Discussion
Stack gas leaves at \( 18 \) m/s from a \( 2.4 \) m diameter stack. The volumetric flow is
Answer: D
Correct answer: 81.4 m\(^3\)/s
The volumetric flow is the exit velocity times the cross-sectional area of the stack:
\[ A = \frac{\pi d^2}{4} = \frac{\pi (2.4)^2}{4} = 4.524\ \text{m}^2 \]
\[ Q = vA = 18 \times 4.524 = 81.4\ \text{m}^3/\text{s} \]
The distractor \( 43.2 \) is velocity times diameter, omitting the area entirely, and \( 162.8 \) uses the radius as if it were the diameter, doubling the answer. The volumetric flow is what fixes the momentum contribution to plume rise and, with the gas temperature, the buoyancy flux.
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