Problem: In an effort to allow for increased ceiling heights, a design engineer specifies a 3-to-1 aspect ratio for a duct that delivers 500 CFM.
Given: 9. In an effort to allow for increased ceiling heights, a design engineer specifies a 3-to-1 aspect ratio for a duct ...
Approach: The velocity is to be kept under 400 feet per minute.
Calc: Okay, so we're going for a 3-to-1 aspect ratio.
Calc: All that means is that the long side of the duct is 3 times the short side of the duct.
Result: Best answer choice is D.
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Student questions asked in live office hours about this problem
OH 25: HVAC 9
Q: For HVAC-9, I can't use Q = 500 × GPM × ΔT because the problem asks for condensate — and should I be using the entering specific volume at state 1 since the entering CFM is given?
A: You're right on both counts — 500 × GPM × ΔT is for sensible heating/cooling of liquid water, which doesn't apply here. And yes, use the specific volume at state 1 (entering conditions) because that's where you know the volume flow rate and need to convert it to mass flow.
OH 30: HVAC 9
Q: Can HVAC-9 be solved using the adiabatic mixing of two moist air streams equations from section 9.2.3 of the reference handbook?
A: Using 9.2.3 is formally the most rigorous approach — arguably the right way to do it — my approach in the solution is faster but slightly less rigorous. Both get to the same answer, so use whichever approach you're more comfortable with.
OH 65: HVAC: HVAC-9
OH 120 · May 11, 2026
Q: A student solved for duct dimensions using Q=VA with a 3:1 aspect ratio and got 1.93 feet (≈23 inches) for the width — why is 24 inches the correct answer instead?
A: The algebra is correct, but the problem requires integer dimensions that satisfy the 3:1 aspect ratio. Since 23 has no integer partner in a 3:1 ratio, you must round up to 24×8 inches, which is the nearest valid integer pair — the next options (27×9 or 21×7) would be either excessive or insufficient.
Q: In HVAC-9, shouldn't we use the hydraulic diameter rather than the geometric area to calculate velocity in the duct?
A: There are two different concepts at play: the hydraulic diameter (D_h = 4A/P) used for friction loss calculations, and the actual cross-sectional area used for velocity calculations. For velocity, use the actual flow area; the hydraulic diameter is specifically for friction loss in non-circular ducts.