Solving for Horsepower w/ Unfamiliar Equation

[kriegera]

Homework Statement

My teacher assigned a horsepower problem except that we never covered horsepower. Here's my attempt:

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?

Homework Equations

The Attempt at a Solution

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
where
Php = power (horsepower, hp)
mmin = mass flow rate per minute (lbm/min)
h = head or height (ft)
g = acceleration of gravity (32 ft/s2)

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

-Am I on track here? Also, I used 9.8 for acceleration of gravity-can anyone tell me if this is the value I should be using? Thanks!

 

[jack action]

Your equation makes a lot of sense, but I'm not sure about the conversion factors. I don't remember what the 33 000 conversion factor includes but in the SI units:

P = \dot{m}gh

Where the units are:

P --> W
\dot{m} --> kg/s
g --> 9.81 m/s²
h --> m

The mass flow rate is equal to the volumetric flow rate (m³/s) times the density of water (1000 kg/m³), not air.

 

[Unit Maestro]

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