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 4.50 105 kg of water when full. (h = 8.10 m.) 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 each house. Ignore the diameter of the delivery pipes. for house A? for house B?

Explanation / Answer

The pressure at any point is governed by the effective head of water above it. In this case, you need to work out the diameter of the sphere first, so that you know the head of water in the sphere. 5.25 x 10^5 kg of water = 5.25x10^5 litres, or 525m^3 Volume sphere = 4/3 pi r^3 525 = 4 x 3.14 x r^3 / 3 r = 5m At house A, the effective head is 15 + 5m = 20m Pressure = denisty x g x h = 1000 x 9.8 x 20 = 196000Pa or 196Kpa (you should always remember 10m head is approximately 100kPa) At house b, the effective head = 15 + 5 - 7.3 = 12.7m P = 1000 x 9.8 x 12.7 = 124460Pa or 124.5kPa

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