# Derivation of formula for pump power

by boshank20
Tags: derivation, formula, power, pump
 P: 3 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
 P: 26 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.
 P: 3 Ah I didn't realise it came from playing around with mgh. Thanks for the help

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