A fountain, for a new municipal building, is designed to spray a column of water

Question

A fountain, for a new municipal building, is designed to spray a column of water 120 meters into the air. It requires an exit velocity of 54 m/s. The nozzle at ground level , has a diameter of 5 cm and the pipe leading to the fountain is 30 cm in diameter. The pump for the system is 6 meters below the fountain.

Part A.What is the hydrostatic pressure due to the height of the nozzle above the pump?

Part B.What is the velocity of the water in the connecting pipe? (Dia =30cm)

Part C.What is the weight of water that flows through the fountain in10minutes?

Part D.What is the pump pressure needed to operate this pump?

Explanation / Answer

A fountain, for a new municipal building, is designed to spray a column of water 120 meters into the air. It requires an exit velocity of 54 m/s. The nozzle at ground level , has a diameter of 5 cm and the pipe leading to the fountain is 30 cm in diameter. The pump for the system is 6 meters below the fountain.

Part A.What is the hydrostatic pressure due to the height of the nozzle above the pump?

g h = 1000 * 9.8 * 6 = 58800 pa

Part B.What is the velocity of the water in the connecting pipe? (Dia =30cm)

v1 D1^2/4 = v2 D1^2/4

v2 = v1 *(D1/D2)^2 = 54 * (5/30) *(5/30) = 1.5 m/s

Part C.What is the weight of water that flows through the fountain in10minutes?

v A g t = 1000 * 54 * 3.1416*5e-2*5e-2/4 * 9.8 * (10*60) = 6.23e5 N

Part D.What is the pump pressure needed to operate this pump?

P2 - P1 = 0.5 (v1^2 - v2^2) + g (h1 - h2)

P2 - 1e5 = 0.5*1000 * (54*54-1.5*1.5) + 1000*9.8*(6 - 0)

P2 = 1.62e6 Pa

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