One of the Niagara turbines uses 172,000 cubic feet of water per minute under a head of 215 ft. What is the horsepower developed?
The Attempt at a Solution
Below is "research findings" and attempt at a solution but I'm a little leary of the 33,000. Can anyone give me some insight if you've done a similar problem.
The total horsepower developed by water falling from a given height is the product of the mass flow rate in pounds per minute times the falling height in feet divided by 33,000. It can be expressed as:
Php = mmin h g / 33000
Php = power (horsepower, hp)
mmin = mass flow rate per minute (lbm/min)
h = head or height (ft)
g = acceleration of gravity (9.8)
Convert 172,000 cubic feet of water per minute to pounds per minute: A cubic foot of air is approximately 0.0807 lbs (172,000)(0.0807)=13880.4 lb/minute
Php = (13,880.4)(215)(9.8) / 33000= 8,862.42 hp