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I have a water pump at a distance of x meters from a water tower located h meters above the pump through a pipe with diameter d. I am not concerned with the exact value just want to make sure my pump is strong enough.

As far as I can remember the pressure required is equivalent to the weight of the water in the pump in kg multiplied by the height in meters of the tower.

What is the formula for pressure required in kg as a function of x, h and d? All units metric.

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2 Answers 2

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Your pump needs to provide enough pressure to push the water all the way up to the deposit. That would amount to $\rho g h$. If your inlet in the deposit is above water level, $h$ is measured to the inlet. If it is underwater, then it is measured to the water level.

That pressure is enough to keep the water from backflowing, but not to push any more water up to the deposit. To do so, you'll need additional pressure, that will go into kinetic energy of the water moving through the pipe, $\frac{1}{2}\rho v^2$, and into overcoming friction losses in the pipe, which can be calculated with the Darcy-Weisbach equation. The velocity of the water in the pipe can be figured out from the pipe diameter and the mass flow being sent through it.

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Thanks for your answer, ρ is the weight of the water in the pipe? Reason I ask is wikipedia for hydrostatic pressure says ρ is the fluid density, not sure where the size of the pipe comes in. – jimmyjambles Dec 3 '12 at 4:07
It is the density. The pipe diameter only comes into play when there is movement, mainly for the losses, but not in the formula for the height. – Jaime Dec 3 '12 at 4:41
I understand now, the pump is specified as having a certain head based on a flow diameter. If I place something like a sediment filter after the pump I imagine that will increase the friction? – jimmyjambles Dec 3 '12 at 4:54

.052 x 8.34 x height above pump. Will provide you with number of pounds of pressure that your pump must provide to push water to your tank. Of course I can give you the formula for diameter of pipe/ and distance; however I'm not sure that anyone wants to begin calculated process factors for the bends, and turns in a friction on water inside a pipe. I'll just keep it simple like the original formula says. For example Your tank water entrance is ten foot high. .052x8.34x10 is the amount of pressure that your completely full tank, will proprovide back against the pump. That means that a pump must be able to push a very minimum of 4.3 pounds, of force only to push clean clear fresh water to that level. I'd recommend that you exceed that number by four pounds if your water source is extremely close to your tower.

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