Derivation of formula for pump power

In summary, the conversation discusses a formula for calculating the power of a centrifugal pump, which involves the variables of density, acceleration due to gravity, volumetric flow rate, and total head. The formula is derived from the concept of the pump doing work against gravity, which is represented by the equation W = F * d. The power is then calculated by dividing the mass flow rate by time and multiplying it by g and H. The formula is found on websites, but the conversation also asks for an explanation of its derivation.
  • #1
boshank20
3
0
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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  • #2
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.
 
  • #3
Ah I didn't realize it came from playing around with mgh. Thanks for the help
 

1. What is the formula for pump power?

The formula for pump power is P = Q x H x ρ x g, where P is power (in watts), Q is flow rate (in m3/s), H is head (in meters), ρ is fluid density (in kg/m3), and g is gravitational acceleration (in m/s2).

2. How is the formula for pump power derived?

The formula for pump power is derived from the basic principles of fluid mechanics and the laws of thermodynamics. It takes into account the flow rate, head, and fluid properties to calculate the amount of power needed to move a fluid through a pump.

3. What does each variable in the pump power formula represent?

P represents power, which is the energy required to move a fluid through a pump. Q represents flow rate, which is the volume of fluid passing through the pump per unit of time. H represents head, which is the height difference between the inlet and outlet of the pump. ρ represents fluid density, which is the mass of the fluid per unit of volume. g represents gravitational acceleration, which is the rate of change of velocity due to gravity.

4. How does the pump power formula relate to the efficiency of a pump?

The pump power formula is used to calculate the amount of power needed to operate a pump. The efficiency of a pump is the ratio of the actual power output to the theoretical power output, which is determined by the pump power formula. A more efficient pump will require less power to achieve the same flow rate and head, resulting in lower operating costs.

5. Can the pump power formula be used for all types of pumps?

Yes, the pump power formula can be used for all types of pumps as long as the flow rate, head, fluid density, and gravitational acceleration are accurately measured. However, the efficiency of different types of pumps may vary, so it is important to use the appropriate efficiency factor when calculating pump power for specific pump types.

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