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 100 meters into the air. It requires an exit velocity of 50 m/s. The nozzle at ground level , has a diameter of 8 cm and the pipe leading to the fountain is 30 cm in diameter. The pump for the system is 5 meters below the fountain.

hydrostatic pressure due to the height of the nozzle above the pump is 4.90 x 10^4 Pascals

velocity of the water in the connecting pipe (Dia =30cm) is 3.56m/s

weight of water that flows through the fountain in9minutes is 1.33 x 10^6 Newtons

Explanation / Answer

If I'm reading your question correctly, the boldfaced stuff are things you've already calculated. If so, great. The last question, the pressure at the pump, can be found by using Bernoullis equation. Choose point 1 to be the nozzle and point 2 to be the pump. Then...

p1 + (1/2) density v1^2 + density * gh1 = p2 + (1/2) density v2^2 + density * gh2

103000 + 500 * 50^2 + 1000 * 9.80*5 = p2 + 500 * 3.56^2 + 1000 * 9.80 * 0

or

1402000 = p2 + 63.37

p2 = 1402000 - 63.37 = 1402000 pascals = 1.402 x 10^ 6 pascals

This is the absolute pressure at the pump. The question might want gauge pressure instead, which is absolute minus one atmosphere, or

1402000 - 103000 = 1.299 x 10^6 Pascals

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