Derivation of formula for pump power

[boshank20]

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?

Thanks

 

[W R-P]

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.

 

[boshank20]

Ah I didn't realize it came from playing around with mgh. Thanks for the help