Q7 - This problem has three parts. I will list the questions for each of the three parts, and any other additional info in the "Description" below.

Question

The pump in a water tower lifts water with a density of p_w = 1.00 kg/liter from a filtered pond at the base of the tower up h_T = 21 m to the top of the tower. The water begins at rest in the pond and comes to rest at the top of the tower. The pump is 100% efficient in lifting the water, and it lifts a volume of V_w = 8.4 L of water up the tower every second. The water tower sits on a hill that is T_e = 95 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 1.9 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 L 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

a) Power = pressure x flow = ρgH*Q= 1000*9.81*21*8.4/1000= 1730 watts

b) Energy = 1730*1.9*3600=11.8E6 Joules

c) E=mgh=10⁶/10³*10³*91=9.1E7 Joules