How to determine the required power of a water pump

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

14 May 2023

Patrick asked me to help him work out the power rating for a pump to deliver water over a distance of about 1km along slightly elevated ground. He estimates that the total elevation from the source to the top of the storage tank is, at most, 5m.

I asked Patrick what was his desired rate of delivery (that is, how many litres per minute) and, initially, he said it doesn’t matter. But then I explained that it matters a lot: any pump can pump water to any elevation. The higher the tank is, the slower the water will flow.

So, he said he has a 10,000-litre tank and would like to fill it up in about half an hour. Now, this means that the pump needs to raise 10,000kg of water to a height of 5m in 30 minutes, or 1,800 seconds. To get the minimum power (in watts), we simply multiply the mass of water by 10 (gravitational intensity) and then by the elevation. Finally, we divide the result by the duration in seconds.

Thus, 10,000 x 10 x 5 = 500,000; dividing this by 1,800 yields 278W. But, in the market, most water pumps come rated in horse-power.  One horse-power is equivalent to about 745W, so, the minimum rating in Patrick’s situation is 0.37hp. In this idealised case, we have assumed that all the energy of the engine/motor is transferred by the pump to the water and that there is no frictional resistance to the flow inside the 1km of piping.

Of course, this is not so in reality. Therefore, may multiply the value calculated above by, say, a factor of 2 to get a more realistic answer. So, Patrick will need at least a 556W [0.75hp] pump to do this job.

I suspect that this question might illicit others with different desired flow rates and elevations, so, here is a quick way of working out the minimum power rating. For every litre per second of flow rate and every one metre of elevation, you will need at least a 20W pump. Keep in mind that 1L/s is equivalent to 3,600L/h!

Thus, if you desire 1L/s raised (3,600L/h) to 15m, then you will need at least a 20 x 15 = a 3,000W-pump (about 4hp). Alternatively, to deliver 0.25L/s (900L/h) to the same 15m-height will require 3,000W x 0.25 = 750W (approximately 1hp). Don’t forget that these are minimum power ratings.