------- wind in the stable layer and tm is the time required to eliminate the inversion from h, the physical height of the stack to hi (Eq. 5.3). tn, is dependent upon both the strength of the inversion and the rate of heating at the surface. Pooler (1965) has derived an expression for esti- mating this time: 2 ; (5.5) time required for the mixing layer to develop from the top of the stack to the top of the plume, sec PB = ambient air density, g m~* cp = specific heat of air at constant pressure, cal g-1 °K-' R = net rate of sensible heating of an air column by solar radiation, cal m~2 sec"1 SQ — = vertical potential temperature gradient, ST °K m"1 ~——\- T (the adiabatic lapse rate) Sz h, = height of base of the inversion sufficient to be above the plume, m h = physical height of the stack, m Note that h( —h is the thickness of the layer to be heated and (—^—L J js the average height of the layer. Although R depends on season, and cloud cover and varies continuously with time, Pooler has used a value of 67 cal m"2 sec"1 as an average for fumigation. Hewson (1945) also suggested a method of esti- mating the time required to eliminate an inversion to a height z by use of an equation of Taylor's (1915, p. 8): (5.6) t = time required to eliminate the inver- sion to height z, sec z = height to which the inversion has been eliminated, m K = eddy diffusivity for heat, m* sec"1 Rewriting to compare with Eq. (5.5), h,' — h' 4 K (5.7) Hewson (1945) has suggested a value of 3 mz sec"1 for K. PLUME TRAPPING Plume trapping occurs when the plume is trapped between the ground surface and a stable layer aloft. Bierly and Hewson (1962) have sug- gested the use of an equation that accounts for the multiple eddy reflections from both the ground and the stable layer: X (x,0,z;H) = -fexp - z + H — 2 NL z — H + 2 NL where L is the height of the stable layer and J •= 3 or 4 is sufficient to include the important reflec- tions. A good approximation of this lengthy equa- tion can be made by assuming no effect of the stable layer until a, = 0.47 L (see Chapter 3). It is as- sumed that at this distance, XL, the stable layer begins to affect the vertical distribution so that at the downwind distance, 2 XL, uniform vertical mix- ing has taken place and the following equation can be used: Q — T „ 6XP ' — ffy L U (5.9) For distances between XL and 2 XL the best approxi- mation to the ground-level centerline concentration is that read from a straight line drawn between the concentrations for points XL and 2 XL on a log-log plot of ground-level centerline concentration as a function of distance. CONCENTRATIONS AT GROUND LEVEL COMPARED TO CONCENTRATIONS AT THE LEVEL OF EFFECTIVE STACK HEIGHT FROM ELEVATED CONTINUOUS SOURCES There are several interesting relationships be- tween ground-level concentrations and concentra- tions at the level of the plume centerline. One of ATMOSPHERIC DISPERSION ESTIMATES

------- these is at the distance of maximum concentration at the ground. As a rough approximation the maxi- mum ground-level concentration occurs at the dis- tance where a, = ~~F ¥L. This approximation is much better for unstable conditions than for stable conditions. With this approximation, the ratio of concentration at plume centerline to that at the ground is: . O.H) --HIT] xU,0,0) exp — H y- [1.0 + exp —0.5(2 V2)=] exp —0.5 (V2)- 4- (1.0 + 0.0182) 0.368 1.38 This calculation indicates that at the distance of maximum ground-level concentration the concen- tration at plume centerline is greater by about one- third. It is also of interest to determine the relation- ship between a, and H such that the concentration at ground-level at a given distance from the source is the same as the concentration at plume level. This condition should occur where: H The value H/w, = 1.10 satisfies this expression, which can be written as ot = 0.91 H (see problem 10). TOTAL DOSAGE FROM A FINITE RELEASE The total dosage, which is the integration of concentration over the time of passage of a plume or puff, can be obtained from: (5.10) where DT = total dosage, g sec m 3 and QT = total release, g The a's should be representative of the time period over which the release takes place, and care should be taken to consider the x-axis along the trajectory or path of the plume or puff travel. Large errors can easily occur if the path is not known accurately. The estimate of this path is usually in- creasingly difficult with shorter release times. DT can also be given in curie sec m~s if QT is in curies. CROSSWIND-INTEGRATED CONCENTRATION The ground-level crosswind-integrated concen- tration is often of interest. For a continuous ele- vated source this concentration is determined from Eq. (3.2) integrated with respect to y from ~x to + v (Gifford 1960a) giving: Xcwi cr. U exp I ^ In diffusion experiments the ground-level cross- wind-integrated concentration is often determined at particular downwind distances from a crosswind line or arc of sampling measurements made at this distance. When the source strength, Q, and average wind speed, u, are known, a. can be estimated in- directly even though no measurements were made in the vertical. If any of the tracer is lost through reaction or deposition, the resulting a, from such estimates will not represent the vertical dispersion (see problem 18). ESTIMATION OF CONCENTRATIONS FOR SAMPLING TIMES LONGER THAN A FEW MINUTES Concentrations directly downwind from a source decrease with sampling time mainly because of a larger ------- Table 5-1 VARIATION OF CALCULATED CONCENTRATION WITH SAMPLING TIME Ratio of Calculated Concentration 2 Q Sampling Time 3 minutes 15 minutes 1 hour 3 hours 24 hours to 3-minute Concentration 1.00 0.82 0.61 0.51 0.36 This table indicates a power relation with time: x at t~°-17. Note that these estimates were based ::pon published dispersion coefficients rather than upon sampling results. Information in the refer- ences cited indicates that effects of sampling time are exceedingly complex. If it is necessary to esti- mate concentrations from a single source for the time intervals greater than a few minutes, the best estimate apparently can be obtained from: Xe = X* ** (5.12) where XB is the desired concentration estimate for the sampling time, t6; x* is the concentration esti- mate for the shorter sampling time, tk, (probably about 10 minutes); and p should be between 0.17 and 0.2. Eq. (5.12) probably would be applied most appropriately to sampling times less than 2 hours (see problem 19). ESTIMATION OF SEASONAL OR ANNUAL AVERAGE CONCENTRATIONS AT A RECEPTOR FROM A SINGLE POLLUTANT SOURCE For a source that emits at a constant rate from hour to hour and day to day, estimates of seasonal or annual average concentrations can be made for any distance in any direction if stability wind "rose" data are available for the period under study. A wind rose gives the frequency of occurrence for each wind direction (usually to 16 points) and wind speed class (9 classes in standard Weather Bureau use) for the period under consideration (from 1 month to 10 years). A stability wind rose gives the same type of information for each stability class. If the wind directions are taken to 16 points and it is assumed that the wind directions within each sector are distributed randomly over a period of a month or a season, it can further be assumed that the effluent is uniformly distributed in the hori- zontal within the sector (Holland, 1953, p. 540). The appropriate equation for average concentration is then either: exp f_J_fJLVl [ 2 U J J 2.03Q a, ux exp I ( H Vl T\~) J (5.13) or 2.55 Q (5.14) depending upon whether a stable layer aloft is af- fecting the distribution. The estimation of x for a particular direction and downwind distance can be accomplished by choosing a representative wind speed for each speed class and solving the appropriate equation (5.13 or 5.14) for all wind speed classes and stabilities. Note that a SSW wind affects a receptor to the NNE of a source. One obtains the average concentration for a given direction and distance by summing all the concentrations and weighting each one accord- ing to its frequency for the particular stability and wind speed class. If desired, a different effective height of emission can be used for various wind speeds. The average concentration can be expressed by: , , 2 Q f (e,s,N) (x,G) N 16 exp (5.15) where f (e, S, N) is the frequency during the period of interest that the wind is from the direc- tion 6, for the stability condition, S, and wind speed class N. «r,s is the vertical dispersion parameter evaluated at the distance x for the stability condition S. UN is the representative wind speed for class N. Hu is the effective height of release for the wind speed UN. Where stability wind rose information cannot be obtained, a first-order approximation may be made of seasonal or annual average concentrations by using the appropriate wind rose in the same man- ner, and assuming the neutral stability class, D, only. METEOROLOGICAL CONDITIONS ASSOCIATED WITH MAXIMUM GROUND-LEVEL CONCENTRATIONS concentra- 1. For ground-level sources tions occur with stable conditions. 38 ATMOSPHERIC DISPERSION ESTIMATES------- 2. For elevated sources maximum "instantaneous" concentrations occur with unstable conditions when portions of the plume that have undergone little dispersion are brought to the ground. These occur close to the point of emission (on the order of 1 to 3 stack heights). These con- centrations are usually of little general interest because of their very short duration; they can- no/ be estimated from the material presented in this workbook. 3. For elevated sources mp*i""im concentrations for time periods of a few minutes occur with unstable conditions; although the concentra- tions fluctuate considerably under these condi- tions, the concentrations averaged over a few minutes are still high compared to those found under other conditions. The distance of this maximum concentration occurs near the stack (from 1 to 5 stack heights downwind) and the concentration drops off rapidly downwind with increasing distance. 4. For elevated sources maximum concentrations for time periods of about half an hour can occur with fumigation conditions when an unstable layer increases vertically to mix downward a plume previously discharged within a stable layer. With small AH, the fumigation can occur close to the source but will be of relatively short duration. For large AH, the fumigation will occur some distance from the stack (perhaps 30 to 40 km), but can persist for a longer time interval. Concentrations considerably lower than those associated with fumigations, but of sig- nificance can occur with neutral or unstable conditions when the dispersion upward is se- verely limited by the existence of a more stable layer above the plume, for example, an inversion. 5. Under stable conditions the p™*imtim concen- trations at ground-level from elevated sources are less than those occurring under unstable conditions and occur at greater distances from the source. However, the difference between maximum ground-level concentrations for stable and unstable conditions is only a factor of 2 for effective heights of 25 meters and a factor of 5 for H of 75 m. Because the maximum occurs at greater distances, concentrations that are below the maximum but still significant can occur over large areas. This becomes increas- ingly significant if emissions are coming from more than one source. CONCENTRATIONS AT A RECEPTOR POINT FROM SEVERAL SOURCES Sometimes, especially for multiple sources, it is convenient to consider the receptor as being at the origin of the diffusion coordinate system. The source-receptor geometry can then be worked out merely by drawing or visualizing an x-axis oriented upwind from the receptor and determining the crosswind distances of each source in relation to this x-axis. As pointed out by Gifford (1959), the con- centration at (0, 0, 0) from a source at (x, y, H) on a coordinate system with the x-axis oriented up- wind is the same as the concentration at (x, y, 0) from a source at (0, 0, H) on a coordniate system with the x-axis downwind (Figure 5-2). The total concentration is then given by summing the indi- vidual contributions from each source (see problem 20). SOURCE (•.r.H) UPWIND RECEPTOR (0,0,0) DOWNWIND d.y.O) Figure 5-2. Comparison of source-oriented and receptor- oriented coordinate systems. It is often difficult to determine the atmos- pheric conditions of wind direction, wind speed, and stability that will result in the ma^mnm combined concentrations from two or more sources; drawing isopleths of concentration for various wind speeds and stabilities and orienting these according to wind direction is one approach. AREA SOURCES In dealing with diffusion of air pollutants in areas having large numbers of sources, e.g., as in urban areas, there may be too many sources of most atmospheric contaminants to consider each source Special Topics 39------- individually. Often an approximation can be made by combining all of the emissions in a given area and treating this area as a source having an initial horizontal standard deviation, aro. A virtual dis- tance, x7, can then be found that will give this standard deviation. This is just the distance that will yield the appropriate value for ------- When estimating concentrations from finite line sources, one must account for "edge effects" caused by the end of the line source. These effects will of course extend to greater cross-wind distances as the distance from the source increases. For concen- trations from a finite line source oriented cross- wind, define the x-axis in the direction of the mean wind and passing through the receptor of interest. The limits of the line source can be defined as ex- tending from y, to y, where y, is less than y2. The equation for concentration (from Button's (1932) equation (11), p. 154), is: X (x,0,0;H) = (5.20) »y "j The value of the integral can be determined from tabulations given in most statistical tables (for ex- ample, see Burrington (1953), pp. 273-276; also see problem 24). INSTANTANEOUS SOURCES Thus far we have considered only sources that were emitting continuously or for time periods equal to or greater than the travel times from the source to the point of interest. Cases of instantaneous re- lease, as from an explosion, or short-term releases on the order of seconds, are often of practical con- cern. To determine concentrations at any position downwind, one must consider the time interval after the time of release and diffusion in the down- wind direction as well as lateral and vertical diffu- sion. Of considerable importance, but very difficult, is the determination of the path or trajectory of the "puff." This is most important if concentra- tions are to be determined at specific points. Deter- mining the trajectory is of less importance if knowl- edge of the magnitude of the concentrations for particular downwind distances or travel times is required without the need to know exactly at what points these concentrations occur. Rewriting Sut- ton's (1932) equation (13), p. 155, results in an equation that may be used for estimates of concen- tration downwind from a release from height, H: (x,y,0;H) = (/ir)J/- o, a, a, exp f - -J- I 2 -l-Hi-)1] (The numerical value of (2»)8/I is 15.75.) The symbols have the usual meaning, with the important exceptions that QT represents the total mass of the release and the a's are not those eval- uated with respect to the dispersion of a continuous source at a fixed point in space. In Eq. (5.21) the o's refer to dispersion sta- tistics following the motion of the expanding puff. The cz is the standard deviation of the concentra- tion distribution in the puff in the downwind direc- tion, and t is the time after release. Note that there is no dilution in the downwind direction by wind speed. The speed of the wind mainly serves to give the downwind position of the center of the puff, as shown by examination of the exponential involving a,. Wind speed may influence the dis- persion indirectly because the dispersion parameters10 4 1.3 a* 15 3.8 0.75 "J 300 120 35 °t 220 50 7 REFERENCES Bierly, E. W., and E. W. Hewson, 1962: Some re- strictive meteorological conditions to be con- sidered in the design of stacks. J. Appl. Mete- orol., 1, 3, 383-390. Burington, R. S., 1953: Handbook of Mathematical Tables and Formulas. Sandusky, Ohio, Hand- book Publishers, 296 pp. Cramer, H. E., 1959: Engineering estimates of atmospheric dispersal capacity. Amer. Ind. Hyg. Assoc. J., 20, 3, 183-189. Special Topics 41 JS9-60I O - 69 - 4 ------- Gifford, F. A., 1959: Computation of pollution from several sources. Int. J. Air Poll., 2, 109- 110. Gifford, F. A., 1960a: Atmospheric dispersion cal- culations using the generalized Gaussian plume model. Nuclear Safety, 2, 2, 56-59, 67-68. Gifford, F. A., 1960b: Peak to average concentra- tion ratios according to a fluctuating plume dis- persion model. Int. J. Air Poll., 3, 4, 253-260. Hewson, E. W., and G. C. Gill, 1944: Meteorolog- ical investigations in Columbia River Valley near Trail, B. C., pp 23-228 in Report submitted to the Trail Smelter Arbitral Tribunal by R. S. Dean and R. E. Swain, Bur. of Mines Bull 453, Washington, Govt. Print. Off., 304 pp. Hewson, E. W., 1945: The meteorological control of atmospheric pollution by heavy industry. Quart. J. R. Meteorol. Soc., 71, 266-282. Hewson, E. W., 1955: Stack heights required to minimize ground concentrations. Trans. ASME 77,1163-1172. Holland, J. Z., 1953: A meteorological survey of the Oak Ridge area, p. 540. Atomic Energy Comm., Report ORO-99, Washington, D. C., 584 pp. Nonhebel, G., 1960: Recommendations on heights for new industrial chimneys. J. Inst. Fuel, 33, 479-513. Pooler, F., 1965: Potential dispersion of plumes from large power plants. PHS Publ. No. 999- AP-16, 1965. 13 pp. Singer, I. A., 1961: The relation between peak and mean concentrations. J. Air Poll. Cont. Assoc., 11, 336-341. Singer, I. A., K. Imai, and R. G. Del Campos, 1963: Peak to mean pollutant concentration ratios for various terrain and vegetation cover. J. Air Poll. Cont. Assoc., 73, 40-42. Slade, D. H., 1965: Dispersion estimates from pol- lutant releases of a few seconds to 8 hours in duration. Unpublished Weather Bureau Report. Aug. 1965. Stewart, N. G., H. J. Gale, and R. N. Crooks, 1958: The atmospheric diffusion of gases discharged from the chimney of the Harwell Reactor BEPO. Int. J. Air Poll., 1, 87-102. Sutton, O. G., 1932: A theory of eddy diffusion in the atmosphere. Proc. Roy. Soc. London, A, 135, 143-165. Taylor, G. I., 1915: Eddy motion in the atmos- phere. Phil. Trans. Roy. Soc., A, 215, 1-26. 42 ATMOSPHERIC DISPERSION ESTIMATES------- Chapter 6 —RELATION TO OTHER DIFFUSION7 EQUATIONS Most other widely used diffusion equations are variant forms of the ones presented here. With re- spect to ground-level concentrations from an ele- vated source (Eq. 3.2): x U,y,0;H) Q v ------- Chapter 7 —EXAMPLE PROBLEMS The following 26 example problems and their solutions illustrate the application of most of the techniques and equations presented in this work- book. PROBLEM 1: It is estimated that a burning .dump emits 3 g sec"1 of oxides of nitrogen. -What is the concentration of oxides of nitrogen, averaged over approximately 10 minutes, from this source directly downwind at a distance of 3 km on an overcast night with wind speed of 7 m sec"1? Assume this dump to be a point ground-level source with no effective rise. SOLUTION: Overcast conditions with a wind speed of 7 m sec"1 indicate that stability class D is most applicable (Statement, bottom of Table 3-1). For x = 3 km and stability D, a, = 190 m from Figure 3-2 and ------- level concentration occur and what is this con- centration on an overcast day with wind speed 4 m sec"1? SOLUTION: On an overcast day the stability class would be D. From Figure 3-9 for D sta- bility and H of 150 m, the distance to the point of m«*'T"»™ ground-level concentration is 5.6 km, and the man'mum xu/Q is 3.0 x 10—. 3.0 x KT* x 151 — 1.1 x 10-* g m- PROBLEM 6: For the conditions given in prob- lem 4, draw a graph of ground-level centerline sulfur dioxide concentration with distance from 100 meters to 100 km. Use log-log graph paper. SOLUTION: The frontal inversion limits the mix- ing to L — 1500 meters. The distance at which4 4 4 4 4 4 4.5 u, m seer1 4.5 4.5 4.5 ------- 2.io-»U IJ" -400 -700 0 ceosswixo DISTANCE «JOO • 400 Figure 7-2. Concentration as a function of crosswind distance (Problem 7). The values necessary to determine the isopleth half widths, y, are given in Table 7-3. Table 7-3 DETERMINATION OF ISOPLETH WIDTHS (PROBLEM 8) *, km 0.5 0.8 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 or m 83 129 157 295 425 540 670 780 890 980 x (centerline), g m-3 3.8 x 10~5 2.3 x 10-' 2.8x10-' 1.4 x 10-' 7.1 x 10-1 4.0 x 10~5 2.4 x 10~s 1.8 x 10-' 1.4 xlO-» 1.1 x 10-' X (isopleth) X (centerline) 0.263 4.35x10-= 3.53x10-' 7.14 x 10-' 1.42x10-' 0.250 0.417 0.556 0.714 0.909 y/ ------- Table 7-4 DETERMINATION OF CONCENTRATIONS FOR VARIOUS HEIGHTS (PROBLEM 9) d. f. g. J-H T 1 / i-H V-'l I+H f I/ c. + e. gin- 0-1.36 30-1.09 60-0.82 90-0.55 120-0.27 150 180 210 240 270 300 330 360 390 420 450 0.0 0.27 0.55 0.82 1.09 1.36 1.64 1.91 2.18 2.45 2.73 0.397 0.552 0.714 0.860 0.964 1.0 0.964 0.860 0.714 0.552 0.397 0.261 0.161 0.0929 0.0497 0.0241 1.36 1.64 1.91 2.18 2.45 2.73 3.00 3.27 3.54 3.82 4.09 4.36 4.64 4.91 5.18 5.45 0.397 0.261 0.161 0.0929 0.0497 0.0241 1.11 x 4.77 x 1.90 x 6.78 x 2.33 x 7.45 x 2.11 x 5.82 x 1.49x 3.55 x 10-' io-3 10-3 10-' 10-' 10-' 10-" 10-* 10~« 10-' 0.794 0.813 0.875 0.953 1.014 1.024 0.975 0.865 0.716 0.553 0.397 0.261 0.161 0.093 0.050 0.024 2.78 x 2.85 x 3.06 x 3.34 x 3.55 x 3.58 x 3.41 x 3.03 x 2.51 x 1.94 x 1.39 x 9.14 x 5.64 x 3.26 x 1.75 x 8.40 x 10-' 10-' lfJ-« 10-' 10-' 10-' 10-' 10-' 10-' 10~5 10~5 10-' 10-* These values are plotted in Figure 7-4. soo 010 10" 2-KT* J-IO'4 4x10"* CONCENTRATION. | •-' Figure 7-4. Concentration as a function of height (Prob- lem 9). Verifying: X (x,0,0) - TT ------- cr (stable) 151 H/8 = 520 + 19 = 539 (539) 330 = 8.5 x 10-" g m-8 of SOZ -Note that the fumigation concentrations under these conditions are about 1.3 times the maxi- mum ground-level concentrations that occurred during the night (problem 11). PROBLEM 13: An air sampling station is located at an azimuth of 203° from a cement plant at a distance of 1500 meters. The cement plant re- leases fine particulates (less than 15 microns diameter) at the rate of 750 pounds per hour from a 30-meter stack. What is the contribution from the cement plant to the total suspended particulate concentration at the sampling sta- tion when the wind is from 30° at 3 m sec"1 on a clear day in the late fall at 1600? SOLUTION: For this season and time of day the C class stability should apply. Since the sam- pling station is off the plume axis, the x and y distances can be calculated: x = 1500 cos 7° = 1489 y = 1500 sin 7° = 183 The source strength is: Q = 750 Ib hr> x 0.126 fjf C~* . — 94.5 g sec'1 . ID br~a At this distance, 1489 m, for stability C, ------- maximum *u/Q as a function of H and stability from Figure 3-9 and multiplying by the appro- priate Q/u. The computations are summarized in Table 7-6, and plotted in Figure 7-5. « \IM 1V S 7 * 9 I I I I 0.5 2 3 4 WIND SPEED. • 10 20 Figure 7-5. Maximum concentration as a function of wind speed (Problem 14). Table 7-6 MAXIMUM CONCENTRATION AS A FUNCTION OF WIND SPED (PROBLEM 14) Stability Class B D U' H, XU^mai' m sec~J m m~2 0.5 1.0 1.5 2 3 5 7 0.5 1.0 1.5 2 3 5 7 10 20 142.2 86.1 67.5 58.1 48.7 41.3 38.0 127.6 78.8 62.6 54.4 46.3 39.8 37.0 34.9 32.4 8.0x10-* 2.0 x 10-' 3.1 x 10-' 4.1 x 10" 5.7 x 10" 7.8 x 10" 8.7 x 10" 4.4 x 10-* 1.42x10-' 2.47x10-' 3.5 x 10-' 5.1 x 10" 7.3x10-' 8.2 x 10" 9.4 x 10" 1.1 x 10-* Q/u, gm-i 144 72 48 36 24 14.4 10.3 144 72 48 36 24 14.4 10.3 7.2 3.6 Xmai1 g m~a 1.15x10-' 1.44 x 10-' 1.49 xlO-»«- 1.48 x 10-" 1.37 x 10-8 1.12x10-' 8.96 x 10-' 6.34 x 10-' 1.02 x 10-' 1.19 xlO-' 1.26 x 10-'*- 1.22 x 10-' 1.05x10-' 8.45x10-* 6.77 x 10-* 3.96x10-* The wind speeds that give the highest maximum concentrations for each stability are, from Fig- ure 7-5: B 1.5, D 2.0. PROBLEM 15: A proposed pulp processing plant is expected to emit % ton per day of hydrogen sulfide from a single stack. The company prop- erty extends a minimum of 1500 meters from the proposed location. The nearest receptor is a small town of 500 inhabitants 1700 meters northeast of the plant. Plant managers have decided that it is desirable to maintain concentrations below 20 ppb (parts per billion by volume), or approximately 2.9 x 10~* g m"', for any period greater than 30 minutes. Wind direction frequencies indicate that winds blow from the proposed location toward this town between 10 and 15 per cent of the time. What height stack should be erected? It is assumed that a design wind speed of 2 m sec"1 will be sufficient, since the effective stack rise will be quite great with winds less than 2 m sec"1. Other than this stipulation, assume that the physical stack height and effective stack height are the same, to incorporate a slight safety factor. SOLUTION: The source strength is: Q _ 1000 Ib day"1 x 453.6 g Ib "' ^ ~ 86,400 sec day-1 FromEq. (4.2): 0.117 Q 0.117(5.25) 5.25 g sec" a, a, ' Xd U 1.06 x 10' m2 (2.9 x 10-') 2 At a design distance of 1500 meters (the limit of company property), c, a, = 1.06 x 10' gives a point from Figure 4-1 about 0.2 from Class C to Class D along the line x = 1500 m. From Figure 3-3, a. = 80 for this stability. H = \/2"a. = 113 meters PROBLEM 16: In problem 15 assume that the stack diameter is to be 8 ft, the temperature of the effluent 250° F, and the stack gas velocity 45 ft sec"1. From Holland's equation for effec- tive stack height and the method used in prob- lem 15, determine the physical stack height required to satisfy the conditions in problem 15. In estimating AH, use T. «= 68°F and p = 920 mb. SOLUTION: First determine the relation between AH and u from Holland's equation. v. = 45 ft sec"1 = 13.7 m sec"1 d = 8 ft — 2.44 m T. - 250°F — 121°C - 394°K T. — 68°F = 20°C = 293°K p <= 920 mb AH 1.5 +2.68 x 10-'p 13.7 (2.44) '1 u 394-293 1.5 + 2.68 x 10-' (920) 394 (2.44) 50 ATMOSPHERIC DISPERSION ESTIMATES ------- [1.5+ (2.46)0.256 (2.44)] (1.5 + 1.54) The relation between a, vt and u is: _ 0.117 Q __ 0.117 (5.25) _ 2.12x10* "'ff* ~ x<» u ^ 2.9 x 10-° u = u The required computations using Figure 4-1 are summarized in Table 7-7: Table 7-7 REQUIRED PHYSICAL STACK HEIGHT AS A FUNCTION OF WIND SPEED (PROBLEM 16) 60 sec min" U, AH,m m2 0.5 1.0 1.5 2.0 2.5 3.0 5.0 7.0 10.0 15.0 204 102 68 51 41 34 20 15 10 7 4.24 x 2.12 x 1.41 x 1.06 x 8.48 x 7.06 x 4.24 x 3.03 x 2.12 x 1.41 x 10* 10' 10< 10* 10* 103 103 103 10s 10s Stability to Give ay a, at 1500m 0.9 0.6 0.9 0.2 0.4 0.6 0.5 0.5 from from from from from from 0 from E from A B B C C C D E to to to to to to to to B C C D D D E F Of m 190 120 96 76 64 56 42 34 28 23 H' = V2*,. m 269 170 136 108 91 79 60 48 40 33 h = H'-AH, m 65 68 68 57 50 45 40 33 30 26 The required physical height is 68 meters. PROBLEM 17: A dispersion study is being made over relatively open terrain with fluorescent particles whose size yields 1.8 x 1010 particles per gram of tracer. Sampling is by membrane filters through which 9 x 10~s m° of air is drawn each minute. A study involving a 1-hour release, which can be considered from ground-level, is to take place during conditions forecast to be slightly unstable with winds 5 m see"1. It is desirable to obtain a particle count of at least 20 particles upon membrane filters located at ground-level 2.0 km from the plume centerline on the sampling arc 8 km from the source. What should the total release be, in grams, for this run? SOLUTION: The total dosage at the sampler is determined by the total sample in grams divided by the sampling rate: DT 20 particles 9 x 10~s m" min"1 1200 16.2 x 10' DT = 7.41 x 1CT6 g sec nT8 The total dosage is given in g sec m~' from DT (x,y,0;0) exp TT U CTj <7. * | 2 where QT is the total release in grams. Therefore QT - u a' "* DT f i ( y } 1 I 2 U J J exp For slightly unstable conditions (Class C) at x = 8 km, ------- PROBLEM 19: At a point directly downwind from a ground-level source the 3- to 15-minute concentration is estimated to be 3.4 x 10~3 g m~3. What would you estimate the 2-hour con- centration to be at this point, assuming no change in stability or wind velocity? SOLUTION: min, s = 2 X 2 liour = Using Eq. (5.12) and letting k hours, and p = 0.2: 2.09 Letting k 15 min, s = 2 hours, and p = 0.17 X 2 bour ' 3.4x10- 8 (3.4 x 10-") 3.4 x IP"3 1.42 2.4 x 10-" g m" The 2-hour concentration is estimated to be between 1.6 x 10~3 and 2.4 x 10"3 g m~\ PROBLEM 20: Two sources of S0a are shown as points A and B in Figure 7-6. On a sunny summer afternoon the surface wind is from 60° at 6 m sec"1. Source A is a power plant emitting 1450 g sec"1 S0a from two stacks whose physical height is 120 meters and whose AH, from Hol- land's equation, is AH (m) = 538 (m2 sec^J/u (m sec"1). Source B is a refinery emitting 126 g sec"1 SOa from an effective height of 60 meters. The wind measured at 160 meters on a nearby TV tower is from 70° at 8.5 m sec"1. Assuming that the mean direction of travel of both plumes is 245°, and there are no other sources of S02, what is the concentration of SO, at the receptor shown in the figure? SOLUTION: Calculate the effective height of Source A using the observed wind speed at 160 meters. AH = 538 63.3 8.5 HA = 120 + 63 = 183 m QA = 1450 g sec'1 HB — 60 m QB -= 126 g sec"1 For a sunny summer afternoon with wind speed 6 m sec"1, the stability class to be expected is C. The equation to be used is Eq. (3.2): IECEPTO* SOUICE I i*l).C in r* 4.0 In Figure 7-6. Locations of sources and receptor (Problem 20). x (x,y,0;H) Q it Oj at U exp I jr- For Source A, x = 24.6 km, y = 8.4 km a, «= 1810 m, «r, = 1120 m, u •= 8.5 m sec" 1450 XA 7, 1810 (1120) 8.5 "^ [ 8400 \*| F _ / 183 exp I—0.5 l f . . / 183 Vl J 6XP I"0'5 (-U20-J J U20 [-0.5 (4. exp [—0.5 (0.164)2] = 2.67 x 10~5) (2.11 x 10-') (0.987) XA — 5.6 x 10-10 g m~3 For Source B, x -= 13.0 km, y = 4.0 km. a, = 1050 m, a, = 640 m, u = 7.0 m sec- 126 XB = w 1050 (640) 7 6XP exp 126 exp [—0.5 (3.81 )2] 1.48 x 107 exp [—0.5 (0.0938)2] — 8.5 x 10-« (7.04 x 10"') (0.996) XB = 6.0 x 10~* g m~s x = XA + XB = 0.56 x 10-* + 6.0 x 10"« = 6.6 x 10-» g m "' 52 ATMOSPHERIC DISPERSION ESTIMATES------- PROBLEM 21: A stack 15 meters high emits 3 g sec"1 of a particular air pollutant. The sur- rounding terrain is relatively flat except for a rounded hill about 3 km to the northeast whose crest extends 15 meters above the stack top. What is the highest 3- to 15-minute concentra- tion of this pollutant that can be expected on the facing slope of the hill on a clear night when the wind is blowing directly from the stack toward the hill at 4 m sec"1? Assume that AH is less than 15 m. How much does the wind have to shift so that concentrations at this point drop below 10~7 g m"3? SOLUTION: A clear night with 4 m sec'1 indi- cates class E stability. Eq. (3.4) for ground- level concentrations from a ground-level source is most applicable (See Chapter 5). At 3 km for class E, ay = 140 m, ------- that it is 1600 on a sunny fall afternoon. What is the concentration directly downwind from one end of the source? SOLUTION: Late afternoon at this time of year implies slight insolation, which with 3 m Bee"1 winds yields stability class C. For C stability at x = 400 m, a, = 45 m,( J-) ay of / life given, multiply by exp I is time and L is half-life. * To determine decay of materials with the half- Q cog + \ ^ - ) •" / where t Source strength of I1'1. Q, (curies sec'1) — 1.157 x KT8 (5.3 x 10') exp / —0.693 t \ L For I1S1 L 6.95 x 10° sec For a clear night with wind speed 2.5 m sec'1, class F applies. Approximate the spreading at the reactor shell by 2.15 af0 = 2.15 o,0 = the radius of the shell = 20 m ------- = 2.7 x 10"" (1.0) The decay of I131 is insig- nificant for 2 hours xi = 2.7 x lO"8 curies nr3 PROBLEM 26: A spill estimated at 2.9 x 10° -grams of unsymmetrical dimethyl hydrazine 'occurs at 0300 on a clear night while a rocket is being fueled. A circular area 60 meters in diameter built around the launch pad is revetted into squares 20 feet on a side to confine to as small an area as possible any spilled toxic liquids. In this spill only one such 20- by 20-foot area is involved. At the current wind speed of 2 m sec"1, it is estimated that the evaporation rate will be 1100 g sec"'. The wind direction is pre- dicted to be from 310° :t 15° for the next hour. Table 7-8 gives the emergency tolerance limits for UDMH vapor. Table 7-8 EMERGENCY TOLERANCE LIMITS FOR UDMH VAPOR VERSUS EXPOSURE TIME Time, minutes 5 15 30 60 Emergency Tolerance Limits, g rrr3 1.2 x 10-' 8.6 x 10-- 4.9 x 10-' 2.5 x 10-= What area should be evacuated? SOLUTION: From Table 3-1, the stability class is determined to be Class F. This is not a point source but a small area source. Allowing 4.3 ay0 to equal the width of the wetted area, 6.1 meters (20 feet), ------- Table 7-10 DETERMINATION OF WIDTHS WITHIN ISOPLETHS (PROBLEM 26) 1 s .0 .0 J.O 1.0 5.0 6.0 km * 0.14 0.54 1.04 2.04 3.04 4.04 5.04 6.04 , av- m 5.5 19 35 66 93 120 149 175 % (centerline), g irr3 13.9 3.6 1.3 7.0 1. x X X 4.8 x 3.5 2.7 X X 1 10-' 10-' 10-' 10-' 10-' 10-' X (isopleth) y X (centerline) aj. 1.8 2.27 6.94 1.92 3.57 5.20 7.14 9.26 x x X X X X X X 10-' 10-' io-= io-> 10- 10-' 10-' 10-' 3.55 2.75 2.31 1.82 1.44 1.14 0.82 0.39 y, m 20 52 80 120 134 137 122 68 SCAlt. km I Figure 7-8. Possible positions of the 2.5 x 1(T g m' isopleth and the evacuation area (Problem 26). 56 ATMOSPHERIC DISPERSION ESTIMATES------- APPENDICES tn-m o - e» -------- Appendix 1: ABBREVIATIONS AND SYMBOLS Abbreviations cal calorie g gram °K degrees Kelvin m meter mb millibar sec second Symbols a ratio of horizontal eddy velocity to vertical eddy velocity Cp specific heat at constant pressure Cy Sutton horizontal dispersion parameter C, Sutton vertical dispersion parameter d inside stack diameter at stack top DT (x,y,0;H) Total dosage e 2.7183, the base of natural logarithms f (0,S,N) frequency of wind direction for a given stability and wind speed class h physical stack height hi height of the base of an inversion H effective height of emission H,, effective height of emission for a particular wind speed k von Karman's constant, approximately equal to 0.4 K eddy diffusivity L two uses: 1. the height of an air layer that is relatively stable compared to the layer beneath it; a lid 2. the half-life of a radioactive material n Button's exponent N an index for wind speed class p three uses: 1. Bosanquet's horizontal disper- sion parameter 2. atmospheric pressure 3. a dummy variable in the equa- tion for a Gaussian distribution. q two uses: 1. Bosanquet's vertical dispersion parameter 2. emission rate per length of a line source Q emission rate of a source Q, total emission during an entire release R net rate of sensible heating of an air column by solar radiation s the length of the edge of a square area source S an index for stability tk a short time period t,,, time required for the mixing layer to develop from the top of the stack to the top of the plume tB a time period T. ambient air temperature TB stack gas temperature at stack top u wind speed u.v a mean wind speed for the wind speed class N. v' horizontal eddy velocity vs stack gas velocity at the stack top v, a velocity used by Calder w' vertical eddy velocity x distance downwind in the direction of the mean wind x------- the angle between the wind direction and a line source concentration crosswind-integrated concentration a ground-level concentration for design pur- poses inversion break-up fumigation concentration concentration measured over a sampling time, tk maximum ground-level centerline concentra- tion with respect to downwind distance X. concentration measured over a sampling time, t. £j- relative concentration y £_ relative concentration normalized for wind Q speed X (x,y,z;H) concentration at the point (x, y, z) from an elevated source with effective height, H. X (x,9) the long-term average concentration at distance x, for a direction 9 from a source. 60 ATMOSPHERIC DISPERSION ESTIMATES------- Appendix 2: CHARACTERISTICS OF THE GAUSSIAN DISTRIBUTION The Gaussian or normal distribution can be de- picted by the bellshaped curve shown in Figure A-l. The equation for the ordinate value of this curve is: (A.I) Figure A-2 gives the ordinate value at any distance from the center of the distribution (which occurs at x). This information is also given in Table A-l. Figure A-3 gives the area under the Gaussian curve from — K to a particular value of p where p = x — x This area is found from Eq. (A.2): F - Area (— ^ to p) = I —7= exp (—0.5 p=) dp (A.2) Figure A-4 gives the area under the Gaussian curve from —p to +p. This can be found from Eq. (A.3): Area (—p exp (—0.5 p5) dp /-HP -p (A.3) -3 Figure A-l. The Gaussian distribution curve. Appendix 2 61 J5S-901 O • »« - »------- 0.01 0.0 0.2 0.4 06 O.e 1.0 1.2 1.4 I » I. Figure A-2. Ordinate values of the Gaussian distribution. C2 ATMOSPHERIC DISPERSION ESTIMATES------- 4.0 s. s 3.0 2.5 2.0 1.5 1.0 0.5 0 •0.5 -1 0 -1.5 2rt -2.5 •1.0 •3.5 •4.0 — — v -L- ~- r~ - *444 - — " - -T*+ _ ~yl — <- — ? — > - E - — -•-t a 1 j •±bt Tr^ -fit •;J — -h jr ^~ + ** -T-T — "* 1 r*l g — • x ^*- — rrr T**j .^' i gJJ • "T4" ^JL r*t — 40. M*l "ri j»^ T • ** f i j i J i -rt- u-^i ; • T'l ' Trtr ^V — 3 v^ f ..-».{ T " 1 ^ '* "rrrr •=f — »** J"**~ I j ! . J 1 T i t • 1 k-j-t- TTT~ ^PJ-L — . — ^< i / ; • i *^l -rr - ~~: w~ ... 4 . X | ^ - j^ "^r ~? ^_. -r — x1 — 0.01 0,1 0.5 1 2 5 10 20 40 *0 BO 90 95 96 99 99.8 99.99 Figure A-3. Area under the Gaussian distribution curve from —« to p. Appendix 2 63------- 4.5 4.0 3.5 dFP 3.0 2.5 2.0 1.5 1.0 0.5 ±2 Figure A-4. Area under the Gaussian distribution curve between —p and +p. €4 ATMOSPHERIC DISPERSION ESTIMATES------- Appendix 3: SOLUTIONS TO EXPONENTIALS Expressions of the form exp [—0.5 A:] where A is H Vr or y/a? frequently must be evaluated. Table A-l gives B as a function of A where B = exp [—0.5 A2]. The sign and digits to the right of the E are to be considered as an exponent of 10. 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OOE -1 8.99E -1 8.04E .1 7.49E -1 6.91E -1 6.31E -1 9.70E .1 9.10E .1 4.92E «1 3.97E -1 3.49E -1 2.96E -1 2.92E -1 2.13E -1 1.77E -1 1.47E -1 1.20E -1. 9.70E -2 7.78E -2 6.17E -2 4.89E -2 3.7BE -2 2.91E -2 2.22E -2 l.67E .2 1.29E .2 9.26E -3 6.79E -3 4.92E -3 3.94E .1 2.91E -3 1.77E -3 1.23E -3 8.91E -4 9.82E -4 3.93E -4 2.63E -4 1.79E -4 1.19E -4 7.49E -9 4.79E -9 3.09E .9 1.93E -9 1.20E -9 7.43E .6 4.99E -6 0.07 9.98C 0.86E 9.64E 9.34E B.99E B.30E 7.99E 7.44E 6.89E 6.29E 9.64E 9.04E 4.46E 3.91E 3.39E 2.92E 2.48E 2.09E 1.74E 1.44E 1.17E 0.30E 7.60E 6.03E 4.73E '.68E 2.83E 2.16E 1.63E 1.22E 8.98E 6.98E *.77E 3.42E 2.43E 1.71E 1.19E 8.20E 9.60E 3.78E 2.93E 1.68E 1.10E 7.13E 4.38E 2.92E 1.84E ».l 9E T.08E 4.33E ^ • «• . « «• w ^ • V w • . - — m . . - -1 .3 -; -j • i .2 ^) .; -3 -3 .3 -3 .3 -3 -3 .4 • 4 .4 .4 -4 .4 • ' m . . , » 0.08 9.97E 9.84E 9.62E 9.30E 8.91E 8.45E T!38E ».79E ».l9E 9.9BE *.99E *.4l£ 3.B6E 3.35E 2.87E 2.4»E 2.05E 1.71E 1.41E 1 1.19E ! 9.29E 1 7.43E ' 9.89E ! 4.62E 1 3.99E ' 2.76E • 2. IDE ! 1.98E ' 1.18E 1 8.7tE 6.37E 4.61E 3.31E 2.39E 1.69E 1.19E T.89E > 9.3BE 3.63E 2.43E 1.61E 1.09E 6.83E *.38E 2.70E 1.75E t . 09E 6.74E 4.12E .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .2 .2 .2 .2 .2 .2 .2 .2 .2 -3 .3 .3 .3 .3 .3 .3 ^4 .4 .4 .4 .4 .4 .9 .9 .9 .9 .9 .6 .6 0.09 9.9»t .1 9.82C .1 9.99C .1 9.27E .1 8.87E .1 8.40E .1 7. BBC .1 7.32E .1 6.73E .1 6.13E .1 9.92C .1 4.93E .1 4.39E .1 3.81C .t 3.30E .1 2.83E .1 2.40E .1 2.02E .1 1.6BE .1 1.38E -1 1.13E .1 9.09E .2 7.27E .2 9.75C .2 4.91E .2 3.49E .2 2.68E .2 2.04E .2 1.34E .2 1.19E .2 8.49E .3 6.17E -3 4.46E .3 3.20E .3 2.27C .3 1.99E -3 1.11E .3 7.6QC .4 3.18E .4 3.49E .4 2.33E .4 1.94E .4 1.01E -4 6.93E .9 4.19E .9 2.66E .9 1.67E -9 1.04E .9 6.42E .6 3.92E .6------- •o •o n a. Table A 1 (continued) SOLUTIONS TO EXPONENTIALS 4 9.00 9.10 5.20 5.30 5.40 5.50 5.60 5.70 5.80 5.90 6.00 6.10 6.20 6.30 6.40 6.50 6.60 6.70 6.80 6.90 7.00 7.10 7.20 7.30 7.40 7.50 7.60 7.70 7.80 7.90 8.00 8.10 8.20 8.30 8.40 8.50 8.60 8.7'J 8.80 8.90 ;oo .10 .20 .30 .40 .50 .60 .70 .80 .90 0.00 B 3.71E -6 2.25E -6 1.3&E -6 7.9^t -7 *.6*E -7 2.70t -7 l.S^t -7 B.fllE -B 4.9«,E -8 2.76E -9 l.52t -B 8.37E -9 4.50E -9 t, *IE -9 1.29E -9 6.69E-10 3.4BE-10 U7ot-10 9.10E-11 4.SOE-11 2.29E-11 1.13E-11 5i"54E-12 2.6RE.12 1.29E-12 6.10E-13 2.87E-13 l.3fcE-l3 6.HE-14 7.BOE-14 1.27E-14 5.66E-1S U10E-19 4.77E-16 2.01E-16 8.71E-17 J.67E-17 1.51E-17 6.31E-18 *.58E-18 U04E-1B 4.lflE-19 1.66t-19 6.50E-20 *.53E-20 9|72E-21 l!«OE-21 5.22E-22 o.ot 1.55E -6 2.14E -6 1.28E -6 7.54E -7 4.41E -7 2.56E -7 1.47E -7 B.32E -8 «.68E -8 2.60E -8 1.43E -8 7.R2E -9 4.?3F -9 2.26E -9 1.20F. -9 6.27E-10 3.25E-10 1.67F-1Q B.50E-U 4.28E-U 2.14E-11 1.05E-M 1.15E-12 Z.49E-12 1.19E-12 5.66E-13 2.66E-13 J.24E-13 S.69E-1* 2.59E-14 1.17E-14 5.22E-13 Z.31E-15 1.01E-15 4.38E-16 1.88E-16 T.99E-17 3.36E-17 1.40E-17 5.77E-18 2.36E-18 9.52E-19 3.81E-19 l.ME-19 5.92E-20 Z.30E-ZO 8.83E-'! 3.36E-*! 1.27E-21 4.73E-Z2 0.02 3.37E -ft 2.0^E ~f> 1.21E -A 7.1-5E -7 4.1PE -7 2.4?c -7 1.39E -7 7«8fE -B 4.41E -B 2.4SE -B 1.39F. -B 7.3SE -•» 3.97E -9 2.12E -9 1.12E -9 5.8"E-10 3.0ISE-10 1 «5*E-10 7.94E-11 4.00E-U 1.99E-11 9. 816-12 4.79E-12 2.32E-12 1.11E-12 5.25E-13 2.46E-13 l.UE-13 5.2(SE-t4 2.39E-U 1.08E-14 4.81E-1S 2.11E-11 9.30E-16 4.03E-16 1.73E-14 7.33E-17 3.04E-17 1.28E-17 5.2RE-1* 2.13E-1B B.69E-19 3.47E-19 1.37E-19 5.31E-20 2.09E-20 6.02E-21 3.09E-21 1.15E-21 4.21E-22 0.03 3.21E -6 1.9?E -6 1.15E -6 6.7HE -7 J.96E -7 Z.29E -7 1.31E -7 '.42E -8 4.16E -8 Z.31E -8 1.27E -8 ft.92E -9 3.73E -9 1.99E -9 1.05E »9 9.50E-10 Z.B5E-10 1.46E-10 7.42E-11 3.73E-U 1.86E-H 9.UE-12 4.46E-12 Z.15E-12 1.03E-12 4.87E-13 Z.2BE-13 1.06E.13 4.86E-14 Z.21E-14 9.96E-15 4.44E-15 1.96E.15 0.56E-16 3.70E-16 1.59E-16 6.72E-17 Z.82E-17 1.17E-17 4.83E-18 1.97E-18 f.93E-!9 3.17E-19 1.25E-19 4.90E-20 1.90E-20 7.29E-21 2.77E-21 1.04E-21 3.qflE-22 0.04 3.05E -6 1.81E -6 I .OT£ -6 0.05 0.06 2.90E -6 2.76E -6 1.74E -6 1.65E -6 l.O^E -6 9.82E -7 *.<•!£ -' 6.09E -7 5.77E -7 3.7SE -7 Z.l'E -7 1.2<«E -7 7.01E -8 3.91E -8 2. IRE -8 1.20E -8 ^.ME -9 3.51E -9 I.R7E -9 9.87E-10 5.16E-10 2.67E.10 1.37E-10 6.93E-11 3.49E-U 1.7^E-11 8.51E-12 4.15E-12 2.00E-12 9.55E-13 4.52E-13 2.11E-13 9.BOE-14 4.50E-14 2.04E-14 9.19E-15 4.09E-15 l.POE-19 7.87E-16 3.4CE-16 1.46E.16 6.17E-17 2.59E-17 1.07E-17 4.41E-18 1.80E-18 7.24E.19 2.89E-19 1.1"E-19 4.46E-20 1.73E-20 4.62E-21 2.51E-21 9.43E-22 3.51E-22 3.55F -7 3.36E -7 2.05E -7 1.17E -7 1.94E -7 L.llE -7 6.62E -8 6.25E -8 3.70E -8 3.49E -8 2.05E -8 1.13E -8 1.94E .8 L.OAE -8 6.12E -9 5.7AE -9 3.29E -9 3.09E -9 1.75E -9 1.63E -9 9.25E-10 8.67E-10 4.83F-10 4.52E-10 2.50E.10 2.34E-10 1.28E-10 1.19E-10 6.47E-11 6.06E-11 3.25E-11 3.03E-11 1.61E-U L.50E-U 7.92E-12 7.3PE-12 3.86E-12 3.59E-12 1.R6E-12 L.73E-12 8.87E-13 8.23E-13 4.19E-13 3.88E-13 1.96E-13 1.81E-13 9.07E-14 8.39E-14 4.16E-14 3.84E-14 1.89E-14 1.74E-14 8.48E-15 7.82E-19 3.77E-15 3.48E-15 1.66E-15 7.24E-16 3.13E-16 1.34E-16 5.66E-17 2.37E-17 9.83E-18 4.04E-18 1.64E-IR 6.61E-19 2.63E-19 1.04E-19 4.06E-20 .53E-15 .66E-16 .87E-16 .23E-16 .19E-17 .17E.17 .OOE-18 .69E-18 .30E-18 .03E-19 .40E-19 .46E-20 .69E-20 1.57E-20 1.43E-20 6.01E-21 5.46E-21 2.28E-21 2.07E-21 8.55E-22 7.75E-22 • 3.18E-22 2.88E-22 0.07 0.08 2.62E -6 2.49E -6 1.57E -6 l.*9E .6 9.32E -7 8.84E -7 3.47E -7 5.19E -7 3.18E -7 3. OlE -7 1.83E -7 1.73E -7 1.05E -7 ,87E - 5.90E -B .57E • 3.29E - .HE - 1.82E - .72E . 9.98E - .39E - 5.41E - ,09E - 2.91E - Z.73E > 1.55E - 1.45E - 8.13E-10 7.62C-10 4.24E-10 3.77C-10 2.19E-10 2.0*E-10 1.12E-10 1.04E-10 5.64E-11 5.27E-1I 2.82E-11 2.63E-11 1.40E-11 1.3oe-ll ».87E-12 6.J9E-12 3.34E-12 3.10E-12 1.60E-12 1.49E-12 7.64E-13 7.09E-H 3.60E-13 3.S4E.1S 1.68E-13 1.96E.13 7.77E-14 7.19E-14 3.55E-14 3.2§E-14 1.61E-14 1.49E-14 7.22E-15 6.66E.13 3.20E-15 2.95E.19 1.41E-13 6.13E-16 2.64E-16 1.13E-16 4.76E-17 1.99E-17 8.23E-18 3.37E-18 1.37C-19 5.50E-19 2.19E-19 B.61E-20 3.36E-20 1.30E-20 4.95E-21 1.87E-21 7.02E-22 2.60E-22 .30E-15 .64E«16 .43E-16 .03E-16 .36E-17 .82E.17 .53E.18 .08E-18 .25E-18 .02E.19 .99E.19 .84E.20 .05E-20 .18E.20 .90E.21 .70E-21 .36E-22 .36E-22 0.09 2.37E .6 1.42C .6 B.38E .7 4.91E -7 2.85E .7 1.64( .7 9.32E . 9.25E - 2.93E . 1.62E . 8.846 . 4.78E - 2.56C . 1.36C . 7.14C-10 S.71C-10 1.91E-10 9.74E-H 4.92E-11 2.46E-11 1.22C.11 9.95C.12 2.88E-12 1.38C.12 6.98E-13 3.09C.13 1.44E-13 6.65E-14 3.04E.14 1.37E-14 6.14B.15 2.72E-13 1.19E-15 9.18E-16 2.23E-16 t. 496-17 4.00E-17 1.67C.17 6.89C.18 2. 826-18 1.146.18 4.586.19 1.826.19 7.146-20 2.786.20 1.076.20 4.086.21 1.946.21 5.766-22 2.136.22------- Appendix 4: CONSTANTS, CONVERSION EQUATIONS, CONVERSION TABLES Constants e = 2.7183 —L_ = 0.3679 e IT == 3.1416 —— = 0.3183 Tr 2r = 6.2832 —L_ = 0.1592 2ir \/2T= 2.5066 -j~ = 0.3989 —|=r = 0.7979 (27r)3/:!= 15.75 Conversion Equations and Tables T(°C) = 5/9 (T(°F) —32) T(°K) = T(°C) +273.16 T(°F) = (9/5T(°C) ) + 32 Appendix 4 69------- CONVERSION FACTORS - VELOCITY J^ H 3 o C/J "0 X i o o V) •fl DESIRED GIVEN UNITS METERS PER SEC FT PER SEC FT PER MIN KM PER HR MKSTAT) PER HR KNOTS MKSTAT) PER DAY TO CONVERT A UNITS METERS PER SEC 1.0000 E 00 3.0480 E-01 5.0800 E-03 2.7778 E-01 4,470* E-01 5,1479 E-01 1,8627 E-02 VALUE FROM A GIVEN gj AND BENEATH THE DESIRED UNIT. V) O •x M V) H H W V) FT PEP SEC 3.2808 E 00 1.0000 E 00 1.6667 E-02 9.1134 E-01 1.4667 E 00 1.6889 E 00 6.1111 E-02 UNIT TO A NOTE THAT FT PER MIN 1.9689 E 02 6.0000 E 01 1.0000 E 00 5.4681 E 01 8.8000 E 01 1.013* E 02 3.6667 E 00 KM PER HR 3.6000 E 00 1.0973 E 00 1.8288 E-02 1.0000 E 00 1.6093 E 00 1.8532 E 00 6.7056 E-02 DESIRED UNIT, MULTIPLY E-xx MEANS MKSTAT) PER HR 2.2369 E 00 6.8182 E-01 1.136* E-02 6.2137 E-01 1.0000 E 00 1.1916 E 00 4.1667 E-02 THE GIVEN KNOTS 1.9425 E 00 5.9209 E-01 9.8681 E-03 5.3959 E-01 8.6839 E-01 1.0000 E 00 3.6183 E-02 VALUE BY MKSTAT) PER DAY 5.3686 E 01 1.6364 E 01 2,7273 E-01 1.4913 E 01 2.4000 E 01 2,7637 E 01 1,0000 E 00 THE FACTOR OPPOSITE THE GIVEN UNITS 10 TO THE -XX POWER.------- •0 •o 8 I CONVERSION FACTORS DESIRED UNITS QtVEN UNITS GRAMS PER SEC GRAMS PER MIN KG PER HOUR KG PER DAY LBS PER MIN LBS PER HOUR LBS PER DAY TONS PER HOUR TONS PER DAY - EMISSION RATES GRAMS PER 1.0000 E 00 1,6667 E-02 2.7778 E-01 1.1574 E-02 T.5599 E 00 1.2600 E-01 5.2499 E-03 2.3200 E 02 1.0500 E 01 GRAMS SEC PER 6.0000 E 01 1.0000 E 00 1.6667 E 01 6.9444 E-01 4.3339 E 02 7.5599 E 00 3.1499 E-01 1.3120 E 04 6.2999 E 02 KG MIN PER HOUR 3.6000 E 00 6.0000 E-02 1.000'' E 00 4,1667 E-02 2,7216 E 01 4.5359 E-01 1.8900 E-02 9.0718 E 02 3.7799 E 01 KG PER 8.64QO E 01 1.4400 E 00 2.4000 E 01 1.0000 E 00 6.3317 E 02 1.0886 E 01 4.3339 E-01 2.1772 E 04 9.0718 E 02 LBS DAY PER M] 1.3228 E-01 2.2046 E-03 3.6744 E-02 1.5310 E-03 1.0000 E 00 1.6667 E-02 6.9444 E-04 3.3333 E 01 1.3889 E 00 LBS [N PER HOUR 7.9366 E 00 1.3228 E-01 2.2046 E 00 9.1839 E-02 6.0000 E 01 1.0000 E 00 4.1667 E-02 2.0000 E 03 8.3333 E 01 LBS PER 1.9048 E 02 3.1747 E 00 5.2911 E 01 2.204ft E 00 1.4400 E 03 2.4000 E 01 1.0000 E 00 4,8000 E 04 2,0000 E 03 TONS DA* PER HOUR 3.9683 E-03 6.6139 E.09 1.1023 E-03 4.5950 E-09 3.0000 £-02 5.0000 £•04 2.0833 £-09 1.0000 E 00 4.1667 E-02 TONS PER 9.924Q E-02 1.5873 E-03 2.6435 E-02 1.1023 E-03 7.2000 E-01 1.2000 E-02 5.0000 E-04 2.4000 E 01 1.0000 E 00 TO CONVERT A VALUE FROM A GIVEN UNIT TO A DESIRED UNIT, MULTIPLY THE GIVEN VALUE BY THE FACTOR OPPOSITE THE GIVEN UNITS AND BENEATH THE DESIRED UNIT. NOTE THAT E-XX MEANS 10 TO THE -XX POWER.------- KILOMETER INCH FOOT Y*RO MILE<*AUT> H 2 O en "B s PJ 91 on v> I w V) H CONVERSION FACTORS - LENGTH DESIRED UNITS METER CM MICRON OtVEN UNITS METER CM MICRON KILOMETER INCH root YARD MILCISTAT) MIlE(NAUT) TO CONVERT A VALUE FROM A GIVEN UNIT TO A DESIRED UNIT. MULTIPLY THE GIVEN VALUE BY THE FACTOR OPPOSITE THE GIVEN UNITS AND BENEATH THE DESIRED UNIT. NOTE THAT E-XX MEANS 10 TO THE -XX POWER. 1.0000 E 00 1.0000 E-02 1,0000 E-06 1,0000 E 03 2.9400 E-02 3.0480 E-01 9.1440 E-01 1.6093 C 03 1.8932 E 03 1.0000 E 02 1.0000 E 00 1.0000 E-04 1.0000 E 05 2.9400 E 00 3.0480 E 01 9.144Q E 01 1.6093 E 09 1,8932 E 09 1.0000 E 06 1.0000 E 04 1.0000 E 00 1.0000 E 09 2.9400 E 04 3.0480 E 03 9.1440 E 09 1.6093 E 09 1.8932 E 09 1.0000 E-03 1.0000 E-03 1.0000 E-09 1.0000 E 00 2.9400 E-09 3.0480 E-04 9.1440 E-04 1.6093 E 00 1.8932 E 00 3.9370 E 01 3.937Q E-01 3.9370 E-09 3.9370 E 04 1.0000 E 00 1.2000 E 01 3.6000 E 01 6.3360 E 04 7.2962 E 04 3.2808 E 00 3.2808 E-02 3.2808 E-06 3.2808 E 03 8.3333 E-02 1.0000 E 00 3.0000 E 00 3.2800 E 03 6,0802 E 03 1.0936 E 00 1.0936 E-02 1.0936 E-06 1.0936 E 03 2,7778 E-02 3,3333 E-01 1,0000 E 00 1.7600 E 03 2.0267 E 03 6.213; E- '4 6,2137 £.06 6,2137 E-10 6,2157 £.01 1.9783 E.09 1.8939 £.04 9.6818 £.04 1,0000 £ 00 1.1916 E 00 9.3939 E-04 3.3999 E-06 3,3939 E-10 3,3999 E-01 1.3706 E-OS 1.6447 E-04 4,9340 E-04 8,6839 E-01 1.0000 E 00 H M (/>------- I re CONVERSION FACTORS • AREA DESIRED 6TVEN UNITS so METER SO KM so CM SO INCH so FOOT SO YARD ACRE so STAT MILE so NAUT MllE UNITS SO METER 1,0000 E 00 1.0000 E 06 1.0000 E-04 6.4916 £•04 9.2903 E-02 S. 9613 E-01 4.0469 E 03 2.9900 E 06 3.4349 E 06 SO KM 1.0000 E-06 1.0000 E 00 1.0000 E-10 6.4316 E-10 9.2909 £•09 8.3613 E-07 4.0469 E-03 2.9900 E 00 3.4345 E 00 SO CM 1.0000 E 04 1.0000 E 10 1.0000 E 00 6.4916 E 00 9.2903 E 02 8.3613 E 03 4.0469 E 07 2.9900 E 10 3.4343 E 10 SO INCH 1.9900 E 03 1.9900 E 09 1.9900 E-01 1.0000 E 00 1.4400 E 02 1.2960 E 03 6.2726 E 06 4.0149 E 09 9.3239 E 09 SO FOOT 1.0764 E 01 1.0764 E 07 1.0764 E-03 6.9444 E-03 1.0000 E 00 9.0000 E 00 4.3960 E 04 2.7878 E 07 3.6969 E 07 SO YARD 1.1960 E 00 1.1960 E 06 1.1960 E-04 7.7160 E-04 1.1111 E-01 1.0000 E 00 4.8400 E 03 3.0976 E 06 4.1076 E 06 ACRE 2.4710 E-04 2.4710 E 02 2.4710 E-08 1.9942 E.07 2.2997 E.09 2.0661 E.04 1.0000 E 00 6.4000 E 02 8.4869 E 02 SO STAT MILE 9.8610 E-07 9.8610 E-01 9.8610 E-ll 2.4910 E-10 3.987Q E-08 9.2283 E-07 1.9623 E-03 1.0000 E 00 1.3261 E 00 SO NAUT MILE 2.9116 E-07 2.9116 E-01 2.9116 E-ll 1.8789 E-10 2.7030 E-08 2.4949 E-07 1.1783 E-03 7.9411 E-01 1.0000 E 00 TO CONVERT A VALUE FROM A GIVEN UNIT TO A DESIRED UNIT. MULTIPLY THE GIVEN VALUE BY THE FACTOR OPPOSITE THE GIVEN UNITS AND BENF.ATH THE DESIRED UNIT. NOTE THAT E-XX MEANS to TO THE -xx POWER.------- CONVERSION FACT07S - D^SIRFU U''IT5 CD GIVEN MNTTS LITE" CM INCH cu Fnnr cu STAT cu NAUT u s FLUID u s QUART u 5 GALLON MILE MILE OUNCE > H S O V) •fl X I O o 55 •d S eg O S! S C/J H § »*b H n en cu METEO LITER cu INCH cu FOOT CU 5TAT MILE CU 'IAUT MILE US FLUID OUMCF U S QUART U S GALLON TO CONVPRT A AND BENFATH 1.0000 9 f no I. 0000 1 F-<13 1.6*87 I r-"s 2.8417 ? F-02 *.UB .7B->3 E O'J U'lp TO 6.1021 F 0* 6.1025 E 01 1.0000 f 00 1.7280 E 03 2.5*36 F L* 3.8«*2 E 1* 1.80*7 F 00 5.7750 E 07 2.3100 F 02 A DESIRE') 3.531* E '»! 3. VMS E-n? 5./H70 E-<>* l.onoo E ''O l.*7?n E 11 2'.?* 7 8 E U 1.0'»** E-03 3.3*20 E o* 1.3168 E.ni UNIT, MULTIPLY *.3991 E-10 2.3992 E-13 3.9315 E-15 6.793ft E-12 I. 0000 E 00 1.5270 E 00 7.0950 E-15 2.270* E-07 9.0817 E-13 THE GIVEN 1.57U E-10 1.5711 E-13 2.57*6 E-15 *.**fl8 E-12 6.5*46 E-Ol 1.0000 E 00 4.6*62 E-15 l.*868 E-07 5.9*72 E-13 VALUE By 3.381* E 0* 3.3815 E 01 5.5*12 E-Ol 9.5751 E 02 l.*09* E 1* 2.1523 E 1* 1.0000 E 00 3.20QO E 07 1.2800 E 02 THE FACTOR 1.0567 E-03 1.0567 E-06 1.7316 E-08 2.9922 E-05 *.*0*5 E 06 6.7259 E 06 3.1250 E-08 1.0000 E 00 *.oooo £.06 OPPOSITE NnTf. THftf E-XX MEANS 10 TO THE -xx POWER. 2.6*17 E 02 2.6*18 E-Ol *.3290 E-03 7.*805 E 00 1.1011 E 12 1.6815 E 12 7.8125 E-03 2.5000 E 05 1.0000 E 00 THE GIVEN UNITS------- 5 IV 0 CONVERSION FACTORS - MASS DESIRED UNITS GRAM GIVEN UNITS GRAM 1.0000 E 00 MICROGRAM i.oooo E-06 KILOGRAM 1.0000 E 03 METRIC TON 1.0000 E 06 SHORT TON 9.0718 E 05 LONG TON 1.0160 E 06 GRAIN 6,4799 E-02 OUNCE 2.8549 (AVDPl E 01 LB (AvDP) 4.5359 E 02 MICROGRAM 1.0000 E 06 1.0000 E 00 1.0000 E 09 1.0000 E 12 9.0718 E 11 1.0160 E 12 6.4799 E 04 2.8349 E 07 4.5359 E 08 KILOGRAM 1.0000 E-03 1.0000 E-09 1.0000 E 00 1.0000 E 03 9.0718 E 02 1.0160 E 03 6.4799 E-05 2.8349 E-02 4.5359 E-01 METRIC TON 1.0000 E-06 1.0000 E-12 1.0000 E-OJ 1.0000 E 00 9.0718 E-01 1.0160 E 00 6.4799 E-08 2.8349 E-05 4.5359 E-04 SHORT TON 1.1023 E-06 1.1023 E-12 1.1023 E-03 1.1023 E. 00 1.0000 E 00 1.1200 E 00 7.1428 E-08 3.1250 E-05 5.0000 E-04 LONG TON 9.0421 E-07 9.8421 £-13 9.B421 E-04 9,8421 E-01 8.9286 E-Oi 1.0000 E 00 6.3775 E-08 2.7902 E-05 4.4643 E-04 GRAIN 1.5432 E 01 1.5432 E-05 1.5432 E 04 1.5432 E 07 1.4000 E 07 1.5680 I 07 1.0000 E 00 4,3750 E 02 7.0000 E 03 OUNCE IAVDP) 5,5274 E-02 3,5274 E-08 4.5274 E 01 *, 5274 E 04 3,2000 E 04 9.584Q E 04 2.2857 E-03 1.0000 "E 00 1.6000 E 01 LB (A\ 2.2Q46 E-03 2.20*6 E-09 2.2Q46 E 00 2,2046 E 03 2,0000 E 03 2,; o E 03 1.4286 E-04 E-02 1.0000 E 00 TO CONVERT A VALUE FROM A GIVEN UNIT TO A DESIRED UNIT, MULTIPLY THE GIVEN VALUE BY THE FACTOR OPPOSITE THE GIVEN UNITS AND BENEATH THE DESIRED UNIT. NOTE THAT E-XX MEANS 10 TO THE -XX POWER.------- CONVERSION FACTORS - FLO* DESIRED UNtTS CU METER CU METER LITER LITER LITER CU FT CU FT CU FT CU C1 PER SEC PER HR PER SEC PER WIN PER HR PER SEC PER MIN PER HR PER SEC GIVEN UNITS Jj, H 3 o V) s I o o 55 •a - O z w Cfl H 3 H M J/) cu METER PER SEC cu METER PER MR LITER PER SEC LITER PER'MIN LITER PER MR CU FT PER SEC cu FT PER MIN cu FT PER MR cu CM PE« SEC TO CONVERT K AND BENEATH 1.0000 E 00 2.7778 E-04 1.0000 E-03 1.6667 E-03 2.7779 E-07 2.8317 E-02 4.7193 E-04 7.8638 E-06 1.0000 E-06 3.6000 E 03 l.OQOo E 00 3.6001 E 00 6.0002 E-02 1.0000 E-03 1.0194 E 02 1.6990 E 00 2.8317 E-02 3.6000 E-03 VALUE FROM A GIVEN UNIT TO A THE DESIRED UNIT. NOTE THAT 9.9997 E 02 2.7777 E-01 1.0000 E 00 1.6667 E-02 2.7778 E-04 2.8316 E 01 4.7194 E-01 7.8636 E-03 9.9997 E-04 DESIRED 9.9998 E 04 1.6666 E 01 6.0000 E 01 1.0000 E 00 1.6667 E-02 1.6990 E 03 2.8316 E 01 4.7194 E-01 9.9998 E-02 UNIT, MULTIPLY 3.5999 E 06 9.9997 E 02 3.6000 E 03 6.0000 E 01 1.0000 E 00 1.0194 E 03 1.6990 E 03 2.8316 E 01 3.9999 E 00 THE GIVEN 3.9314 E 01 9.8096 E-03 3.3313 E-02 3.8839 E-04 9.8098 E-06 I. 0000 E 00 1.6667 E-02 2.7778 E-04 3.3314 E-05 VALUE BY 2.1189 E 03 3.8837 E.01 2.1189 E 00 3.3313 E-02 3. 8839 E-04 6.0000 E 01 1.0000 E 00 1.6667 E-02 2.1189 E-03 THE FACTOR 1.2713 E 09 9.3314 E 01 1.2714 E 02 2.1189 E 00 9.9313 E-02 9.6000 E 03 6.0000 E 01 1.0000 E 00 1.2713 E-01 OPPOSITE 1.0000 E 06 2.7778 E 02 1.0000 E 03 1.6667 E 01 2.7779 E-01 2,8317 E 04 4.7193 E 02 7.8658 E 00 1.0000 E 00 THE GIVEN UNITS E-XX MRANS 10 TO THE -XX POWER.------- •0 V n a ft X CONVERSION FACTORS - CONCENTRATION, DENSITY DESIRED GIVEN UNITS GRAM PER CU METER MG PER CU METER MICROGRAM PER CU M MICROGRAM PER LITER GRAIN PER CU FT OUNCE PER CU FT LB PER CU FT GRAM PER CU FT LB PER CU METER UNITS GRAM PER cu METER 1.0000 E 00 l.OQOO E-03 1.0000 E-06 9.9997 E-04 2.2883 E 00 1.0011 E 03 1.6018 E 04 3.5314 E 01 4,3359 E 02 MG PER CU METER 1.0000 E 03 1.0000 E 00 1.0000 E-03 9.9997 E-01 2.2883 E 03 1.0011 E 06 1.6018 E 07 3.3314 E 04 4.3359 E 05 MICROGRAM PER cu M 1.0000 E 06 1.0000 E 03 1.0000 E 00 9.999T E 02 2,2883 E 06 1,0011 E 09 1.6018 E 10 3.331* E 07 4.5359 E 08 MICROGRAM PER LITER 1.0000 E 03 1.0000 E 00 I. 0000 E-03 1.0000 E 00 2.2884 E 03 1.0012 E 06 1.6019 E 07 3.3315 E 04 4.5360 E 05 GRAIN PER CU FT 4,3700 E-01 4,3700 E-0* 4,3700 E-07 4,3699 E-04 1,0000 E 00 4.3730 E 02 7.0000 E 03 1.5432 E 01 1.9822 E 02 OUNCE PER CU FT 9.9883 E-04 9.9885 E-07 9,9885 E-10 9.9883 E-07 2,2837 E-03 1.0000 E 00 1,6000 E 01 3.3274 E-02 4.5307 E-01 L8 PER CU 6.2428 E-05 6.2428 E-08 6.2428 E-ll 6.2427 E-08 1.4286 E-04 6.2500 E-02 1.0000 E 00 2.2046 E-03 2.8317 E-02 GRAM PER FT CU PT 4,8317 E-02 4.8317 E-03 4,8317 E-08 4.8316 E-05 6.4799 E-02 4.83*9 E 01 4.5359 E 02 1.0000 £ 00 1.284* E 01 UB PER CU M 2.2046 E-03 2.2046 E-06 2.2046 E-09 2,2046 E-06 3.U449 E-03 2.2072 E 00 3.3314 E 01 7.7835 E-02 1.0000 E 00 TO CONVERT A VALUE FROM A GIVEN UNIT TO A DESIRED UNIT, MULTIPLY THE GIVEN VALUE BY THE FACTOR OPPOSITE THE GIVEN UNITS AND BENFATH THE DFSI9ED UNIT. NOTE THAT E-XX MEANS 10 TO THE -XX POWER.------- -1 oo CONVERSION FACTORS - DEPOSITION RATF •SHORT TON .STAT. MILE) DESIRED UNITS GM PER SO KG PER SO MG PER SO TON PER SO OZ PER SO LB PER GN PER SO *G PER SO M PER MO KM PER MO CM PER MO MI PER MO FT PER MO ACRE PERMO FT PER MO IN PER MO GIVEN UNITS •^ H 3 O •3 SC I n g 55 "0 3 Cfl O M cn N4 H M GM PER SO M PER MO KG PER SO KM PER MO MG PER SO CM PER MO TON PER SO MI PER MO 01 PER SO FT PER MO LB PER ACRE PERMO GM PER SO FT PER MO MG PER SO IN PER MO TO CONVERT AND BENEATH 1.0000 E 00 1.0000 E-03 1.0000 E 01 3.5026 E-01 3.0919 E 02 1.1208 E-01 1.0764 E 01 1.9900 E 00 A VALUE FROM A GIVEN THE DESIRED UNIT. I. 0000 E 03 1.0000 E 00 1.0000 E 04 3.9026 E 02 3.0519 E 09 1.1208 E 02 1.0764 E 04 1.9900 E 03 UNIT TO A NOTE THAT 1.0000 E-01 1.0000 E-04 1.0000 E 00 3.9026 E-02 3.0919 E 01 1.1208 E-02 1.0764 E 00 1.9900 E-01 DESIRED 2.8550 E 00 2.8590 E-03 2.8990 E 01 1.0000 E 00 8.7120 E 02 3.2000 E-01 3.0731 E 01 4.4292 E 00 UNIT. MULTIPLY E-XX MEANS 10 TO THE - 3.2771 E-03 3.2771 E-06 3.2771 E-02 1.1478 E-03 1.0000 E 00 3.6731 E-04 3.9274 E-02 9.0799 E-03 THE GIVEN XX POWER. 8.9218 E 00 8.9218 E-03 8.9218 E 01 3.1250 E 00 2.7225 E 03 1.0000 E 00 9.6033 E 01 1.3829 E 01 VALUE BY 9.2903 E-02 9.2903 E-05 9.2903 E-01 3.2541 E-02 2.8349 E 01 1.0413 E-02 1.0000 E 00 1.4400 E.01 THE FACTOR 6.4516 E-01 6.4516 E-04 6.4516 E 00 2.2598 E-01 1.9687 E 02 7.2313 E-02 6.9444 E 00 1.0000 E 00 OPPOSITE THE GIVEN UNITS------- CONVERSION FACTORS - PRESSURE DESIRED UNITS MILLIBAR BAR GIVEN UNITS ATMOSPHERE OYNES KG LBS MM MERCURY IN MERCURY PER SO CM PER SO CM PER SO IN MILLIBAR BAR ATMOSPHERE DYNES PER SO CM KG PER SO CM LBS PER SO IN MM MERCURY IN MERCURY 1.0000 E 00 1.0000 E 0) 1.0199 E OS 1.0000 E-09 9.8066 E 02 6,8947 E 01 1.3932 E 00 3. 386* E 01 1.0000 E-03 1.0000 E 00 1.0133 E 00 1.0000 E-06 9.8066 E-01 ». 89*7 E-02 1.3332 E-03 3.3B«4 E-02 9.8692 E-04 9. 8692 E-01 1.0000 E 00 9.8692 E-07 9.6784 E-01 6.8046 E-02 1*3138 E-03 3.3421 E-02 l.OQOO E 0) 1.0000 E 06 1.0193 E 06 1.0000 E 00 9. 8Q66 E 09 6.8947 E 04 1.3332 E 09 9.9864 E 04 1.0197 E-03 1.0197 E 00 1.0992 E 00 1.0197 E-06 1.0000 E 00 7.0907 E-02 1.9999 E-03 3.4332 E-02 1.4904 E-02 1.4904 E 01 1.4696 E 01 1.4904 E-03 1.4229 E 01 1.0000 E 00 1.9997 E-02 4.9119 E-01 7.9006 C-01 7.9006 E 02 7.6000 E 02 7.3006 E.04 7.3936 E 02 9.1719 E 01 1*0000 E 00 2.9400 E 01 2.9990 E-02 '.9990 E 01 2.9921 E 01 2.999Q E-09 2.8999 E 01 2,0960 E 00 •.9970 E-02 1.0000 E 00 TO CONVERT A VALUE FROM A GIVEN UNIT TO A DESIRED UNIT. MULTIPLY THE GIVEN VALUE BY THE FACTOR OPPOSITE THE GIVEN UNITS AND BENEATH THE DESIRED UNIT. NOTE THAT E-XX MEANS 10 TO THE -XX POWER.------- CONVERSION FACTORS - TIME DESIRED UNITS SECOND GIVEN UNITS MINUTE HOUR WEEK MONTH (28) MONTH[J, H g O C/J "B a M o 2 V) •fl « O 5! W V) H H PJ 7) SECOND MINUTE WOUR WEEK MONTH (28) MONTH (30) MONTH 131) YEAR (365) YEAR (366) TO CONVERT A AND BENEATH I. 0000 E 00 1.6667 E-02 2.7778 E-04 1.6534 E-06 4.1336 E-07 3.8980 E-07 3.7336 E-07 3.1710 E-08 3.1623 E-08 VALUE FROM A GIVEN THE DESIRED UNIT. 6.0000 E 01 1.0000 E 00 1.6667 E-02 9.9206 E-05 2.4802 E-05 2.3148 E-05 2.2401 E-05 1.9026 E-06 1*8974 E-06 UNIT TO A NOTE THAT 3.6000 E 03 6.0000 E 01 1.0000 E 00 5.9524 E-03 1.4881 E-03 1.3889 E-03 1.3441 E-03 1.1416 E-04 1.1984 E-04 6.0480 E 05 1.0080 E 04 1.6800 E 02 1.0000 E 00 2.5000 E-01 2.3333 E-Ol 2.2581 E-01 1.9178 E-02 1.9126 E-02 DESIRED UNIT. MULTIPLY E-xx MEANS 2.4192 E 06 4.0320 E 04 6.7200 E 02 4.0000 E 00 1.0000 E 00 9.3333 E-01 9.0323 E-Ol 7,6712 E-02 7,6503 E-02 THE GIVEN 2.5920 E 06 4.3200 E 04 7.2000 E 02 4.2857 E 00 1,0714 E 00 1.0000 E 00 9.6774 E-01 8.2192 £-02 8.1967 E-02 VALUE BY 2.6784 E 06 4.4640 E 04 7.4400 E 02 4.4286 E 00 1*1071 E 00 1*0333 E 00 1.0000 E 00 8.4932 E.02 8.4699 E-02 THE FACTOR 3,1936 E 07 5.2360 E 09 8.7600 E 03 5.2143 E 01 1.3036 E 01 1.2167 E 01 1,1774 "E 01 1.0000 E 00 9.9727 E.Ol OPPOSITE THE 3.1622 E 07 5.2704 E 09 8.7840 E 03 9,2286 E 01 1,3071 E 01 1.2200 E 01 1.1806 E 01 1.0027 E 00 1.0000 E 00 GIVEN UNITS 10 TO THE -XX POWER. ------- •8 1 rnNi/Fueip.si P \. LJ" V ^ ^ .^ I '.• ''I ~ DfSlpFO GfVEM UNITS WATT (INT) Kll OWATT (INT) MERAWATT (INT) CA| (IMT) PER SEC BTU PER 'UN BTU PER MR JOULES ABS PER SEC *ATT uns) ELECT. HORSEPOWER TT0"5 - P"d£3 U'MTS xMT (INT) I. o^oo r n-j l.ynon F 03 1.0000 E 06 4.1H7A F 10 1.7S8H F 01 2.9313 E-il 9.9081 E-01 9.90H1 F.-Ol 7.4586 f. 02 KILO"*' r (I'M! 1 .00110 t-0* 1.0000 E 00 1.00'»0 t o* 4.18'6 E-0* 1.75M8 E-OiJ 2.0313 E-04 9.99H1 E-0* 9.09HI E-0«« '.45M6 E-01 v|F.G««ATr (INT) 1.0000 E-06 1.0000 F-03 1.0000 F 'JO 4.1-76 F.-O& 1.758fl F-05 2.9313 F.«-07 9.99H1 E-07 9.9981 E-07 7.4^86 E-04 CAI. tl'JT) dTU I'EP SFC PEP MI 2.3-«flO 5.6P57 E-'U E-02 2.4HflO 5.6857 E '•?. E 01 2.3'^HO 5.6H5? E "5 E 04 1 l.OOQO 2.3B10 E "0 E-01 4.2000 1.0000 E '.'0 E 00 7.o;inn 1.6667 E-o? E-02 2.3Hf5 »,6S46 E-rM E-02 2.3H75 5.6846 E-01 E-02 I. '"11 4.2407 E "2 E 01 BTU N PPR HR 3.4114 E 00 3.4114 E 03 3.4114 E 06 1.4285 E 01 6.0000 E 01 1.0000 E 00 3.4108 E 00 3.4108 E 00 2.5444 E 03 JDULES PER 1.0002 E 00 1.0002 E 03 1.0002 E 06 4.188* E 00 1.7591 E 01 2.9319 E-01 1.0000 E 00 1.0000 E 00 7.4600 E 02 ABS wATT (ABS) SEC 1.0002 E 00 1.0002 E 03 1.0002 E 06 4.188* E 00 1.7591 E 01 2.9319 E-01 1.0000 E 00 1,0000 E 00 7.4600 E 02 ELECT. HORSEPI 1.3*0? E-03 1.3*0? E 00 1.3*0? E 03 5.61*5 E-03 2.3581 E-02 3.9301 E-O* 1.3*05 E-03 1.3*05 E-03 1.0000 E 00 TO CQNVrRT A v/A| AND BENFATH 1ME FROM A GlVtN UNI" T3 A DESIRF^ UNIT, MULTIPLY THE GIVEN VALUE »Y THE FACTOR OPPOSITE THE GIVEN UNITS UNIT. NOTr. THAT E-X* MFANS 10 TO THE -XX POWER.------- I o VJ o g 35 •« S — o w 3 CONVERSION FACTORS - ENERGY. WORK DESIRED UNITS ERG DYNE-C* GIVEN UNITS ERG DYNE-CM ABS JOULE ASS JOULE CAL (INT) CAL (15) INT KW-HR ABS KW-HR BTU 1.0000 E 00 1.0000 E 00 1.0000 C 07 4.1868 E 07 4.1899 E 07 3.6007 E 13 3.6000 E 13 1.0991 E 10 1.0000 E 00 1.0000 E 00 1.0000 E 07 4.1868 E 07 4.1899 E 07 3.6007 E 13 3.6000 E 13 1.0991 E 10 1.0000 E-07 1.0000 E-07 1.0000 E 00 4.1868 E 00 4.1899 E 00 3.6007 E 06 3.6000 E 06 1.0391 E 03 2.3884 E-Ofl 2.3884 E-OB 2.3884 E-01 1.0000 E 00 9.9968 E-01 8.6QOO E 09 8.9984 E 09 2.9200 E 02 2.3892 E-08 2.3892 E-08 2.3892 E-01 1.0003 E 00 1,0000 E 00 8.6027 E 09 8.6011 E 03 2.9208 E 02 2.7773 E-14 2.7773 E-14 2.7773 E-07 1.1628 E-06 1.1624 E-06 1.0000 E 00 9.9981 E-01 2.9302 E-04 2,7778 E-14 2.7778 E-14 2.7778 E-07 1.1630 C-06 1.1626 E-06 1,0002 E 00 1.0000 E 00 2,9307 E-04 9.4781 E-ll 9.4781 E-U 9.4781 E-04 9.96B3 E-03 3,9671 E-03 3.4128 E 03 3.4121 E 03 1,0000 E 00 CAL (13) INT KW-HR ABS KW-HR BTU TO CONVERT A VALUE FROM A GIVEN UNIT TO A DESIRED UNIT, MULTIPLY THE GIVEN VALUE BY THE FACTOR OPPOSITE THE GIVEN UNITS AND BENEATH THE DESIRED UNIT, NOTE THAT E-XX MEANS 10 TO THE -XX POWER. H W V)------- CONVERSION FACTORS - ENERGY PER UNIT AREA DESIRED UNITS LANGLEY CAL <19» BTU INT KM-HR ABS JOULES PER SO CM PER SO FT PER SO M PER SO CM GIVEN UNITS LANGLEY CAL 119) PER SO CM BTU PER SO FT INT KW-HR PER SO M ABS JOULES PER SO CM 1.0000 E 00 1.0000 E 00 2.7193 E-01 8.6029 E 01 2.3892 E-01 1.0000 E 00 1.0000 E 00 2.7133 E-01 8.6029 E 01 2.3892 E-01 3.6899 E 00 3.6899 E 00 1.0000 E 00 3.1706 E 02 8.8094 E-01 1.1624 E-02 1.1624 E-02 3.1940 E-03 1.0000 E 00 2.7772 E-03 4.1899 E 00 4.1899 E 00 1.1397 E 00 3.6007 E 02 1.0000 E 00 TO CONVERT A VALUE FROM A GIVEN UNIT TO A DESIRED UNIT. MULTIPLY THE GIVEN VALUE BY THE FACTOR OPPOSITE THE GIVEN UNITS AND BENEATH THE DESIRED UNIT. NOTE THAT E-XX MEANS 10 TO THE -XX POWER. oo CO------- CONVERSION FACTORS - POWER PER UNIT AREA ARE OEG) DESIRED UNITS CAL PER SO CAL PER SO LANflLEY CAL PER SO BTU PER SO BTU PER SO ABS HATT M PER SEC CM PER MIN PER MlN CM PER DAy FT PER MIN FT PER DAY PER SO CM GIVEN UNITS * GO 8 9 E Q a i § 3 M i V O M O H 3 O CA TJ 2 2 n 2 CA TS CA 0 S! M CA H H M CAL PER SO M PER SEC CAL PER SO CM PER MIN LANGLEY PER MIN CAL PER SO CM PER DAY BTU PER SO FT PER MIN BTU PER SO FT PER DAY ABS WATT PER SO CM TO CONVERT A AND BENEATH 1.0000 E 00 1.6667 E 02 1.6667 E 02 1.1574 E-01 4.5222 E 01 3.140* E-02 2.3892 E 03 VALUE FROM A GIVEN THE DESISED UNIT. 6.0000 E-03 1.0000 E 00 1.0000 E 00 ft. 9444 E-04 2.7133 E-01 1.8843 E-0* l.*335 E 01 UNIT TO A NOTE THAT 6.0000 E-03 1.0000 E 00 1.0000 E 00 6.9444 E-04 2.7133 E-01 1.8843 E-04 1.4339 E 01 DESIRED 8.6400 E 00 1.4400 E 03 1.440Q E 03 1.0000 E 00 3.9072 E 02 2.7133 E-01 2.0643 E 04 UNIT, MULTIPLY 2.2113 E-02 3.6835 E 00 3.6855 E 00 2.5594 E-03 1.0000 E 00 6.9445 E-04 5,2833 E 01 THE GIVEN 3.1843 E 01 5.3071 E 03 3.3071 E 03 3.6855 E 00 1.4400 E 03 1.0000 E 00 7,6079 E 04 VALUE BY 4.1855 E.04 6.9758 E-02 6.9758 E-02 4.8443 E-05 1.8928 E-02 1.3144 E-03 1.0000 E 00 THE FACTOR OPPOSITE THE GIVEN UNITS E-XX MEANS 10 TO THE -XX POWER.-------

AP-26 ENVIRONMENTAL HEALTH SERIES Air Pollution WORKBOOK OF ATMOSPHERIC DISPERSION ESTIMATES H U. S. DEPARTMENT OF HEALTH, EDUCATION, AND WELFARE Public Health Service Consumer Protection and Environmental Health Service ------- WORKBOOK OF ATMOSPHERIC DISPERSION ESTIMATES D. BRUCE TURNER Air Resources Field Research Office, Environmental Science Services Administration U. S. DEPARTMENT OF HEALTH, EDUCATION, AND WELFARE Public Health Service Consumer Protection and Environmental Health Service National Air Pollution Control Administration Cincinnati, Ohio Revised 1969 ------- The ENVIRONMENTAL HEALTH SERIES of reports was established to re- port the results of scientific and engineering studies of man's environment: The com- munity, whether urban, suburban, or rural, where he lives, works, and plays; the air, water, and earth he uses and re-uses; and the wastes he produces and must dispose of in a way that preserves these natural resources. This SERIES of reports provides for professional users a central source of information on the intramural research activities of the Centers in the Bureau of Disease Prevention and Environmental Control, and on their cooperative activities with state and local agencies, research institutions, and industrial organizations. The general subject area of each report is indicated by the letters that appear in the publication number; the indicators are AP — Air Pollution RH — Radiological Health UIH — Urban and Industrial Health Triplicate tear-out abstract cards are provided with reports in the SERIES to facilitate information retrieval. Space is provided on the cards for the user's accession number and additional key words. Reports in the SERIES will be distributed to requesters, as supplies permit. Re- quests should be directed to the Center identified on the title page. Public Health Service Publication No. 999-AP-26 ------- PREFACE This workbook presents some computational techniques currently used by scien- tists working with atmospheric dispersion problems. Because the basic working equa- tions are general, their application to specific problems usually requires special care and judgment; such considerations are illustrated by 26 example problems. This workbook is intended as an aid to meteorologists and air pollution scientists who are required to estimate atmospheric concentrations of contaminants from various types of sources. It is not intended as a complete do-it-yourself manual for atmospheric dispersion estimates; all of the numerous complications that arise in making best esti- mates of dispersion cannot be so easily resolved. Awareness of the possible complex- ities can enable the user to appreciate the validity of his "first approximations" and to realize when the services of a professional air pollution meteorologist are required. iii ------- ACKNOWLEDGMENTS The author wishes to express his appreciation to Robert A. McCormick, Paul A. Humphrey, and other members of the Field Research Office for their helpful dis- cussions and review; to Jean J. Schueneman, Chief, Criteria and Standards Develop- ment, National Center for Air Pollution Control, who suggested this workbook; to Phyllis Polland and Frank Schiermeier, who checked the problem solutions; to Ruth Umfleet and Edna Beasley for their aid; and to the National Center for Air Pollution Control, Public Health Service, and Air Resources Laboratory, Environmental Science Services Administration, for their support. iv ------- CONTENTS ABSTRACT yii Chapter 1. INTRODUCTION 1 Chapter 2. BACKGROUND 3 Chapter 3. ESTIMATES OF ATMOSPHERIC DISPERSION 5 Coordinate System _ 5 Diffusion Equations _ 5 Effects of Stability _ 6 Estimation of Vertical and Horizontal Dispersion 7 Evaluation of Wind Speed _ 7 Plots of Concentrations against Distance - 7 Accuracy of Estimates 7 Graphs for Estimates of Diffusion _ 10 Plotting Ground-Level Concentration Isopleths _ 10 Areas Within Isopleths _ 17 Calculation of Maximum Ground-Level Concentrations _ 17 Review of Assumptions _ 17 Chapter 4. EFFECTIVE HEIGHT OF EMISSION _ 31 General Considerations _ 31 Effective Height of Emission and Maximum Concentration ._ 31 Estimates of Required Stack Heights 31 Effect of Evaporative Cooling 32 Effect of Aerodynamic Downwash 32 Chapter 5. SPECIAL TOPICS 35 Concentrations in an Inversion Break-up Fumigation 35 Plume Trapping _ 36 Concentrations at Ground Level Compared to Concentrations at the Level of Effective Stack Height from Elevated Con- tinuous Sources _ 36 Total Dosage from a Finite Release 37 Crosswind-Integrated Concentration 37 Estimation of Concentrations for Sampling Times Longer than a Few Minutes 37 Estimation of Seasonal or Annual Average Concentrations at a Receptor from a Single Pollutant Source - 38 Meteorological Conditions Associated with Maximum Ground-Level Concentrations 38 Concentrations at a Receptor Point from Several Sources 39 Area Sources 39 Topography 40 Line Sources 40 Instantaneous Sources 41 Chapter 6. RELATION TO OTHER DIFFUSION EQUATIONS 43 Chapter 7. EXAMPLE PROBLEMS - 45 Appendices: 57 1 — Abbreviations and Symbols - 59 2 — Characteristics of the Gaussian Distribution _ 61 3 — Solutions to Exponentials 65 4 — Constants, Conversion Equations, Conversion Tables _ 69 ------- ABSTRACT This workbook presents methods of practical application of the binormal con- tinuous plume dispersion model to estimate concentrations of air pollutants. Estimates of dispersion are those of Pasquill as restated by GifTord. Emphasis is on the estima- tion of concentrations from continuous sources for sampling times up to I hour. Some of the topics discussed are determination of effective height of emission, extension of concentration estimates to longer sampling intervals, inversion break-up fumigation concentrations, and concentrations from area, line, and multiple sources. Twenty-six example problems and their solutions are given. Some graphical aids to computation are included. VH ------- Chapter 1 — INTRODUCTION During recent years methods of estimating at- mospheric dispersion have undergone considerable revision, primarily due to results of experimental measurements. In most dispersion problems the relevant atmospheric layer is that nearest the ground, varying in thickness from several hundred to a few thousand meters. Variations in both thermal and mechanical turbulence and in wind velocity are greatest in the layer in contact with the surface. Turbulence induced by buoyancy forces in the atmosphere is closely related to the vertical temperature structure. When temperature decreases with height at a rate higher than 5.4°F per 1000 ft (1°C per 100 meters), the atmosphere is in un- stable equilibrium and vertical motions are en- hanced. When temperature decreases at a lower rate or increases with height (inversion), vertical motions are damped or reduced. Examples of typ- ical variations in temperature and wind speed with height for daytime and nighttime conditions are illustrated in Figure 1-1. 600r 500 400 300 o 200 100 0 -I 23456 TEMPERATURE. °C 7 8 9 10 II 12 1 2 3 4 5 6 7 8 WIND SPEED, m/»«c 9 10 II Figure 1-1. Examples of variation of temperature and wind speed with height (after Smith, 1963). The transfer of momentum upward or down- ward in the atmosphere is also related to stability; when the atmosphere is unstable, usually in the daytime, upward motions transfer the momentum "deficiency" due to eddy friction losses near the earth's surface through a relatively deep layer, causing the wind speed to increase more slowly with height than at night (except in the lowest few meters). In addition to thermal turbulence, rough- ness elements on the ground engender mechanical turbulence, which affects both the dispersion of material in the atmosphere and the wind profile (variation of wind with height). Examples of these effects on the resulting wind profile are shown in Figure 1-2. As wind speed increases, the effluent from a continuous source is introduced into a greater vol- ume of air per unit time interval. In addition to this dilution by wind speed, the spreading of the material (normal to the mean direction of trans- port) by turbulence is a major factor in the dis- persion process. The procedures presented here to estimate at- mospheric dispersion are applicable when mean wind speed and direction can be determined, but meas- urements of turbulence, such as the standard de- viation of wind direction fluctuations, are not avail- able. If such measurements are at hand, techniques such as those outlined by Pasquill (1961) are likely to give more accurate results. The diffusion param- ------- eters presented here are most applicable to ground- level or low-level releases (from the surface to about 20 meters), although they are commonly applied at higher elevations without full experimental valida- tion. It is assumed that stability IB the same throughout the diffusing layer, and no turbulent transfer occurs through layers of dissimilar stability characteristics. Because mean values for wind direc- tions and speeds are required, neither the variation of wind speed nor the variation of wind direction with height in the mixing layer are taken into ac- count. This usually is not a problem in neutral or unstable (e.g., daytime) situations, but can cause over-estimations of downwind concentrations in stable conditions. REFERENCES Davenport, A. G., 1963: The relationship of wind structure to wind loading. Presented at Int. Conf. on The Wind Effects on Buildings and Structures, 26-28 June 63, Natl. Physical Lab- oratory, Teddington, Middlesex, Eng. Pasquill, F., 1961: The estimation of the dispersion of wind borne material. Meteorol. Mag. 90, 1063, 33-49. Smith, M. E., 1963: The use and misuse of the at- mosphere, 15 pp., Brookhaven Lecture Series, No. 24, 13 Feb 63, BNL 784 (T-298) Brook- haven National Laboratory. 600,— URBAN AREA SUBURBS LEVEL COUNTRY GRADIENT WIND 1-2. Examples of variation of wind with height over different size roughness elements (ngures are percentages of gradient wind); (from Davenport 1963). ATMOSPHERIC DISPERSION ESTIMATES ------- Chapter 2 —BACKGROUND For a number of years estimates of concentra- tions were calculated either from the equations of Sutton (1932) with the atmospheric dispersion parameters Cy, Cf, and n, or from the equations of Bosanquet (1936) with the dispersion parameters p and q. Hay and Pasquill (1957) have presented experi- mental evidence that the vertical distribution of spreading particles from an elevated point is re- lated to the standard deviation of the wind eleva- tion angle, <7K, at the point of release. Cramer (1957) derived a diffusion equation incorporating standard deviations of Gaussian distributions: a, for the distribution of material in the plume across wind in the horizontal, and ot for the vertical distribution of material in the plume. (See Appendix 2 for prop- erties of Gaussian distributions.) These statistics were related to the standard deviations of azimuth angle, CTA, and elevation angle, *K, calculated from wind measurements made with a bi-directional wind vane (bivane). Values for diffusion param- eters based on field diffusion tests were suggested by Cramer, et al. (1958) (and also in Cramer 1959a and 1959b). Hay and Pasquill (1959) also pre- sented a method for deriving the spread of pollut- ants from records of wind fluctuation. Pasquill (1961) has further proposed a method for esti- mating diffusion when such detailed wind data are not available. This method expresses the height and angular spread of a diffusing plume in terms of more commonly observed weather parameters. Sug- gested curves of height and angular spread as a function of distance downwind were given for sev- eral "stability" classes. Gifford (1961) converted Pasquill's values of angular spread and height into standard deviations of plume concentration distri- bution, a, and OE. Pasquill's method, with Gifford's conversion incorporated, is used in this workbook (see Chapter 3) for diffusion estimates. Advantages of this system are that (1) only two dispersion parameters are required and (2) results of most diffusion experiments are now being re- ported in terms of the standard deviations of plume spread. More field dispersion experiments are being conducted and will be conducted under conditions of varying surface roughness and atmospheric sta- bility. If the dispersion parameters from a specific experiment are considered to be more representative than those suggested in this workbook, the param- eter values can be used with the equations given here. REFERENCES Bosanquet, C. H., and J. L. Pearson, 1936: The spread of smoke and gases from chimneys. Trans. Faraday Soc., 32, 1249-1263. Cramer, H. E., 1957: A practical method for esti- mating the dispersion of atmospheric contami- nants. Proc. 1st Natl. Conf. on Appl. Meteorol. Amer. Meterol. Soc. Cramer, H. E., F. A. Record, and H. C. Vaughan, 1958: The study of the diffusion of gases or aerosols in the lower atmosphere. Final Report Contract AF 19(604)-1058 Mass. Inst. of Tech., Dept. of Meteorol. Cramer, H. E., 1959a: A brief survey of the mete- orological aspects of atmospheric pollution. Bull. Amer. Meteorol. Soc., 40, 4, 165-171. Cramer, H. E., 1959b: Engineering estimates of atmospheric dispersal capacity. Amer. Ind. Hyg. Assoc. J., 20, 3, 183-189. Gifford, F. A., 1961: Uses of routine meteorological observations for estimating atmospheric disper- sion. Nuclear Safety, 2, 4, 47-51. Hay, J. S., and F. Pasquill, 1957: Diffusion from a fixed source at a height of a few hundred feet in the atmosphere. J. Fluid Mech., 2, 299-310. Hay, J. S., and F. Pasquill, 1959: Diffusion from a continuous source in relation to the spectrum and scale of turbulence, pp 345-365 in Atmos- pheric Diffusion and Air Pollution, edited by F. N. Frenkiel and P. A. Sheppard, Advances in Geophysics, 6, New York, Academic Press, 471 pp. Pasquill, F., 1961: The estimation of the dispersion of windbome material. Meteorol. Mag., 90, 1063, 33-49. Sutton, O. G., 1932: A theory of eddy diffusion in the atmosphere. Proc. Roy. Soc., A, .735, 143- 165. Background ------- Chapter 3 —ESTIMATES OF ATMOSPHERIC DISPERSION This chapter outlines the basic procedures to be used in making dispersion estimates as sug- gested by Pasquill (1961) and modified by Gifford (1961). COORDINATE SYSTEM In the system considered here the origin is at ground level at or beneath the point of emission, with the x-axis extending horizontally in the direc- tion of the mean wind. The y-axis is in the hori- zontal plane perpendicular to the x-axis, and the z-axis extends vertically. The plume travels along or parallel to the x-axis. Figure 3-1 illustrates the coordinate system. DIFFUSION EQUATIONS The concentration, x, of gas or aerosols (parti- cles less than about 20 microns diameter) at x,y,z from a continuous source with an effective emission height, H, is given by equation 3.1. The notation used to depict this concentration is x (x,y,z;H). H is the height of the plume centerline when it 7 becomes essentially level, and is the sum of the physical stack height, h, and the plume rise, AH. The following assumptions are made: the plume spread has a Gaussian distribution (see Appendix 2) in both the horizontal and vertical planes, with standard deviations of plume concentration distri- bution in the horizontal and vertical of a, and a,, respectively; the mean wind speed affecting the plume is u; the uniform emission rate of pollutants is Q; and total reflection of the plume takes place at the earth's surface, i.e., there is no deposition or reaction at the surface (see problem 9). x (x,y,z;H) (3.1) 'Note: exp —a/b = e~«/b where e is the base ol natural logarithms and is approximately equal to 2.7183. (x,-y,Z) (x,-y,0) Figure 3-1. Coordinate system showing Gaussian distributions in the horizontal and vertical. Estimates ------- Any consistent set of units may be used. The most common is: X (g m"-) or, for radioactivity (curies m~s) Q (g sec"1) or (curies sec"1) u (m sec"1) CTy, a,, H,x,y, and z (m) This equation is the same as equation (8.35) p. 293 of Sutton (1953) when a's are substituted for Sut- ton's parameters through equations like (8.27) p. 286. For evaluations of the exponentials found in Eq. (3.1) and those that follow, see Appendix 3. x is a mean over the same time interval as the time interval for which the a's and u are representative. The values of both a, and a, are evaluated in terms of the downwind distance, x. Eq. (3.1) is valid where diffusion in the direc- tion of the plume travel can be neglected, that is, no diffusion in the x direction. This may be assumed if the release is continuous or if the duration of release is equal to or greater than the travel time (x/u) from the source to the location of interest. For concentrations calculated at ground level, i.e., z = 0, (see problem 3) the equation simplifies to: X (x,y,0;H) a, a, U exp [-4(^)1 (3.2) Where the concentration is to be calculated along the centerline of the plume (y = 0), (see problem 2) further simplification results: (3.3) For a ground-level source with no effective plume rise (H = 0), (see problem 1): Q x U,0,0;0) ir a, a, U (3.4) EFFECTS OF STABILITY The values of af and a, vary with the turbulent structure of the atmosphere, height above the sur- face, surface roughness, sampling time over which the concentration is to be estimated, wind speed, and distance from the source. For the parameter values given here, the sampling time is assumed to be about 10 minutes, the height to be the lowest several hundred meters of the atmosphere, and the surface to be relatively open country. The turbulent structure of the atmosphere and wind speed are considered in the stability classes pre- sented, and the effect of distance from the source is considered in the graphs determining the parameter values. Values for o, and ------- Some preliminary results of a dispersion experi- ment in St. Louis (Pooler, 1965) showed that the dispersion over the city during the daytime behaved somewhat like types B and C; for one night experi- ment |