# Relationship between output mechanical power and max pressure for a pump?

If an air pump needs to able to generate a particular pressure at a particular flow rate.

How do we size the electrical motor for this particular scenario? The electric motor would be coupled to the pump shaft in this case.

I mean how do I calculate the mechanical power the motor shaft has to deliver to achieve this?

Does the pump technology have any bearing on this I mean diaphragm, piston etc.

Lets take an example pressure of 1 psi at a flow rate of 10 liters / min. I need to know the wattage of the motor that would be a suitable fit for this specification.

• I think you're looking for equation 2 here - this is not what the poster gave below. – Chuck Nov 16 '16 at 21:56

Generally speaking, for fluid systems the mechanical power can be computed as the product of pressure and volumetric flow rate:

$\dot{E} = P\dot{V}$

where $\dot{E}$ is the power, $P$ is the pressure and $\dot{V}$ is the flow rate. Therefore, for your application (with unit conversions to get the output in watts):

$\dot{E} = (1 \text{ psi})(\frac{6894.76 \text{ Pa}}{1 \text{ psi}})(10 \text{ L/min})(0.001 \text{ m}^3/\text{L})(\frac{1 \text{ min}}{60 \text{ s}}) \approx 1.15 \text{ W}$

However, the required flow and pressure are not the only considerations. You need to consider all the sources of friction and other energy losses in the system: friction in the motor bearings, efficiency losses when converting mechanical energy in the impeller to fluid flow in the system, etc. Therefore you would need an electrical motor with more than just 1.15 W of power. The energy losses from the impeller to the fluid flow would be difficult to estimate if you're building your own pump.

Also consider that an electric motor cannot output 1.15 W for any combination of speed and torque, so you need to check the motor's spec sheet to make sure that it can provide the power you need at the desired motor speed.

• you have converted L/min to L/m^3 why was that? or is it m^3/ min? Do the units have to be P in pascals and V in m3/min for calculating the Shaft power in watts – Miguel Sanchez Nov 17 '16 at 9:48
• Would this equation apply to any kind of pumping device? I mean diaphragm, piston etc.? – Miguel Sanchez Nov 17 '16 at 9:49
• shouldn't the flow rate be in m3/hr ? – Miguel Sanchez Nov 17 '16 at 10:00
• In wikipedia Power article it says P(t) = pQ where p is pressure in pascals and Q is volumetric flow rate in m3/s so that makes it P = 6894.76 * 0.000166667 which is 1.15W so what would be the correct answer? – Miguel Sanchez Nov 17 '16 at 10:10
• @MiguelSanchez This equation is for the power contained in any flowing fluid, whether it is air or water. As for compressibility considerations, that comes up when you try to determine the efficiency of your impeller in transferring energy to the fluid flow. Energy would be lost in compressing the fluid or in turbulence and other frictional losses. At the very least you can use this answer to get an order of magnitude for your power requirements. You will likely need something on the order of 5-10W, but 100 W would be too much – BarbalatsDilemma Nov 17 '16 at 16:16