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11.35 For slightly unstable atmospheric conditions, what are the values the dispersion
coefficients, σy and σz, 3 km downstream in a rural area? Provide your values for (a) the
correct Briggs formula and (b) a graphical method that allows you to estimate the
dispersion coefficients from established figures. (c) How do these values change if the
atmosphere is moderately stable?
Solution:
11.36 Wind is measured at 10 m above the ground surface at 2 m/sec. Estimate the
wind speed at an effective stack height of a 40 m in (a) smooth rural terrain for unstable
atmospheric conditions and (b) for rough urban terrain for the most stable atmospheric
conditions.
Solution:
Use equation 11.32:
11.37 What is the estimated wind speed at a 45 m effective stack height located in the
country side? Assume there are very unstable atmospheric conditions near the stack and
wind measurements made close to the stack location showed the wind speed was 3 m/sec
at a height of 5 m.
Solution:
11.38 What is the ground level concentration of a pollutant (µg/m3) 250, 500, 750, and
1,000 meters downwind for a stack release along the centerline of the plume? The
pollutant is released from a 45-m tall stack at a rate of 8.5 grams per second in an urban
area. The plume rises an additional 10 meters. The wind speed is 3 m/sec and there are
slightly unstable atmospheric stability conditions.
Solution: Note here that y = 0 (we are estimating the concentration along the centerline).
2(145𝑚)2𝑒−(45+10𝑚)2
2(150𝑚)2×106𝜇𝑔
11.39 NOx is emitted from a 75-m high stack at a rate of 65 g/s. Calculate the ground
level concentration of NOx 90 m from the centerline. The plume rises 20 m and the wind
speed is 5 m/sec. Assume σy = 120 m and σz = 47 m and there is reflection from the
ground.
Solution: This problem asked for the concentration at ground level (z = 0) but 90 m in
11.40 Estimate the downwind distance (x) at which the maximum pollutant
concentration would occur at the ground surface for an emission that occurs from a stack
that is 60 m high? Assume the pollutant is SO2, it is emitted at a rate of 3,000 g/sec, the
wind speed is 4 m/s, the plume rises an additional 14 m after being emitted, and there are
slightly unstable atmospheric conditions in this urban area. Calculate your value using
two methods, equations and curves provided in the chapter.
Solution:
11.41 An air pollutant is released at a rate of 2 g/s from the top of a tall stack that is 110
m high. The plume initially rises upward an additional 10 m above the stack exit, after
which it travels with a wind speed of 5 m/s. The atmosphere has moderately stable
conditions in the open country. (a) What is the concentration of the pollutant (µg/m
3
) in
the very center of the plume 750 downwind of the stack and at the effective stack height?
(b) What is the concentration of the pollutant (µg/m3) at ground level 750 downwind of
the stack? (c) At what distance downwind does the maximum ground level
concentration occur? (d) What is the concentration of the pollutant (µg/m3) at this
location you identify in part (c)?
Solution:
2 𝑔/𝑠×106𝜇𝑔
1 𝑔
2(29𝑚)2𝑒−(120𝑚)2
2(9.8𝑚)2=𝟏.𝟐𝑬−𝟑𝟎 𝝁𝒈/𝒎𝟑
11.42 An air pollutant is released at a rate of 0.72 g/s 4 meters above ground level. The
wind speed is 2 m/s. What is the maximum ground level concentration 1 km downwind?
Assume that
σy = 45 m and σz = 26 m.
Solution: we assume this problem is asking for the concentration along the centerline
