Problem: Fluids 26, 390% efficient, secondary chilled water pumps operate in a parallel redundant N plus 1 configuration supplying a total of 1500 gpm again...
Given: 1500 gpm against 200 feet of total dynamic head; 900 rpm; 1500 gpm with a total dynamic head which I'll call HA of 20...
Approach: Okay, so let's draw this system under the normal operation and under the failure mode and then describe what the difference is ...
Calc: And that system provides a volume flow rate of 1500 gpm with a total dynamic head which I'll call HA of 200 feet.
Calc: Well, the cooling loads demand their 1500 gpm, right?
Result: The best answer choice is D and that's an argument for having multiple pumps in parallel, not only for redundancy in this failure mode, but also fo...
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Student questions asked in live office hours about this problem
OH 16: 5. FLUIDS-26
Q: Why can't you use Q·ΔH/3960 right off the bat when you already know Q and H for the failure state, without using the pump affinity laws?
A: The issue is that Q and H for the failure state aren't directly given—they have to be derived using the affinity laws because the operating point shifts when a pump is removed from a parallel arrangement. Once you've correctly determined Q and H for each pump in the failure state, you can absolutely use Q·ΔH/3960. The affinity laws are the required intermediate step, not a substitute for the WHP formula.
OH 41: HVAC: Fluids-26
Q: Why did you use the pump affinity laws—if the volume flow rate stays constant, wouldn't the pumping pressure stay at 200 feet rather than increasing?
A: When one pump fails in a parallel arrangement, the two remaining pumps must now each supply more flow to maintain system demand—so Q per pump increases, not stays constant. With more flow per pump, the head they must develop also changes according to the affinity laws and the system curve. It's counterintuitive but the head doesn't stay fixed; the operating point for each pump shifts.
OH 73: HVAC: Fluids Module #26
Q: Why can't we just use the BHP formula directly with the known Q and head for each pump in the failure state, instead of the affinity laws?
A: You can use the BHP formula once you have the correct Q and H for the failure state, but the problem is that H in the failure state isn't simply the same 200 feet—it changes as the operating point shifts. The affinity laws let you find the new operating conditions; then the BHP formula can be applied. Using the original H without accounting for the shift in operating point is what leads to the incorrect 42 HP answer.
OH 74: HVAC: Fluids Module #26
Q: Why don't you double the BHP result, since there are two pumps running during the failure scenario?
A: The question was asking for the BHP required to drive each of the two remaining pumps, not the total for both—that was ambiguous wording on my part. If you interpreted it as the total and calculated 190 HP instead of 95 HP, you get full credit for that reasoning. Just be aware of whether a question asks for 'each pump' or 'total,' and note that the problem language could be clearer.
OH 87: HVAC: Fluids Module #26
Q: I understand each of the three pumps handles 500 GPM in normal operation, but how does Q per pump become 750 GPM when one fails?
A: In the normal 3-pump arrangement, the total 1500 GPM is split equally at 500 GPM per pump. When one pump fails, the system still needs 1500 GPM total, and the remaining two pumps must split that demand equally—so each now carries 750 GPM. Q2 per pump goes up, not down, because the total system demand is unchanged.
OH 96: HVAC: Fluids Module #26
Q: I used the pump affinity laws to check the head relationship with speed change, but head isn't supposed to change in a parallel operation—can you explain how the affinity laws still give the right answer?
A: You're right that head doesn't change—the system requirement stays fixed regardless of how many pumps are running. The affinity laws aren't being used to relate speed; they're being used to relate the change in operating point between the 3-pump and 2-pump states. Since flow per pump increases when one fails, each pump moves to a new operating point on its curve, and the power (which scales with Q³) increases accordingly.