Derivation of formula for pump power

AI Thread Summary
The formula for calculating the power of a centrifugal pump is derived from the work done against gravity, expressed as P = ρ * g * Q * H. This equation represents power as the product of fluid density, gravitational acceleration, volumetric flow rate, and total head. The derivation involves understanding that power is the rate of doing work, which can be expressed in terms of mass flow rate and gravitational potential energy. The discussion clarifies that the formula stems from manipulating the basic physics equation for work, W = mgh. This insight helps in understanding the underlying principles of pump power calculations.
boshank20
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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
 
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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.
 
Ah I didn't realize it came from playing around with mgh. Thanks for the help
 
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