Question

Most towns use a water tower to store water and provide pressure in the pipes that deliver water to customers. The figure below shows a spherical water tank that holds 5.80 105 kg of water when full. Note that the tank is vented to the atmosphere at the top and that the pipe delivering water to customer Smith is a height h = 3.75 m above the level of the pipe delivering water to customer Jones. Determine the gauge pressure of the water at the faucet of each house when the tank if full.
There is a spherical water-filled chamber with a vent on top and underneath it is a pipe 18 m long that leads down to the ground. At ground level a horizontal pipe connects the faucet in the Jones house to the water supply. The faucet in the Smith house is connected to the water supply with a pipe at a height h above ground level.
(a) Jones house
Pa

(b) Smith house
Pa

Answer 1

The effective height of the water for Smith's house will be 24.61m.

How to calculate the height?

Based on the information given, the volume of the water in sphere will be:

= 4/3πr³ = (5.80 × 10^5)/1000

= 4.18r³ = 580

r³ = 138.7

r = 5.18m

The effective height of the water will be:

= 18.0 + 2(5.18)

= 28.36

The gauge pressure at Faucet of Jones house will be:

= pgh

= 1000(9.8)(28.36)

= 277.9kPa

The effective height of the water for Smith's house will be:

= 18.0 + 2(5.18) - 3.75

= 24.61m

The gauge pressure at Faucet of Jones house will be:

= 1000 × 9.8 × 24.61

= 241.2kPa

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