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 3.22 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 3.22 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 (a) house A and (b) house B. Ignore the diameter of the delivery pipes.

Explanation / Answer

Since the density of water is 1000 kg/m^3 and we have 3.22 X 10^5 kg of water in the sphere, we can find the diameter of the sphere.

Density = m/V

1000 = 3.22 X 10^5/V

V = 322 m^3

Volume of a sphere is 4/3pir^3

322 = 4/3(pi)(r^3)

r = 4.25 m

The diameter = 2r = 8.5 m

Thus the height of the water from the top of the tower to ground = 8.5 + 15 = 23.5 m

The pressure = pgh

At faucet A, Pressure = (1000)(9.8)(23.5) = 2.30 X 10^5 Pa

At faucet B, Pressure = (1000)(9.8)(23.5 - 7.3) = 1.59 X 10^5 Pa

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