Question

The rate of emission of SO₂ from the stack of a power plant is 150 gm/sec. The stack height is 50 m. Calculate the effective plume height on a sunny September day when the wind velocity is 5 m/sec. Use Class B stability. The effluents are being released at 10m/s and at a temperature of 310^oK. The atmospheric temperature is 293^oK. The stack diameter is 0.5 m

Answer 1

1) Deacon power law for calculating wind speed at stack height

u = u₁ * (z/z₁)^p

Where,

u = desired but unknown wind speed,  (u_s)

u₁ = wind speed at known height, (u₁₀)

z = height where wind speed is unknown, h_s

z₁ = height where wind speed is known, 10m

p = exponent from table 3-3 in the text = 0.15

Therefore, u = u₁ * (z/z₁)^p = 5* (50/10)^0.07 = 5.6 m/sec

2) Check for downwash:

V_s / u >= 1.5 (downwash conditions need not be considered) = 10.0/5.6 = 1.787 >1.5 (therefore downwash need not be considered)

Where,

V_s = stack velocity in m/sec

u = wind speed at plume elevation

3) Calculate buoyancy flux parameter

F_b = g * v_s * d² * ΔT / (4 * T_s)   = 9.81 *  10* 1² * (310- 293) / (4 *310) = 1.3435m⁴/s³ (F_b <55m⁴/s³)

4) Calculate temperature difference

ΔT = T_s - T_a = 310 - 293 = 17⁰K

5) Calculate cross over temperature difference (ΔT)_c

for F_b< 55m⁴/s³

(ΔT)_c = 0.0297 * T_s * v_s ^1/3 / d_s^2/3  = 0.0297 * 310 * 10^1/3 / 1 ^2/3  = 19.8⁰K

6) Evaluate temperature differences

if ΔT > (ΔT)_c  plume rise is buoyancy dominated or else momentum dominated

Here, ΔT< (ΔT)_c hence the plume rise is momentum dominated

7) Calculate final plume rise Δh

Δh for momentum dominated plumes and unstable atmospheric conditions

Δh = 3 * d_s * (V_s / u) = 3 * 1 * (10 / 5.6) = 5.4 m

8) Calculate final effective plume height H

H = 5.4 + 50 = 55.4 m