HYDRAULICS

"Horsepower, Part 1"

Water and Wastewater

The following is from our text "MATH TEXT for WATER and
WASTEWATER TECHNOLOGY,
THIRD EDITION" by GROVER WRIGHT

(In the text we start with the "basic level" topic such as this, show an example, and then have you do several just like it. You are able to check your answers against ours for each problem. We then move to the intermediate level, and then to the advanced level. We show an example at each level, and have several additional problems for you to do on your own at each level... all with answers!)

This is meant to be printed out... that is the only way you will be able to properly view the two math graphics.

 

A person decides to carry a box, weighing 100 pounds, up a flight of stairs, whose vertical distance is 2,000 feet. Two things come to mind...the first is that the person must really want this box at the top of the stairs, and the second, this is going to TAKE SOME WORK TO ACCOMPLISH! In mathematics, this work is expressed in ft-lb units.
Lets use our example:

Work = ft-lbs = (2,000 ft)(100 lbs) = 200,000 ft-lbs of work

OK, that's A-LOT of work, and we wondered why we were tired?

That is the basic idea behind work. The only problem with WORK is that it does not specify HOW LONG we have to accomplish it. (And we also know that it will take some of us longer to do this than others!) When we start to figure into the equation the time that it takes to do WORK, then we have a new concept, called POWER...


Power is the rate at which we do work. The equation now has the new dimension of time added to it. Lets say the person takes 10 minutes to haul that 100 pound box up the stairs:

If we get our super-active great aunt to do this in 5 minutes:


Obviously, our great-aunt has produced TWICE the power of the person who did the work in ten minutes. Finally, we need to realize that we can be working with some really large numbers here.... but we are saved by the definition of

We need to convert the above "power" values into horsepower:

(Notice how the units cancel out... do the "invert and multiply" to prove it to yourself!)


Its now very easy to see why everyone always says our great aunt works like a horse, as she is the only one who rates a full horsepower! Pumping water is accomplished in the manner as the 100 pound box. All we need to do, is to convert the gallons of water into pounds of water, and use the same "mathematical logic"! That we will do next in Part 2.

 

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