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 4.55 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 4.55 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.

Explanation / Answer

If the reservoir contains 4.55x10^5 kg of water and water has a density of 10^3 kg/m^3, then the reservoir has a volume of 455 m^3 and a radius of 4.7713 m.
P = (rho)gh where rho is the density.
For house A, P = rho g h = (1000)*(9.8)*(15+2*4.7713) = 2.41 x 10^5 Pa
For house B, P = rho g h = (1000)*(9.8)*(15-7.30+2*4.7713) = 1.69 x 10^5 Pa

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