Question

The pump in a water tower raises water with a density of ρ_w = 1.00 kg/liter from a filtered pool at the bottom of the tower up h_T = 25 m to the highest point of the tower. The water begins at rest in the pool and comes to rest at the highest point of the tower. The pump is 100% efficient in lifting the water, and it raises a volume of V_w = 8.6 liters of water up the tower every second. The water tower sits on a hill that is T_e = 45 m above sea level. Let gravitational potential energy be zero at ground level.

Part (a) Calculate the power, P_p in Watts, of the pump.

Part (b) If the pump runs for 2.7 hours, calculate the increase in the potential energy, ΔU_w in J, of the water in the tower.

Part (c) The water tower, when full, holds 10⁶ liters of water. Calculate the gravitational potential energy of the water, U_w in J, of a full water tower relative to sea level.

Answer 1