through the
remainder of the conduit. The flow below the shock front appeared to
contain bubbles of air which might have been released from solution in
the low-pressure region upstream of the shock front. The shock front
was shifted bodily within the conduit when the discharge was changed.
For the small discharges the shock front occurred at a relatively high
elevation and tended to move downstream as the discharge increased until
it reached a minimum elevation. Vith further increases in the discharge,
the shock front developed at successively higher elevations until the
conduit was running full and the shock front disappeared. On the basis
of visual observation, provisions were made for measuring the several
variables that appeared to have a bearing on the phenomenon. These in-
cluded the discharge, the shock front elevation with respect -to the
conduit outlet, and the longitudinal distribution of pressure and vapor
concentration. The measurements were made to provide detailed informa-
tion about the nature of the flow and to serve as a basis for analytical
relationships to describe the flow under these cavitating conditions
which would aid in the design of drop shafts of other sizes and lengths.
In addition to those described above, some experiments were made to ex-
amine the effect of increasing the pressure in the conduit to a value
above the cavitation pressure by injecting air into the system. This
prevented cavitation and provided a uniform and more smoothly flowing
air-water mixture. In such a system cavitation did not occur, and hence
there was no likelihood of cavitation damage to the inside surface of
the drop shaft. In these experiments, measured quantities of air were
introduced into the system at the inlet, and the longitudinal distribu-
tion of pressure and air concentration was measured to delineate the
characteristics of the mixture. The introduction of the air trans-
formed the flow pattern from a cavitating flow with a shock front to
a milky white mixture flowing smoothly through the system.
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SECTION IV
EXPERIMENTAL APPARATUS
The hydraulic apparatus which was used for these experiments was a
transparent vertical conduit 5 inches in diameter and approximately
U3 feet high. This was the maximum height that could be obtained with-
in the confines of the hydraulic laboratory without extensive modifica-
tion of laboratory facilities. The model permitted the use of gravity
flow from the Laboratory supply system. The water supply used in the
experiments was obtained from the Mississippi River upstream of St.
Anthony Falls. The discharge from the model was directed back to the
river through the wasteway below the falls. In this way the full head
available at the falls could be utilized for gravity flow through the
system. The hydraulic model was open to the atmosphere at both the in-
let and the outlet.
The discharge was controlled by a valve in the 6 inch pipe leading from
the supply tank and was measured by means of a calibrated orifice.
Figure 1 is a diagrammatic sketch of the apparatus and its appurte-
nances. Figure 2 is an overall view of the upstream portion of the
drop shaft showing the supply pipe from the supply channel in the back-
ground. The flow through the conduit was controlled by the angle valve
and measured by means of the orifice in the pipeline.
The drop shaft model was fitted with pressure gages and ports for the
measurement of vapor concentration. These measurements were made with
standard equipment or with instruments previously developed by the Labo-
ratory. The pressures at various elevations along the conduit were
measured by Bourdon gages fitted to piezometer taps drilled through the
side of the conduit. Figure 3 shows a portion of the conduit and the
pressure taps and gages for measuring the pressures. Ports for the in-
sertion of the air concentration meter were fitted at various points
along the pipe as shown in Fig. l+. Two types of vapor concentration
instruments, shown in Fig. 5> were used. In one the vapor concentra-
tions were determined by measuring the electrical resistance between two
electrode surfaces. This is a function of the relative volume of water
vapor moving between the electrodes. The other instrument measured
vapor concentration at a point rather than taking the mean of a larger
volume. This instrument simply registered the amount of time that the
very tiny needle point was in a regime of vapor in relation to the time
it was in contact with solid water (Ref. 1,2).
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DETAILS OF DROP SHAFT
Plug at "A" Sea e 1 in. = 2 ft
Size
FIGURE 1
-------
Fig. 2 - Inlet to Vertical Conduit showing Discharge Measuring Orifice and
Control Valve
Fig. 3 - Transparent Experimental Vertical Conduit showing Pressure Gages
and Instrument Ports
-------
Fig. 4 - Detail of Instrument Ports for Vapor Concentration Measurements
Fig 5 - Two types of Vapor-Concentration Sensors: (a) Parallel Plate Probe
(b) Needle Probe
10
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SECTION V
EXPERIMENTAL RESULTS
Cavitation Studies
Measurements of the various flow properties are shown in Figs. 6 through
10. In Fig. 6, the pressure head, P/y, has been plotted in terms of
the elevation above the "bottom of the conduit for various discharges
through the system. Throughout the upper regionthat is, above the
shock frontand for all discharges the pressure is essentially con-
stant at -31«75 ft of water. This is presumably the pressure at which
cavitation occurs for the water being used in these experiments. The
fact that this pressure is somewhat greater than the vapor pressure of
pure water at this temperature is probably due to the dissolved air
that is found in the natural river water. The figure also shows for
each discharge a rather sudden increase in pressure as the shock is
traversed and a relatively uniform rate of increase in the pressure
gradient downstream of the shock front. These data have been replotted
in Fig. 7 i-11 terms of the piezometric head (P/y + Z) to develop the
hydraulic gradient along the conduit. The plots show that the gradient
in the upper region decreases linearly with the elevation and is the
same for all discharges. At a particular elevation, which is a function
oftthe discharge, there is a sudden increase in piezometric pressure
across the shock front followed by a relatively flat gradient due to
the frictional effects of the flow of the water phase through the lower
regions of the conduit. The figure also gives some indication of the
nature of the shock front, since for the smaller discharges (particu-
larly 0.5 and 1.0 cfs) the hydraulic gradient shows a much more gradual
transition to the solid water phase than the rather abrupt transition
that occurs for the higher discharges.
In Fig. 8 longitudinal water-vapor concentration profiles have been
plotted for various discharges, and the plot shows that the vapor con-
centration is reasonably constant upstream of the shock front and under-
goes an abrupt reduction in the region of the shock front to relatively
low values in the lower portions of the conduit. The concentration
downstream of the shock front may, in fact, be air that was released
above the shock front but which has not had time to be redissolved in
the distance remaining below the shock front. The graph also shows
that the vapor concentration above the shock front decreases system-
atically as the discharge increases. For a discharge of 0.5 cfs the
mean concentration above the shock front is approximately 82 per cent,
while that for a discharge of 3.65 cfs has been reduced to only i|0 per
cent. Below the shock front the air concentration is considerably less
than the vapor concentration above the shock front and also decreases
with the discharge.
One important result of these experiments is the delineation of the
shock front that is observed when flow takes place down the conduit.
Its elevation has been plotted in terms of the discharge in Fig. 9»
For very small discharges the shock front occurs at an elevation roughly
equivalent to the barometric height of the water; for increases in
11
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-35 -30
-25 -20 -15 -10
Pressure Head, P/y, Feet of Water
-5
OPERATING CONDITIONS
1) Channel Water Level: El. 49.00
2) Water Temperature: 36°F
(Refer to Drwg. No. 194B492-2 for
geometry.)
Symbol
o
A
0
a
o-
Discharge, cfs
0.5
1.0
2.0
3.0
3.45
Run Nos. 123, 119, 121(b), 122(b)
Nov. 14, 23, 24, and 30, 1970
FIGURE 6 a
STORW WATER DROP SHAFTS
Federal Water Quality Administration
PRESSURE HEAD VARIATION ALONG SHAFT1
SAIHT ANTHONY FALLS HYDRAULIC LABORATORY
UNIVEHBITY OP MINNESOTA
OttAWH CSC | CMKCKKO PPV ! ApmOV«D
OUTM 12-70 I NO 1948492-11
-------
-35 -30
-20
-15
-10
-5
Pressure Heod, L Feet of Water
r
OPERATING CONDITIONS
1) Channel Water Level: El. 49.00
2) Water Temperature: « 80°F
(Refer to Drwg. No. 194B492-2 for
geometry.)
Symbol
O
A
0
a
o
Discharge in cfs
0.5
1.0
2.0
3.0
3.45
June 29 and July 1, 1970
FIGURE 6b
STORM WATER DROP SHAFTS
Federal Water Quality Adminiitration
PRESSURE HEAD VARIATION ALONG SHAF1
SAINT ANTHONY FALLS HYDRAULIC LABORATORY
UNIVERSITY OF MINNESOTA
DA
PPV
rTvfaw-
-------
-15
Piezometric Head, (L+ Z), Feet of Water
OPERATING CONDITIONS
1) Channel Water Level: El. 49.00
2) Water Temperature: ^ 80 F
(Refer to Drwg. No. 194B492-2 for
geometry.)
Symbol
O
A
0
a
O
Discharge In cfs
0.5
1.0
2.0
3.0
3.65
FIGURE 7a
STORM WATER DROP SHAFTS
Federal Wafer Quality Adminiitration
PIEZOMETRIC HEAD ALONG SHAFT
SAINT ANTHONY FALLS HYDRAULIC LABORATORY
DA
PPV
o. 1946492-3
-------
VJ1
OPERATING CONDITIONS
1) Channel Water Level: El. 49.00
2) Water Temperature: »36°F
(Refer to Drwg. No. 194B492-2 for
geometry.)
Symbol
o
A
0
A
D
-e-
Discharge, cfs
0.5
1.0
2.0
2.5
3.0
3.45
Run Nos. 122(a), 122(b), 123, 119
Nov. 16, 23, 24, and 30, 1970
FIGURE 7b
Piezometric Head, (- + Z), Feet of Water
STORM WATER DROP SHAFTS
Federal Water Quality Administration
PIEZOMETRIC HEAD ALONG SHAFT
SAINT ANTHONY FALLS HYDRAULIC LABORATORY
UNIVERSITY OF MINNESOTA
DRAWN CSC CHECKED PPV I APPROVED
12-70
~o. 194B492-12
-------
20
40 60 80
Vopor Concentration, Per Cent
100
OPERATING CONDITIONS
1) Channel Water Level: El. 49.00
2) Water Temperature: »36°F
(Refer to Drwg. No. 194B492-2 for
geometry.)
Symbol
Discharge, cfs
0.5
1.0
2.0
2.5
3.0
3.45
FIGURE 8a
Run No>. 119, 121(b), 122, 123
Nov. 24, 23, 16, and 30, 1970
STORM WATER DROP SHAFTS
Federal Water Quality Administration
VAPOR CONCENTRATIONS
SAINT ANTHONY FALLS HYDRAULIC LABORATORY
UNIVERSITY OF MINNESOTA
OHAWM CSC CMKCKKO PPV
»CALlGzU>hIc CATC 12-70
-------
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OPERATING CONDITIONS
1) Channe Water Level: El. 49.00
2) Water Temperature: » 80°F
(Refer to Drwg. No. 194B492-2 for
geometry.)
Symbol Discharge in cfs
O 0.5
A 1.0
0 2.0
D 3.0
O 3.65
August 25 thru 31, 1970
FIGURE 8b
STORM WATER DROP SHAFTS
Federal Water Quality Administration
VAPOR CONCENTRATIONS
100 SAINT ANTHONY FALLS HYDRAULIC LABORATORY
Vapor Concentration, Per Cent
UNIVERSITY OF MINNESOTA
DKAWN DA CHECKED PPV \ APPROVED
,cAuG » 1 2-70 1 HO. 1 94B492-5
-------
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OPERATING CONDITIONS
Channel Water Level: El. 49.00
(Refer to Drwg. No. \ 94B492-2 for
geometry.)
FIGURE 9
STORM WATER DROP SHAFTS
Federal Water Quality Adminiitrotion
SHOCK-FRONT ELEVATION v» DISCHARGE
A c SAINT ANTHONY FALLS HYDRAULIC LABORATORY
*J UNIVERSITY OF MINNESOTA
DltAWN DA 1 CHECKCD PPV ' APFHOVKO
.o.L.Grapr,:
-------
discharge the shock front elevation is lowered until it reaches a mini-
mum at a discharge (i-n these experiments) of approximately 2.5 cfs. For
discharges larger than this the shock front elevation again increases
with increasing discharge. The maximum discharge obtainable in the
present apparatus was 3.65 cfs, but it appears from the graph that if
the discharge could have been increased above this value, the elevation
of the shock front would also have risen further and would ultimately
have reached the top of the conduit. In Fig. 10 the concentration of
vapor in the region shows clearly that the vapor concentration, as sug-
gested in Fig. 8, decreases with increasing discharge. It would appear
from these two graphs that if the shock front were to reach the top of
the conduit, so that the pipe flowed full, the vapor concentration
would approach zero.
Air Injection
The most apparent characteristic of the flow when atmospheric air is
injected into the system is the immediate disappearance of the shock
front and the development of a continuous hydraulic gradeline through-
out the conduit. This is shown in Fig. 11, in which has been plotted
the piezometric head (P/y + Z) with respect to elevation above the
pipe outlet. These graphs do not show the discontinuities in pressure
which are inherent in the flows in which cavitation occurs. The same
effect is observed in the longitudinal air concentration profiles shown
in Fig. 12. The air concentration tends toward constancy in the pipe
below the point of injection. As would be expected for a constant rate
of air injection, the air concentration is less for the higher water dis-
charges than it is for the lower value. ₯tien a given water discharge
is flowing through the system under a given gravitational head, the in-
jection of air has the effect of reducing the water discharge. This is
shown in Fig. 13, in which water discharge, again for a fixed total
head, is plotted in terms of the rate of air flow injected into the sys-
tem in pounds per second. Since the injection of a small quantity of
air will effectively eliminate the shock front, it appears from Fig. 13
that this can be done with only a small reduction in the water discharge.
This is perhaps shown more clearly in Fig. llj., in which the ratio of
the air discharge to the water discharge, both in cfs, has been plotted
in terms of the pressure at tap 5 (see Fig. l) near the pipe inlet. All
the data are grouped about a single curve and show that for small values
of the ratio, the pressure at tap 5 is appreciably increased to a value
well above the cavitation pressure for the flow.
19
-------
NOTE: Observations of Concentrations relate
to region above shock Front and at
location 'A1 in sketch.
OPERATING CONDITIONS
Channel Water Level: El. 49.0+
(Refer to Drwg. No. 194B492-2
for geometry.)
NOTE: Vapor Concentration =
Vol. of Vapor
Vol. of Vapor + Vol. of Water
Temp °F
36
80
FIGURE 10
STORM WATER DROP SHAFTS
Federal Water Quality Administration
VAPOR CONCENTRATION vs DISCHARGE
SAINT ANTHONY FALLS HYDRAULIC LABORATORY
UNIVERSITY OF MINNESOTA
HAWM CSC I CHICKED PPV j ****PMD
EAuiGophic PAT. 12-70 1 MO. 194B492-8
-------
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OPERATING CONDITIONS
1) Channel Water Level: El. 49.0
2) Water Temperature: 35°F
(Refer to
Drwg. No.
194B492-2 for
geometry)
Pressure
Qw cfs
Reg Tap *5 No With
--0 17.5 -13.4 3 2.155
^ 34 -17.1 2.5 2.08
Qa
0.0761 1.76
0.0562 1.68
Q Q
Q Q +Q
v/ w a
% %
81.7 44.9
80.8 44.7
Note: Air injected through 4 equally spaced taps at El. 40.68
Run No. ax>.
Jan. 27, 1971
FircilRF 11 n
25 30
Wafer
STORM WATER DROP SHAFTS
Federal Water Quality Administration
PIEZOMETRIC HEAD ALONG SHAFT
SAINT ANTHONY FALLS HYDRAULIC LABORATORY
UNIVERSITY OF MINNESOTA
D»»H CSC
SCALE Graphic
CH ECKE D C 5C
D*T« 2-71
A^pftOVKO
HO 1 94B492- 26
-------
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OPERATING CONDITIONS
1) Channel Water Level: El. 49.00
2) Water Temperature
(Refer to Drwg. No.
geometry)
Pressure Qw cfs
Reg Top *5 No With
: » 35°F
194B492-2 for
Qo
Symbol psi in Hg air air Ibs/sec cfs
A 40 -23.9 3.65 3.2 0.0227 1.492
Q 20 -22.0 2.0 1.97 0.0242 1.20
D 20 -12.6 1.5 1.25 0
.0516 1.13
Note: Air injected through 4 equally spaced taps
Qa Qa
w w a
% %
46.7 31.8
60.9 37.9
90.4 47.5
at El. 40.68
Run No. 201, Feb. 1, 1971
FIGURE lib
STORM WATER DROP SHAFTS
Federal Water Quality Administration
PIEZOMETRIC HEAD ALONG SHAFT
SAINT ANTHONY FALLS HYDRAULIC LABORATORY
of Water UNWEMITY OF MINNESOTA
OTAWN CSC
CHCCKCO CSC
DAT. 2-71
APFROVCD
NO. 1 94B492- 28
-------
40
35
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OPERATING CONDITIONS
Channel Water Level: El. 49.0
(Refer to Drwg. No. 1 94B492-2 for
geometry)
Water Discharge, cfs Air Flow
Before After ^oter
air air Temp Run
Symbol injection injection Ibs/sec cfs F No. Date
-+ 1.0 0.78 0.0533 0.935 33.5 213 3-25-71
4 2.0 1.86 0.0519 1.415 35 213 3-25-71
3.0 2.45 0.0544 1.855 35 213 3-25-71
O 3.65 2,7 0.0541 1.77 33.5 213 3-25-71
Note: 1) Air flow in cfs calculated corresponding to pressure at
Tap *5, 33.83 ft above shaft bottom
2) Air concentration measurements made at location A -
Drwg. No. 194B492-8
3) Air injected through 4 equally spaced taps at El. 40.68
FIGURE 12
STORM WATER DROP SHAFTS
Federal Water 'Qual ity Administration
AIR CONCENTRATIONS ALONG SHAFT
0 20 40 60 80 1 00 SAINT ANTHONY FALLS HYDRAULIC LABORATORY
Per Cent Air Concentration
UNIVERSITY OF MINNESOTA
DRAWN PPV CHECKED PPV ' APPROVED
scALEGaphic DATE 3-71 NO. 194B492-29
-------
ro
3 0|
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12 0.
14 0.1
OPERATING CONDITIONS
Channel Wafer Leve : El. 49.0
(Refer to Drwg. No. 194B492-2 for
geometry)
Water
Discharge w T
(before air r
Symbol injection) °F Run No. Date
0 0.5 34 209 3-16-71
--A-- 1.0 35 205 3-9-71
--*-- 1.0 35 208 3-16-71
A 1.5 35 204 3-9-71
9 2.0 35 207 3-11-71
* 2.0 34 203 3-8-71
-# 2.0 34 201 3-1-71
*- 2.5 34 212 3-19-71
-*(- 2.5 34 200 1-27-71
3.0 35 206 3-11-71
-» 3.0 34 200 1-27-71
3.5 35 211 3-19-71
Note: .Air injected through 4 equally spaced taps at
El. 40.68
FIGURE 13
STORM WATER DROP SHAFTS
Federal Water Quality Administration
, EFFECT OF AIR INJECTION ON
WATER DISCHARGE
SAINT ANTHONY FALLS HYDRAULIC LABORATORY
UNIVERSITY Of MINNESOTA
DRAWN V CHCCKCO PPV 1 APFMOVBO
.cAijGophic D.T. 3-71 INO. 194B4 92-31
-------
VJI
u
i
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3.5
3.0
2.5
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30 -25 -20 -15 -10 -50 5 1(
Pressure at Tap ^5 (El, 33.83), Inches of Mercury
OPERATING CONDITIONS
Channe Water Level: El. 49.00
(Refer to Drwg. No. 194B492-2 for
geometry)
Water Discharge, cfs
Symbol (before air injection)
1.0
1.5
2.0
2.5
3.0
3.5
(Data of Run Nos. 202 through
213)
Note: 1) Air injected through 4 equally spaced taps at
El. 40.68
2) Air flow in cfs calculated corresponding to pressure
at tap *5, 33.83 ft above shaft bottom
FIGURE 14
STORM WATER DROP SHAFTS
Federal Water Quality Administration
EFFECT OF AIR INJECTION ON
SHAFT PRESSURE
SAINT ANTHONY FALLS HYDRAULIC LABORATORY
DKAWN CSC CHECKED CSC 1 APPROVED
scALEGaohic DAT. 4-71 INC. 194B492-32
-------
SECTION VI
ANALYSIS OF DATA
The experiments described above provide some insight into the mechanism
by which cavitating flow may take place in a long vertical conduit.
One can visualize three regions of flow. In the upper segment the flow
of solid water is taking place in a receptacle of arbitrary shape (such
as a sewer) with the prescribed free surface elevation. The water flows
into the inlet of a long vertical conduit where the pressure is reduced
to the cavitation pressure of the water if the depth of water over the
conduit is sufficiently large to prevent air from being sucked into the
flow. This condition can also be obtained if a valve exists in the sys-
tem so that an appropriate head loss can be introduced to create a
negative effective head. In the second region a mixture of water vapor
and water droplets forms and continues to flow down the conduit at this
constant cavitation pressure. The mixture may also contain a small
amount of air released from solution in this region. In the third seg-
ment below the shock front the recondensed solid water flows down the
pipe and discharges into the atmosphere. The pressures in this segment
are considerably above the cavitation pressure. The water vapor in the
air-water mixture must be recondensed at an elevation such that the
piezometric pressure is greater than the atmospheric pressure at the
end of the conduit. One can consider the overall phenomenon as being
made up of a typical water flow in the upper supply channel and an
essentially typical conduit flow at the lower end connected by a region
of constant cavitation pressure in which a water-vapor mixture is
flowing and whose length is determined by the overall length of the
conduit and the discharge flowing through it. The cavitating segment
serves, in effect, as the connecting link between the upper and lower
water flows. On the basis of this somewhat simplified description one
can develop a mathematical model which to some degree describes the
flow (Eefs. 3»4>5)» Figure 15 is a diagrammatic sketch of a long ver-
tical conduit through which water is flowing from an upper reservoir.
Shown in the sketch are the free surface of the upper reservoir, the
cavitation region between the inlet and the shock front, and the lower
region in which essentially solid water is flowing.
One characteristic of the water vapor-water mixture in the cavitation
region is the dramatic reduction in the velocity of sound. It has been
shown (Ref . 6) that for such bubbly mixtures the sonic velocity can be
expressed as
_
Vs ~
V2
where V is the sonic velocity within the mixture, P is the abso-
lute preisure of the medium, p is the density of the water, and C
is the vapor concentration. This relationship, computed for the cavi
tation pressure, is shown in Fig. 16. The curve illustrates the gen-
erally low values of the sonic velocity over a wide range of vapor
27
-------
Constant
level tank
s
!
o
n
s!
o ;
If
O >
* I"
o
FIGURE 15
28
-------
VD
1C VELOCITY
f AT CAVITY
PRESSURE = -31.8 ft of \
Voter
40 50 60
Per Cent Air Concentration
70
80
90
100
Sonic velocity calculated using V =
- C)o
1/2
FIGURE 16
where P = absolute pressure
C = concentration of gas in the mixture by volume
P0 ~ density of liquid
STORM WATER DROP SHAFTS
Federal Water Quality Administration
SONIC VELOCITY vs AIR CONCENTRATION
SAINT ANTHONY FALLS HYDRAULIC LABORATORY
UNIVERSITY OF MINNESOTA
CSC CHECKE
0«T. 3-71
CSC APPROVED
I ,«,. 1 946492^53"
-------
concentrations. In addition, this sonic velocity is considerably
lower than the mean velocity in the cavitation region, so that the
flow is supersonic, and hence a shock front represents the transition
to subsonic flow in the lower part of the conduit. When the vapor re-
condenses in the shock front, the sonic velocity increases rapidly, so
that the flow downstream of the shock front is subsonic.
It is assumed that the mixture of vapor and water is homogeneous, that
the velocity of the vapor is the same as that of the water, and that
the temperature of the system remains constant. The energy balance,
then, between the free water surface (point l) and section 2 in the
cavitation zone just above the shock front must include the energy re-
quired to vaporize the water in the cavity region. The energy balance
between these two points can then be written as
v2 v2
-|- + ^ + g Z1 = -f- + h2 + g Z2 (2)
where ^ = (P^/PV) + \ and h2 = (P2/P2) + u2. Here V, and V2
are the velocities, h, and h? are the enthalpies, and Z.. and 2>0
axe the elevations at points 1 and 2, respectively; P.. and Pp are
the pressures and u, and u? are the internal energies at points 1
and 2, respectively; g is the acceleration due to gravity; P is
the density of water at point 1; and P~ is the density of the mix-
ture of water and water vapor at point 2. At point 2 the enthalpy
depends upon the enthalpy of both the water and the vapor. Let
x = mass of vapor per unit mass of mixture
and 1 - x = mass of water per unit mass of mixture
then
h0 = xh + (l - x)h = h + x(h - h ) (3)
^ V W W V W \-^/
but
h = + u
w p w
w
so
h2 = (-F
w
-------
Then with substitution for the enthalpies, Eq.. (2) can be written as
2 2
V P V P
-|-H--^ + gZ1+u1=-|- + -^ + gZ2-l-u2+ x(hy - hw) (5)
W W
The change in internal energy u? - u, is due to friction on the
boundary in the cavity region and to the friction, valves, orifice, and
other obstructions in the inlet pipe, which can be lumped together as
h... Then
where f is the effective Darcy friction factor for the cavitation
region, h. is the lumped head losses in the inlet conduit, D is
the conduit diameter, and Az is the net length of conduit above point
2 over which frictional loss takes place. In addition, the mass vapor
fraction can be expressed in terms of the volumetric concentration. If
C is the volume of vapor per unit volume of water plus vapor, then by
definition
PC PC
V V
- c) + PC P(I - c)
where P is the density of the water vapor. Further,
where ft is the water discharge before cavitation and A is the
cross-sectional area of the vertical conduit. The pressure at point
2 is the cavitation pressure that is,
P2 = Pc (9)
Wow substitution of Eqs. (6), (?), (8), and (9) into Eq. (5), and
noting that Y-j^ = 0, P-j^ = 0, and VQ = Q/L, results in
-------
where h and h now are in BTU/lb (in which units they can be ob-
tained from steam tables) and J is the mechanical equivalent of the
heat exchange. The vapor concentration in the cavity section can be
computed from Eq. (10).
Utilizing the momentum equation and the equation of continuity through
the shock front, the pressure downstream of the front can be written as
P P V
o « ** r*
£ C_ O 0 fll}
y ~ y g 1 - C
Then the energy balance between section 3 downstream of the shock front
and the pipe outlet can be written as
U U / \J \ , T _ * " U
v + ft VL _ c) + ** - D 2ff
so that the elevation of the shock front referred to the pipe outlet
becomes
Pc 7p2 c
L = T + * 2(l - G) (13)
(£-?*-- 1)
kD 2g 1;
In Eq. (13) all the terms are known, since P /y = -31.75 ft or the
vapor pressure of the water, V = Q/A where Q is the water dis-
charge and A is the cross-sectional area of the conduit whose diam-
eter is D, C is computed from Eq. (10), and f is the friction
factor for the conduit.
The calculated elevation of the shock front in terms of the discharge
and the experimental geometry has been plotted in Fig. 17. In these
computations it was assumed that the friction factor for the flow of
the water-vapor mixture in the cavitation zone was negligible for all
discharges below that which corresponded to the minimum value of the
shock front elevation. For discharges above this point the friction
factor was linearly increased to that corresponding to the TnayiTtnini dis-
charge. The experimental data for the shock front elevation in terms
of discharge are also plotted in Fig. 17 for comparison. The experi-
ments indicated that above the Ttiim'TiniTn the elevation of the shock front
tended to increase until for a certain discharge it would presumably
reach the conduit inlet and the entire system would run full. This is
also indicated by Eq. (l3)> which gives the discharge for which the
shock front has reached the top of the pipe. Any further increase in
32
-------
VJJ
0.5
1.0
1.5 2.0 2.5
Discharge, cfs
3.0
3.5
4.0
FIGURE 17
STORM WATER DROP SHAFTS
Federal Water Quality Administration
COMPUTED AND OBSERVED SHOCKFRONT
ELEVATIONS
SAINT ANTHONY FALLS HYDRAULIC LABORATORY
UNIVERSITY OF MINNESOTA
CSC
gCKKO CSC Aff
T. 5-7' INO.
194B492-38
-------
discharge requires a corresponding increase in total head. Figure 1?
shows that with the proper choice of constants in the equations, reason-
able agreement can be obtained between experimental and computed results.
In Pig. 18 the experimental values of the vapor concentration in the
cavitating region have been plotted in terms of the discharge for com-
parison with the computed relationship. Here the experimental values
of the concentration follow the same trend as is indicated by the theo-
retical computations and show that as the discharge increases toward the
the vapor concentration decreases and approaches zero.
The experimental results and the analysis based upon these results show
that as the discharge increases, the elevation of the shock front also
increases until the conduit runs full. The relatively short (42 ft)
hydraulic model upon which these experiments were made was not compar-
able in length to the vertical drop shafts which would represent the
prototype. Therefore, utilizing the relationship developed above, the
results were extrapolated to conduits of the same size and roughness,
but of greatly increased length such as is found in practice. Figure
19 shows the theoretical elevation of the shock front for various dis-
charges and conduit lengths for a constant net head. These computations
show that the elevation of the shock front rises very rapidly for small
increases in discharge as full flow is approached. This suggests that
the shock front may lose its identity in an almost instantaneous con-
densation of the water vapor to solid water throughout the remaining
pipe length as the maximm discharge is approached. In addition, the
curves for different conduit lengths tend to separate as the minimum
shock front elevation is approached. All the curves tend toward the
elevation corresponding to that of a water column for zero discharge.
34
-------
VJ1
1.0
0.8
0.6
i 0.4
u
5
S
8-
>0.2
Computed curve
(Eq. 10)
(Wafer Temp » 80°F)
0.5 1.0 1.5 2.0 2.5
Discharge, cfs
3.0
3.5
4.0
FIGURE 18
STORM WATER DROP SHAFTS
Federal Water Quality Administration
COMPUTED AND OBSERVED VAPOR
' CONCENTRATIONS ABOVE SHOCKFRONT
SAINT ANTHONY FALLS HYDRAULIC LABORATORY
UNIVERSITY OF MINNESOTA
PPV
. 5-71
194B492-39
-------
ON
NOTE:
1) Calculations based on Eqs. (10) and (13)
2) Pipe diameter: 5 inches
3) Water temperature: 80°F
FIGURE 19
STORM WATER DROP SHAFTS
Federal Water Quality Administration
rHEORETICAL CURVES showing SHOCKFRONT
ELEVATION for VARYING PIPE LENGTHS
SAINT ANTHONY FALLS HYDRAULIC LABORATORY
UNIVEMITY OF MINNESOTA
PPV
.194M92-40
-------
SECTION VII
HEAD DISCHARGE RATING CURVES
Although the experimental studies dealt primarily with the cavitation
regime for flow in long vertical culverts, it is appropriate to consider
this regime in relation to the complete head-discharge rating curve
for the system. The nature of the flow, including the existence of
cavitation flow, depends upon the interaction between the head, the
discharge, and the conduit length, diameter, roughness, and inlet
geometry. In a particular drop shaft system a number of flow regimes
can be visualized. When the discharge is sufficiently large, the con-
duit may flow full without cavitation. If the conduit is very long,
the flow may cavitate in the upper regions. If there is a valve in the
inlet system and the conduit is long enough, it can be made to cavitate
for relatively low discharges. For an open system that is, one without
a control valve the system may act as an orifice or weir in which air
is insufflated into the conduit through the upper pool. The head-dis-
charge curves can be plotted on a single chart so that the several flow
regimes can be delineated (Refs. 7»8).
Transitional Flow
Transitional flow is restricted to the so-called open systems: vertical
conduits which are open to the atmosphere at the inlet and have no inter-
vening flow control device such as a valve. In such a system the ver-
tical conduit is connected directly to the bottom of the supply channel
or sewer. Initially, for very low discharges, the water will trickle
over the edge of the conduit like flow over a weir. As the discharge
increases, the jets over the edge will become large enough to meet in
the pipe and effectively seal the inlet so that the flow approximates
that through a horizontal orifice. Below the inlet, however, the flow
will tend to fill the conduit with water or at least a dense spray. As
more of the pipe is filled, the pressure in the region below the inlet
will decrease below the atmospheric pressure in accordance with the
Bernoulli principle. This pressure difference will increase and ul-
timately break the surface and permit air to be insufflated through
the inlet and into the conduit. As the discharge increases, the head
over the inlet will increase and the pressure in the region below the
inlet will tend to decrease still more, since there will be a succes-
sively greater opportunity for the downflowing water to fill the con-
duit. This situation can be described by the equation
5/2
where Q/D ' is a semi-dimensionless discharge since the constant
1/2
(g) ' has been transposed, H is the head over the inlet, D is
the conduit diameter, and P2/y is the pressure head just below the
inlet. For low values of H/D, Pp/y approaches zero and the flow
37
-------
approaches that through an orifice. As the discharge increases, H
increases and Pp/y decreases until air is insufflated. The mi m'mum
value of Pp/y is P /y = -31.75 ft when the flow in the conduit
cavitates. TTor a given head the pressure head Pp/y also depends
upon the geometry of the inlet and the flow pattern in the supply
channel. For purposes of illustration, the head-discharge curve for
a weir in the form
-^=
D5/o - 10-27 (S) (15)
has been plotted in Figs. 20, 21, and 22 and labeled "weir flow."
A wide band of uncertainty has been sketched on either side of this
curve in the region where the head is positive. It is recognized that
the flow in this transitional region is not a weir flow, but the pres-
sures given by Eq. (14) are typical of those that might be expected for
such heads and discharges.
Cavitation Flow
In the experiments described earlier it was found that when the flow in
the upper part of the conduit was cavitating, the pressure was constant
throughout the cavitating region at a value of P0/y = P /y = -31.75 ft.
< C
In those experiments, however, the flow took place in a closed system
i.e., one in which the total head H_ was constant and the flow was
controlled by a valve which introduced the appropriate headless into the
system. The valve permitted the net head to be negative so that cavi-
tating flow could be generated. In this case the net head H is the
total head above the top of the vertical conduit minus the headloss in
the valve and associated piping, or
H = H.J, - hL (16)
in which h. may be larger than H_, giving rise to negative net
heads. Experiments showed that as the discharge increased, the ele-
vation of the shock front also increased and tended to fill the pipe.
Assuming that just at the instant when the pipe ran full the pressure
head was still approximately -31.75 ft, the head-discharge relation
could be described by Eq_. (14) with Pp/y replaced by PVy» "the
cavitation pressure. Then
. 6.3(| + ) (17)
It will be noted that in this case the head-discharge relationship
depends upon the absolute value of D, and a separate curve will be
developed for each conduit diameter. To show the effect of conduit
38
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-80
FLOW REGIME EQUATIONS
1. Weir flow:
2. Cavitation flow:
3. Full flow:
,3/2
\i * f-£.
t = 0.01 (assumed)
FIGURE 20
STORM WATER DROP SHAFTS
Federal Wafer Quality Administration
DISCHARGE RATING CURVES - Dia. ? 5.0 in
SAINT ANTHONY FALLS HYDRAULIC LABORATORY
UNIVERSITY OP MINNESOTA
PPV
«T. 5-71
MO. 194B492-35
-------
-80
572
FLOW REGIME EQUATIONS
1 . Weir flow:
2. Cavitation flow:
10.27 |
P M
6.3 1 - -^- 1
1/2
DT
f = 0.01 (assumed)
FIGURE 21
STORM WATER DROP SHAFTS
Federal Water Quality Administration
DISCHARGE RATING CURVES - Dia. » 1.0 ft
SAINT ANTHONY FALLS HYDRAULIC LABORATORY
UNIVKMSITV OF MINNESOTA
,. PPV
T71
_no. 194B492-3A
-------
FLOW REGIME EQUATIONS
1 . Weir flow:
2. CavitaHon flow:
3. Full flow:
Q = 10>27
\3/2
«w
,V2
T V2
/S + ^V
: 6.3 f_2 2_|
f = 0.01 (assumed)
FIGURE 22
STORM WATER DROP SHAFTS
Federal Water Quality Administration
DISCHARGE RATING CURVES - Dia. = 2.0 ft
SAINT ANTHONY FALLS HYDRAULIC LABORATORY
UNIVERSITY OP MINNESOTA
D ICH.O
MPhicI DAT.
KED PPV j APPROVED
»cAL.EGnphic| DATE 5-71 »o. 194B492-37
-------
diameter on the rating curves, computations were made for a 5 in. con-
duit such as was used in the experimental program (Fig. 20) , a 1 f t
diameter drop shaft (Fig. 2l) and a 2 ft diameter drop shaft (Fig. 22).
These individual curves have been labeled "cavitation flow" on the
graphs. It is apparent from Eq. (17) and the respective plots that the
larger the conduit, the larger is the relative head for cavitation flow.
Further, as the relative discharge Q/D ' increases, the relative
head, H/D, required for cavitation also increases. That portion of
the curve lying below the abscissa H/D = 0 applies to a closed system,
while the portion above the curve applies to either system.
Full Flow
As the discharge for cavitating flow increases, the elevation of the
shock front also increases until ultimately the conduit is running full.
The discharge for which this occurs will depend upon the length of the
conduit as well as on its diameter and roughness. Curves can be plotted
to show the head-discharge relationship for various pipe lengths. Ap-
plication of the Bernoulli equation between the inlet and the outlet
results in
(18)
where in addition to the terms previously defined, L is the length
of the conduit and f' is the Darcy friction factor Tor the conduit.
It is apparent from Eq. (18) that a separate head-discharge curve will
result for each L /D value. A set of such curves for typical L /D
ratios from zero to 1000 has been plotted on each of Figs. 20, 21, and
22. On the graphs these lines intersect the curves for transitional
flow and cavitation flow and thus show how the several flow transitions
take place.
Flow Behavior Patterns
The curves in Figs. 20, 21, and 22 show the behavior patterns for three
conduits of different diameters. The graphs differ only in the position
of the cavitation flow curve, which shifts along with the conduit diam-
eter. Figure 20 has been drawn for the 5 in. experimental conduit.
This was a closed system, since a valve was used to initiate cavitation
for relatively low discharges. The region covered by the experiments
is shown by the experimental points plotted at the lower end of the
cavitation flow curve.
In a closed or valve-controlled system such as that used in the experi-
mental program, the path followed by the head-discharge relationship can
be traced by considering the various curves. Assume that initially the
discharge is zero; then the head is zero and the point starts at the
42
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origin. If the valve is initially open a small amount, the point will
move along the so-called "weir flow" curve until the valve takes con-
trol and no more air is insufflated into the conduit. At this point
cavitation will occur and the head-discharge point will drop to the
cavitation flow curve with a significantly negative net relative head.
As the valve is opened to increase the discharge, the point follows
the cavitation flow curve until it intersects the full flow curve having
the appropriate length-diameter ratio, L /D. At this intersection the
point follows the full flow curve until tne maximum discharge is reached.
If, as for short conduits, the full flow curve does not intersect the
cavitation flow curve, the head-diameter ratio H/D will fall only to
the full flow curve and the conduit will Immediately run full without
cavitating. For very long conduits the point may follow the cavitation
flow curve until H/D becomes positive before the conduit flows full.
In an open system, since h^ is negligible, the net head will never be-
come negative. In this case the head-discharge locus follows along the
transitional curve labeled "weir flow" until it intersects the appropri-
ate curve for full flow. It then moves up the full flow curve to the
TnaTJTrimn value. However, if the conduit is very long and the head avail-
able is adequate, the head-discharge locus moves along the weir flow
curve until it intersects the cavitation flow curve, along which it then
moves until it reaches the appropriate full flow curve.
It appears that a variety of flow patterns are available, depending upon
the geometry of the system. This variety provides the designer with
several possibilities for developing a system within the constraints
imposed by external conditions.
Better curves can be drawn with respect to a particular installation
so that the head can be determined more accurately, but the graphs in
these figures indicate the nature of flow in long vertical conduits and
can be used to describe the flow qualitatively.
43
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SECTION VIII
ACIOTOWLEDGMENTS
This research project was conducted "by the St. Anthony Palls Hydraulic
Laboratory, University of Minnesota, Prof. Edward Silberman, director.
Prof. Alvin G. Anderson, principal investigator, directed the project
and also wrote the report. Mr. P. P. Yaidyaraman, graduate research
assistant, performed the experiments with the assistance of Mr. Chung
Sang Chu, research assistant. The apparatus and some of the instru-
mentation were constructed in the laboratory shops, of which Mr. Prank
R. Dressel is the superintendent. Mrs. Shirley Kii prepared the
manuscript.
The project was sponsored by the Water Quality Office of the Environ-
mental Protection Agency, and Mr. Clarence C. Oster was Project
Officer.
45
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SECTION IX
REFERENCES
1. Lamb, 0. P. and Killen, J. M. , An Electrical Method of Measuring
Air Concentration in Flowing Air-Water Mixtures, Technical Paper
No. 2-B, St. Anthony Falls Hydraulic Laboratory, University of
Minnesota, March 1950.
2. Neal, L. G. and Bankoff , S. G. , "A High Resolution Resistivity
Probe for Determination of Local Yoid Properties in Gas-Liquid
Plow," AIChE Journal. July 1963.
3. Griebe, R. W. ; Winter, E. R. P.; and Schoenhals, R. J. , Two-
Phase Plow in Vibrating Discharge Lines, Final Report, Part III,
School of Mechanical Engineering, Purdue University, Lafayette,
Indiana, July 1968.
4. Eddington, R. B. , Investigation of Supersonic Shock Phenomena in
a Two-Phase (Liquid-Gas) Tunnel , Technical Paper No. 32-1096,
Jet Propulsion Laboratory, Pasadena, California, March 196?
5. Wallis, G. B. , One-Dimensional Two-Phase Flow, McGraw-Hill Book
Company, New York,
6. Schiebe, F. R. ; Vetzel, J. M. ; and Foerster, K. E. , Studies of
Flow Characteristics of a Compressible Bubbly Mixture about
Supercavitating Bodies in a Converging-Diverging Nozzle,
Technical Paper No. 48-B, St. Anthony Falls Hydraulic Labo-
ratory, University of Minnesota, April 1964.
7. Blaisdell, F. W. , Hydraulics of Closed Conduit Spillways - Fart I -
Theory and Its Applications, Technical Paper No. 12-B, St. Anthony
Falls Hydraulic Laboratory, University of Minnesota, February 1958.
8. Straub, L. G. ; Anderson, A. G. ; and Bowers, C. E. , Effect of Inlet
Design on Capacity of Culverts on Steep Slopes, Project Report
No. 37, St. Anthony Falls Hydraulic Laboratory, University of
Minnesota, April 1954-
47
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SECTION X
GLOSSARY OF SYMBOLS
2
A = Area of pipe, ft
C = Yapor concentration by volume
D = Diameter of pipe, ft
f = Darcy friction factor for the cavitating portion of the pipe
f' = Darcy friction factor for the pipe
Q
g = Acceleration due to gravity, ft/sec
H = Head at inlet to pipe, ft
h = Enthalpy, BTU/lb
h_ = Headless, ft
J = Conversion factor, 778 ft-lb/BTU
L = Distance to shock front from bottom of shaft, ft
L = Overall length of pipe, ft
P = Pressure, Ibs/ft
P/y = Pressure head, ft of water
P/y = Cavitation pressure, ft of water
Q, = Discharge, cfs
u = Internal energy, BTU/lb
V = Velocity, ft/sec
V = Bulk velocity = Q./A, ft/sec
O v»
Y = Sonic velocity, ft/sec
s
x = Yapor quality
Z = Elevation above datum, ft
P = Density, slugs/ft*
y = Specific weight, lbs/ft*
Subscripts;
a = air v = vapor w = water
49
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1
Accession Number
w
5
« Subject Field & Group
08A
SELECTED WATER RESOURCES ABSTRACTS
INPUT TRANSACTION FORM
Organization
Hydraulic Lab.
Title
HYDRAULICS OF LONG VERTICAL CONDUITS AND ASSOCIATED
CAVITATION
i Q Authors)
Anderson, A.
Vaidyaraman,
(J.
P. P.
16
21
Project Designation
EPA, VQP Contract No.
Project Number 11034
Note
14-12-861
FLU
Chu, C. S.
22
Citation
23
Descriptors (Starred First)
*Drains, *Sewers, *Cavitation, Air Entrainment, Closed Conduits
25
Identifiers (Starred First)
*Dropshafts, *Cavitation Flow, Pressure Conduits
27
Abstract
Experimental studies have been undertaken to examine the flow in long vertical
conduits with particular reference to the design of storm water drop shafts. A dis-
tinguishing characteristic of such flow is the cavitation regime which may exist in
the head-discharge relationship. The cavitation regime will develop when the conduit
is sufficiently long and the head sufficiently large. It can also be generated at a
lower head if a control valve is installed in the supply line so that the net head
can be negative. The cavitation region consists of a rather finely divided mixture
of water and water vapor at a constant cavitation pressure of about -32.0 ft of water
throughout the region and for all discharges. The concentration of vapor, while
relatively constant throughout the cavitation region, decreases with increasing dis-
charge. The location of the shock front is also a function of the discharge.
If a small amount of air is introduced into the system, the cavitation region is
eliminated, the pressure gradient is more uniform, and the flow consists of a white
mixture of air and water.
The study also showed that the cavitation region is only one phase of the total
head-discharge regime and that its existence depends upon the design of the structure.
Abstra
Mvin G. Anderson
Institution
Ejt. Anthony Falls Bydr. Lab., TT. of Minn., Minneapolis
WR;102 (REV. JULY 1969)
WRS1C
SEND, WITH COPY OF DOCUMENT, TOl WATER RESOURCES SCIENTIFIC INFORMATION CENTER
~- U.S. DEPARTMENT OF THE INTERIOR
WASHINGTON, D. C. 20240
* OPO! 1970389-930
51
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Continued from inside front cover....
11022 08/67
11023 09/67
11020 12/67
11023 05/68
11031 08/68
11030 DNS 01/69
11020 DIH 06/69
11020 DBS 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 DOK 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.
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