Question

The following information was recorded on August 12, 2011 at 10 p.m.:

• Wind Speed at 75m = 10.8 m/s
• Wind Direction at 75 m = 120 ^o
• Sigma Theta at 75 m = 9.2 ^o
• Atmospheric Temperature = 21.2 ^oC
• Stack Exit Temperature = 200 ^oC
• Stack Height = 75 m
• Stack Diameter = 0.2 m
• Stack Exit Velocity = 10.2 m/s
• Source Strength = 100 g/s
• Air Contaminant = VOC

Plot C _u/Q versus downwind distance under night-time conditions and compare your results with calculations using day-time conditions. Use sigmas from Problem 4. Choose the one of the following statement using your results:

		In general, night-time concentrations are the same as day-time conditions.
		In general, day-time concentrations are higher than the night-time concentrations.
		In general, night-time concentrations are higher than the day-time concentrations.
		None of the above.

Answer 1

Given

• Wind Speed at 75m = 10.8 m/s = u
• Wind Direction at 75 m = 120 ^o
• Sigma Theta at 75 m = 9.2 ^o
• Atmospheric Temperature = 21.2 ^oC
• Stack Exit Temperature = 200 ^oC
• Stack Height = 75 m
• Stack Diameter = 0.2 m
• Stack Exit Velocity = 10.2 m/s = V_s
• Source Strength = 100 g/s
• Air Contaminant = VOC

Answer :

1)Check for downwash:

V_s / u >= 1.5 (downwash conditions need not be considered)

= 10.2/10.8 = 0.944 >1.5 (therefore downwash needs to be considered)

Where, V_s = stack velocity in m/sec

u = wind speed at plume elevation

2)Now lets calculate reduced stack height:

h' = 75 + 2* 0.2 ((10.2 /10.8) - 1.5)

= 74.77

3) Calculate buoyancy flux parameter

4) Calculate temperature difference

ΔT = T_s - T_a = 473 - 294.2 = 178.8⁰K

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 * 473* 10.2^1/3 / 0.2 ^2/3  = 89.1⁰K

6) Evaluate temperature differences

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

Here, ΔT > (ΔT)_c for both the cases hence the plume rise is buoyancy dominated

7) Calculating plume height, Δh

Plume Rise, Δh for unstable atmospheric conditions, F_b < 55m⁴/s³ and buoyancy domination is given by the equation

Δh = 21.425 (F_b^3/4 / u)

Where,

u = wind speed in m/sec = 1m/sec

Hence, Δh = 21.425 (F_b^3/4 / u) = 21.425 (0.38^3/4 / 10.8) = 0.942 m

8) Calculate final effective plume height H

H = 74.77 + 0.94 = 75.71m

9) Calculate concentration, C from excel

10) graph

11) Compare to day-time   

The stability conditions for day-time and night-time vary very little for this wind speed.

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