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Homework Help: Horsepower in a pump

  1. May 16, 2010 #1
    1. The problem statement, all variables and given/known data

    A pump has to raise water from a depth of 50m and eject it at 10m/s. If the flow rate is 2 kg/s, what horsepower is needed.

    2. Relevant equations



    3. The attempt at a solution

    t = s/v = 5 seconds

    m = t/flow rate = 2.5kg

    E = mgh = 1250J

    P = E/t = 250W

    Horsepower = 0.34Hp
     
  2. jcsd
  3. May 16, 2010 #2

    Borek

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    Staff: Mentor

    Ejection speed is not necessarily the speed at which water travels up. Besides, time you have calculated doesn't matter - each second you have to move 2 kg of water 50 meters up.

    Check your units - you will see it is wrong. Time divided by flow rate is not [STRIKE]seconds[/STRIKE] kg.

    You need to do two things - transfer water up, and accelerate it to 10 m/s. Calculate energies involved.
     
    Last edited: May 16, 2010
  4. May 16, 2010 #3
    Is it not 10m? erm is the calculation Mass = flow rate/ time?

    I'm still confused
     
  5. May 16, 2010 #4

    Borek

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    Staff: Mentor

    No, check units.

    Don't think about formula, just how do you feel - if you transfer 2 kg per second, how much will you transfer in 5 seconds? How have you calculated it?

    Flow rate means just that: each second you have to move 2 kg of water up and accelerate it to 10 m/s.
     
  6. May 16, 2010 #5
    hmm it seems so simple but i'm struggling to grasp the concept. It takes 10Kg in 5 seconds then? Was any of my working correct?
     
  7. May 16, 2010 #6

    D H

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    Staff Emeritus
    Science Advisor

    To be brutally honest, no. You have not followed Borek's advice. I'll repeat it, highlighting the key concept:
    How much energy is needed to lift one kilogram of water 50 meters?
    How much energy is needed to make that one kilogram of water move at 10 meters/second?
     
  8. May 17, 2010 #7
    Ep = mgh for one kg lifted 50 meters?

    Ek = 1/2 mv^2 for one kg at 10m/s?
     
  9. May 17, 2010 #8

    Borek

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    OK, how many kg per sec?
     
  10. May 17, 2010 #9
    2 kg/s ?
     
  11. May 17, 2010 #10

    Borek

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    OK. How much energy is needed per sec then?

    And if you think after seeing the answer I will ask any further questions, you are wrong. You are so close to the solution it is a shame you still need to be pushed.
     
  12. Feb 6, 2011 #11
    Hi,
    I calculated the Potential energy(work done)= 2*9.81*50=981 Js-1
    Kinetic energy=mv^2/2= 2*100/2=100 Js^-1.
    But how do you calculate using thees, the horsepower...or at least in Joules cause then converting into horsepower is easy.
    Thanks.
     
  13. Feb 6, 2011 #12

    Borek

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    Staff: Mentor

    Show the units. How did you get J/s?
     
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