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 85 meters into the air. It requires an exit velocity of 44 m/s. The nozzle at ground level , has a diameter of 8 cm and the pipe leading to the fountain is 36 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?
PH =

Pascals
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Part B
What is the velocity of the water in the connecting pipe? (Dia = 36 cm)
V2 =

m/s
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Part C
What is the weight of water that flows through the fountain in 9 minutes?
Weight =

Newtons
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Part D
What is the pump pressure needed to operate this pump?
P2 =

Pascals
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Explanation / Answer

a)

P = g h = 1000 * 9.8 * 6 = 58800 Pa

b)

A2 v2 = A1 v1

v1 = A2 v2/A1 = D2^2 v2/D1^2 = 8*8 * 44/36/36 = 2.1728 2.17 m/s

c)

W = V g t = 1000 * (3.1416*0.08*0.08/4) * 44 * 9.8 * 9*60 = 1.17e6 N

d)

P1 = P2 + 0.5 * (v2^2 - v1^2) + g (y2 - y1)

P1 = 1e5 + 0.5*1000*(44*44-2.1728*2.1728) + 1000*9.8*(6-0)

P2 = 1.12e6 pa

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