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Power of a pump

  1. Feb 15, 2013 #1
    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. jcsd
  3. Feb 16, 2013 #2

    haruspex

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    I assume the radius is the radius of the nozzle.
    What mass of water is sprayed in one second? What energy is it given?
     
  4. Feb 16, 2013 #3
    Nope. Only the speed and radius was given.
     
  5. Feb 16, 2013 #4

    haruspex

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    These are things you can work out from the speed and radius.
     
  6. Feb 16, 2013 #5
    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?
     
  7. Feb 16, 2013 #6

    haruspex

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    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.
     
  8. Feb 16, 2013 #7
    Thank you very much for helping and advising.
     
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