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AIR POLLUTION 507has developed the following equations that provide an approximate fit.Sy = axO.894," (6-22)Sz = cxd + f (6-23)where the constants a, c, d, and f are defined in Table 6-7. These equations weredeveloped to yield Sy and Sz in meters for downwind distance x in kilometers.Example 6-4. It has been estimated that the elnission of 502 from a coal-fired powerplant is 1,656.2 gis. At 3 kIn downwind on an overcast summer afternoon, what isthe centerline concentration of 502 if the wind speed is 4.50 m/s? (Note: "centerline"implies y = 0.)Stack parameters:Height = 120.0 mDiameter = 1.20 mExit velocity = 10.0 m/sTemperature = 315°CAtmospheric conditions:Pressure = 95.0 kPaTemperature = 25.0°CSolution. We begin by determining the effective stack height (H).dB = QQ~~ [1.5 + (2.68 X 10-i95.0)~~~~ 1.20) ]dB = 8.0mH = 120.0 + 8.0 = 128.0 mNext, we must determine the atmospheric stability class. The footnote to Table 6-6 indicates that the D class should be used for overcast conditions.From Figures 6-19 and 6-20, we can determine that at 3 kIn downwind with a Dstability the plume standard deviations are as follows:Sy = 190mSz = 65 mThus,1,656.2[ 1(0 )2] [ 1(128 )2]X = 1T(190)(65)(4.50)exp -2:;; exp -2 65= 1.36 X 10-3 gim3 or 1.4 X 10-3 gim3 of 502508 INTRODUCTION TO ENVIRONMENTAL ENGINEERINGVertical Profile ofPollutant ConcentrationZTXL XLI~ -.I~ -~IFIGURE 6-21Effect of elevated inversion on dispersion.Inversion aloft. When an inversion is present, the basic diffusion equation must bemodified to take into account the fact that the plume cannot disperse vertically once itreaches the inversion layer. The plume will begin to mix downward when it reachesthe base of the inversion layer (Figure 6-21). The downward mixing will begin at adistance XL downwind from the stack. The XL distance is a function of the stabilityin the layer below the inversion. It has been determined empirically that the verticalstandard deviation of the plume can be calculated with the following formula at thedistance XL:Sz = O.47(L -H) (6-24)where L = height to bottom of inversion layer, mH = effective stack height, mWhen the plume reaches twice the distance to initial contact with the inver-sion base, the plume is said to be completely mixed throughout the layer below theinversion. Beyond a distance equal to 2XL the centerline concentration of pollutantsmay be estimated by using the following equation:EX = (2'7T)1/2Sy(u)(L) (6-25)Note that Sy is determined by the stability of the layer below the inversion and thedistance to the receptor. We call this the "inversion" or "short form" of the dispersionequation.Example 6.5. Detennine the distance downwind from a stack at which we must switchto the "inversion fonn" of the dispersion model given the following meteorologicsituation:Effective stack height: 50 mInversion base: 350 mWind speed: 7.3 m/sCloud cover: noneTime: 1130 hSeason: summer.AIR POLLUTION 509Solution. Determine the stability class using Table 6-6. At > 6 rn/s with strong radi-ation, the stability class is C.Calculate the value of Sz.Sz = 0.47(350 m -50 lIt) = 141 mUsing Figure 6-20, find XL. With Sz = 141, draw a horizontal line to stability class C.Drop a vertical line to the "distance downwind." Find XL = 2.5 kIn.Therefore, at any distance equal to or greater than 5 kIn downwind (2XL), usethe "inversion form" of the equation (Equation 6-25.)For distances less than 5 kIn, we use Equation 6-19 with s z determined from thedistance to the point of interest and the stability. Thus, in no case do we use Sz computedfrom Equation 6-24 to calculate X.6-9 INDOOR AIR QUALITY MODELIf we envision a house or room in a house or other enclosed space as a simple box(Figure 6-22), then we can construct a simple mass balance model to explore the be-havior of the indoor air quality as a function of infiltration of outdoor, indoor sourcesand sinks, and leakage to the outdoor air. If we assume the contents of the box arewell mixed, thenRate of Rate of Rate of Rate of Rate of11 tant pollutant pollutant pollutant 11 tant~o u = entering + entering box -leaving box -POl ~b (6-26)Increase .eavmg ox. b box from from Indoor by leakageb dm ox d .. d Y ecayout oors eInlSSlOnS to out oorsordCVd! = QCa + E -QC -kCV (6-27)Volume=VConcentration = CQ, Ca Q, CEmission Decay RateRate=E =k~ ~FIGURE 6-22Mass-balance model for indoor air pollution.510 INTRODUCTION TO ENVIRONMENTAL ENGINEERINGTABLE 6-8Reaction rate coefficients for selected pollutantsPollutant k, S-1CO 0.0HCHO 1.11 x 10-4NO 0.0NO, (as N) 4.17 x 10-5Particulates « 0.5 ,...m) 1.33 X 10-4Radon 211 X 10-6SO2 6.39 X 10-5Source: G. W. Traynor, et al.. Indoor Air Pollution from PortableKerosene-Fired Space Heaters, Wood-Burning Stoves, and Wood-Burning Furnaces, Lawrence Berkeley Laboratory, Report No. LBL-14027. March, 1982.where V = volume of box, m3C = concentration of pollutant, g/m3Q = rate of infiltration of air into and out of box, m3 IsCa = concentration of pollutant in outdoor air, g/m3E = emission rate of pollutant into box from indoor source, glsk = pollutant reaction rate coefficient, S-lReaction rate coefficients for a selected list of pollutants are given in Table 6-8.The general solution for Equation 6-27 isE QCt = ~ [1- exp(- (~+ k)t)] + coexp[ -(~+ k)t] (6-28)VThe steady-state solution for Equation 6-27 may be found by setting dCldt = 0 andsolving for C:C = QCa + E (6-29)Q+kVWhen the pollutant is conservative and does not decay with time or have a signif-icant reactivity, k = O. In the special case when the pollutant is conservative andthe ambient concentration is negligible and the initial indoor concentration is zero,Equation 6-27 reduces to:Ct = g[l-exp(-(~)t)] (6-30)Example 6-6. An unvented kerosene heater is operated for one hour in an apartmenthaving a volume of 200 m3. The heater emits 802 at a rate of 50 p, g/s. The ambient airconcentration (Ca) and the initial indoor air concentration (Co) of 802 are 100 p,g/m3.AIR POLLUTION 511If the rate of ventilation is 50 LIs, and the apartment is assumed to be well mixed, whatis the indoor air concentration of 802 at the end of one hour?Solution. The concentration may be determined using the general solution form of theindoor air quality model (Equation 6-28). The decay rate for 802 from


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