# Homework Help: Power of a pump

1. Feb 15, 2013

### New_bee

A pump taking water from a large reservoir, is used to spray a jet of water with speed 20 m/s and radius 0.05 m, from a nozzle level with the surface of the reservoir. Calculate the power of the pump.

Workdone = Force * distance
Power = Force * velocity

I have no idea

2. Feb 16, 2013

### haruspex

What mass of water is sprayed in one second? What energy is it given?

3. Feb 16, 2013

### New_bee

Nope. Only the speed and radius was given.

4. Feb 16, 2013

### haruspex

These are things you can work out from the speed and radius.

5. Feb 16, 2013

### New_bee

Density of water is 1000 kg/m^2.

So the mass of water = volume of water.

Volume of water is = pi * r^2 * h

Since the water flows 20 meters per second, h = 20.

Volume = pi * 0.05^2 * 20 = 1/20 pi

So the mass = (1/20) pi * 1000 = 50 pi

Workdone = 1/2 * 50 pi * 20^2 = 31.4 kJ

Since the time = 1 sec...

The power is 31.4 kW

Am I right? Did I make any mistake?

6. Feb 16, 2013

### haruspex

Looks right, but it would be good to get into the habit of quoting units throughout. E.g. the mass in 1 sec is 50 pi kg. And statements like "mass of water = volume of water" could lose you marks; a mass can never equal a volume.

7. Feb 16, 2013

### New_bee

Thank you very much for helping and advising.