Pump pressure required to fill water tower

Question

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.

Answer 1

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.