A water tower is a familiar sight in many towns. The purpose of such a tower is

Question

A water tower is a familiar sight in many towns. The purpose of such a tower is to provide storage capacity and to provide sufficient pressure in the pipes that deliver the water to customers. The drawing shows a spherical reservoir that contains 6.96 x 105 kg of water when full. The reservoir is vented to the atmosphere at the top. For a full reservoir, find the gauge pressure that the water has at the faucet in (a) house A and (b) house B. Ignore the diameter of the delivery pipes.

A water tower is a familiar sight in many towns. The purpose of such a tower is to provide storage capacity and to provide sufficient pressure in the pipes that deliver the water to customers. The drawing shows a spherical reservoir that contains 6.96 times 105 kg of water when full. The reservoir is vented to the atmosphere at the top. For a full reservoir, find the gauge pressure that the water has at the faucet in house A and house B. Ignore the diameter of the delivery pipes.

Explanation / Answer

If the reservoir contains 6.96 x10^5 kg of water and water has a density of 10^3 kg/m^3, then the reservoir has a volume of 696 m^3 and a radius of 4.874 m.
P = (rho)gh where rho is the density.
Volume sphere = 4/3 pi r^3
696 = 4 x 3.14 x r^3 / 3
r = 5.49 m

At house A, the effective head is 15 + 5.49m = 20.49 m

Pressure = denisty x g x h = 1000 x 9.8 x 20.49 = 200877Pa or 200Kpa

(you should always remember 10m head is approximately 100kPa)

At house b, the effective head = 15 + 5.49 - 7.3 = 13.19 m

P = 1000 x 9.8 x 13.19 = 129262 Pa or 129 kPa

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