Question

Given a water tower with the lower end at 50.0 meters above the ground, and the top 60.000 meters above the ground and a radius of twenty meters. What is the minimum power needed on the pump to fill it from empty to full in 13.35 hours.

Answer 1

Find the mass of this water:

$$m=\rho V=\rho Ay=\rho \pi r^2(H-h).$$

If we fill this mass of water from the top of the tank, the power is

$$P=\frac{E}{t}=\frac{mgH}{t},\\\space\\ P=\frac{\rho\pi r^2(H-h)gH}{t}=153.7\text{ kW}.$$