What is the power of a pump spraying water at 20 m/s with a 0.05 m radius?

[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

 

[haruspex]

I assume the radius is the radius of the nozzle.
What mass of water is sprayed in one second? What energy is it given?

 

[New_bee]

Nope. Only the speed and radius was given.

 

[haruspex]

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

Nope. Only the speed and radius was given.

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

 

[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?

 

[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.

 

[New_bee]

Thank you very much for helping and advising.