Problem: Fluids 15, 20,000 GPM of water flows through a turbine in a hydroelectric power application.
Given: 000 GPM of water flows through a turbine in a hydroelectric power application; 50 psi G and the exit pressure is 1 at...
Approach: If you think about what a pump is, you put electrical power into a motor and it changes that into mechanical power, BHP, and th...
Calc: Of course there's efficiency going on throughout that process and we have an overall efficiency given here of 80%.
Calc: Some inefficiency there are losses, losses of 20% that leave us with only 80% of the electricity that we could have if it was p...
Result: And we get an electrical power of 348 KW, which is closest to an inch of choice A.
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Student questions asked in live office hours about this problem
OH 41: HVAC: Fluids-15
Q: Can you elaborate on the relationship between total pressure, gauge pressure, and absolute pressure for this turbine problem?
A: Gauge pressure plus atmospheric pressure equals absolute pressure—think of atmosphere as the floor you're standing on; gauge is your height above the floor, and absolute is your total height from the ground. In this turbine problem, the inlet is 50 PSIG and the outlet discharges to atmosphere (0 PSIG), so delta P is simply 50 PSI regardless of gauge or absolute reference. As long as you're consistent, atmospheric pressure cancels in the subtraction.
OH 68: HVAC: Fluids Module #15
Q: In the solution, the pressure drop across the turbine was 50 PSIG minus 1 ATM—if exit pressure is 1 ATM, why isn't it 14.7 PSI instead of 0?
A: One atmosphere is 14.7 PSIA in absolute terms, but in gauge terms it equals exactly 0 PSIG—so 'discharge to atmosphere' means 0 PSIG, not 14.7. Whether you subtract in gauge (50 − 0 = 50 PSI) or convert both to absolute (64.7 − 14.7 = 50 PSI), you get the same delta P. The atmosphere cancels in any delta P calculation.
OH 74: HVAC: Fluids Module #15
Q: How do you determine which conversion factor for one atmosphere to use, since the handbook lists several different values?
A: They're all the same quantity in different units—14.7 PSI, 29.9 inches of mercury, 33.9 feet of water, and 101.325 kPa all equal one atmosphere. Don't try to memorize every form; just internalize the PSI and kPa values and know how to convert between units. Pick the unit system your problem is in and use the corresponding value.