# Horsepower Help

## 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?

## 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!

Related Introductory Physics Homework Help News on Phys.org
jack action
Gold Member
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.

I know, it is super useful to have memorized all the conversion factors. But, once you understand what is happening there are tools that make unit conversion awesome! One of the best ones I've found is the Unit Conversion in Excel (http://www.unitconversionaddin.com [Broken]). This simply works because you ( a student like me) are able to do the unit conversion automatically in excel like a program. You don't have to either search on the internet for the conversion value or have to write out some excel function. The download is like 5 bucks and has saved me hours of stress and time. The conversions are really detailed and accurate too, like to 5 decimal places where applicable.

Last edited by a moderator: