Problem: a 70% efficient fan is driven by a 90% efficient motor at standard conditions.
Given: 7.5 horsepower; 2.8 inches of water; 7.5 horsepower motor, then it produces 7
Approach: The fan is then used in heating application delivering 110 degree air.
Calc: The fan is then used in heating application delivering 110 degree air.
Calc: So if this is a 7.5 horsepower motor, then it produces 7.5 horsepower.
Result: But this works out to right around 126,000, 12650 and we'll go with answer choice D.
Office Hours
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Student questions asked in live office hours about this problem
OH 16: HVAC 16
Q: In HVAC-16, you assumed airflow is proportional to temperature (Q2/Q1 = T2/T1), but when I used specific volume ratios instead I got a different answer — why is the temperature ratio correct?
A: The temperature ratio comes from the ideal gas law: at constant pressure, V ∝ T (absolute), so Q2/Q1 = T2/T1 is physically correct. Let me back up and frame what we're actually trying to achieve here before diving into the derivation.
OH 33: HVAC: HVAC-16
Q: Can you explain the derivation of Q2/Q1 = T2/T1 for a fan operating at elevated temperature?
A: This comes from the ideal gas law: at constant pressure, PV/T is constant, so V2/V1 = T2/T1 (using absolute temperatures in Rankine). The fan delivers the same mechanical action, but hotter air occupies more volume per unit mass, so the volumetric flow scales with absolute temperature.
OH 45: HVAC: HVAC-16
Q: Can you explain how Q2/Q1 = T2/T1 was derived for the elevated-temperature fan problem — is it because of direct proportionality?
A: Yes — it comes from the ideal gas law: at constant pressure, V ∝ T (absolute), giving Q2/Q1 = T2/T1. Always use absolute temperatures (Rankine) in that ratio, not Fahrenheit.
OH 65: HVAC: HVAC-16
Q: I used density ratios from the properties-of-air chart to scale volume flow from STP to 110°F, getting 12,800 CFM instead of 12,600 — is this valid?
A: Yes, it's valid — the ~1% deviation is perfectly acceptable. The density ratio approach and the temperature ratio approach both derive from the same ideal gas law, so they should give essentially the same result.
OH 73: HVAC: HVAC-16
Q: The current reference handbook (page 467) states that fan air horsepower efficiency includes both fan and motor efficiency (product of both), which leads me to answer B instead of D — can you address this discrepancy?
A: That's a fair catch and I'll look at the exact handbook language you're referencing — if the handbook has been updated in a way that changes the correct answer, that's something I need to address in the course material. Share your reasoning so I can evaluate it properly and update the problem if needed.