Question

A new industrial facility is proposed at a location 5 km upwind from an existing multi- family residential development. The exhaust of the factory emits chloropicrin at the rate of 2500 g/s. The detection threshold for chloropicrin is 10 μg/m2. The atmospheric stability conditions for the area changes between stability classes D&F and the average wind speed is 5.0 m/s. Would should be the minimum recommended height for the smoke stack of that industrial facility? (Hint: we are concerned with the maximum downwind concentration) Diameter 1.20m Stack velocity = 10 m/s Temperature- 100 °C Pressure 95.0 kPa Temperature- 25 °C = 21.425F,0.75 38.71 F0.5 v,stack velocity, m/s d stack diameter, m u = wind speed, m/s P-pressure, kPa T stack temperature, K Tair temperature,K F55 Ah plume rine V. Stack exit velocity, m/s d: top inside stack diameter, m T.: stack gas temperature, K T: ambient temperature, K g: gravity, 9.8 m/s2

Answer 1

Let us consider H to be the effective height of the stack.

H can be written as, $H= h+\Delta H$ where h is the height of the stack, $\Delta H$ is the height of the plume.

It is given, the amount of chloropicrin emitted is 2500 g/s

The concentration of the chloropicrin at a multi-family residence 5 km away from the factory is 10$\mu g$/ m³ .

It is stated that the atmospheric condition changes between stability classes D & F.

So, considering an average atmospheric condition we are considering the stability class E.

Now, the concentration of pollutants is given by the equation,

1H (e) - C(x0)
since the y coordinate is zero, where H is the effective height of the stack, u is the mean wind speed, Q is the emitting pollutant, $\sigma_{z}$ is the vertical dispersion coefficient, $\sigma_{y}$ is the vertical dispersion coefficient.

We have to find the $\sigma_{z}$ and $\sigma_{y}$ value from the charts provided below,

661 10 A - Extremely unstable B - Moderately unstable C - Slightly unstable D - Neutral E- Slightly stable F Moderately stable 10 10 10 Downwind distance (x) from source in m 7, O, Vs x for different atmospheric stabilities.

Chart for $\sigma_{y}$ value (fig 18.7)

2 3 x 10 10 10 A- Extremely unstable B- Moderately unstable C - Slightly unstable D - Neutral E- Slightly stable F- Moderately stable 10 10) 10 Downwind distance (x) from source in m Fig.18.8. Ơz Vs x for different atmospheric sta c stabilities
Chart for $\sigma_{z}$ determination (fig 18.8)

From the charts we get the $\sigma_{z}$ value as 60 m and the $\sigma_{y}$ value as 200 m, as the multi-family residence is 5 km along the center line of the plume.

Here given are, C_(x,0) = 10$\mu g$/ m³ = 10 x 10^-6 g/m³ , Q = 2500 g/s , u = 5 m/s,  $\sigma_{z}$ = 60 m, $\sigma_{y}$ = 200 m

Putting the above values in the equation to find the effective stack height, we get,

H = 160.89 m. It is the effective stack height.

Now, we have to find the plume rise height, which is given by the below equation. (Holland's equation).

The symbol meanings are already mentioned in the question.Pressure should be converted to millibars.

2.68 x 10-2(P) (4-4) d AH = 1.5 + Ts Lu

Thus substituting the values we get,

$\Delta H$ = 18.34 m. It is the plume rise height.

Thus the minimum recommended stack height should be, h = H - $\Delta H$ = 160.89 - 18.34 = 142.55 m = 143 m

Now, if we consider the Buoyancy flux the answer will be more or less same.

Thus the minimum height recommended height of the plume stack is 143 m.