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Lime25 · Jun 28, 2010, 07:02 PM

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?

Unknown008 · Jul 1, 2010, 03:10 AM

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.

Lime25 · Jul 3, 2010, 11:02 AM

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?

Unknown008 · Jul 3, 2010, 11:13 AM

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.

Lime25 · Jul 3, 2010, 11:38 AM

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

Unknown008 · Jul 3, 2010, 11:51 AM

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

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]

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