# Is there an equation for horsepower?

• kriegera

## Homework Statement

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
where
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

What is this 33,000 number you're using? Considering there are cars with engines with a power rating in excess of 1,000 hp, 8,800 hp is obviously way way off.

What is this 33,000 number you're using? Considering there are cars with engines with a power rating in excess of 1,000 hp, 8,800 hp is obviously way way off.

that was a tip equation i got from someone else but they couldn't identify what the 33,000 was which is why I'm skeptical...So -
There are 172,000 cubic ft. of water and
1 cubic feet of water=28.32 kg(approximately)
AND
215 feet = 65.532 meters
power=work/time=mgh/time=(172,000)(28.32)(9.8)(65.532)/60=52,137,468.90watt

Is this better? How do you convert to horsepower? I've seen two methods:

52137468.90/746=69889.36 Horsepower.
OR
(52137468.90)(.00134)=69864.21 Hp

however, i tested it with an online unit converter and it gave a third answer: 69917.4974904738

very confused!

Every answer is about the same, it just depends on how many units you keep. The conversion from horsepower to watts is exact so when you do your calculation, keep as many significant figures as possible. In your question, however, you have 3 significant figures so when you have your answer, it's accurate to 3 significant figures. So as you can see, all 3 answers are 69,900 HP.