Derivation of formula for pump power

  1. Hi

    I was given the following formula for to calculate the power of a centrifugal pump:

    P = ρ * g * Q * H
    i.e. Power = Density * acceleration due to gravity * volumetric flow rate * total head

    I have found websites that state this formula but I haven't been able to find anywhere that explains how the formula was derived. Could anyone point me in the right direction?

  2. jcsd
  3. Well we've got a vertical outlet, moving the fluid upwards against gravity by a certain height, H(the head).
    SO we can say the pump is doing work against gravity
    ie [W][/pump]= Force x distance
    = weight of fluid x head
    = m g H
    power is the rate of doing work so.. [P][/pump]= mgH/t = (m/t) x g x H
    = (mass flow rate) x g x H
    = (density of fluid x volumetric flow rate )x g x H
    Hope this helps.
  4. Ah I didn't realise it came from playing around with mgh. Thanks for the help
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