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?

Find the energy it develops each minute, using the formula:

E_p = mgh

Pay attention to the units.

This is the energy in one minute. Power is defined as the rate of doing work, use that time you were given.

Mass= 1.72 x 10^5 m3/min (1000kg/m3)= 172,000,000
Ep=1.72 x 10^8(9.81 m/s2)(215ft) = 3.63 x 10^11

What else do I need to do to finish the problem?

You didn't pay attention to the units. Are they 'feet' in your question? If so, you need to convert them to metres first before doing any calculations.

okay so...
172000 cubic feet= 20,388.1295 meters
Mass= 20,388.1295m3/min (1000kg/m3)= 20,388,129.5
Ep=20,388,129.5(9.81 m/s2)(215ft) = 4.30 x 10^10

172 000 ft^3 = 4 870.497 613 8 m^3

1 cubic metre of water weighs 1000 kg.

215 ft =65.532 m

Then, using the formula;

E_p = (4 870m^3)(1000kg/m^3) \times (9.81ms^{-2}) \times (65.5m) = 3.13 GJ

Now, using the definition of power, we know that:

\frac{E}{t} = P

So,

1 min = 60 secs

Power = \frac{3.13 \times 10^9 J}{1 \times 60 s} = 52.2 MW

Then, converting to horsepower...

52.2 MW = 700 HP [international]

[Note: I'm using the conversions from ]Online Conversion - Convert just about anything to anything else (http://www.onlineconversion.com/)