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 7.02 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.

Note: The drawing referred to in the question is attached below

gauge pressure that the water has at the faucet in house A = 254878.4 Pa

gauge pressure that the water has at the faucet in house B = 186278.4 Pa

Explanation:

Mass of water,

Calculate the volume of water in the reservoir:

Where = density of water = 10³ kg/

Since the reservoir is spherical in shape, the volume of a sphere is given by the equation:

By observing the diagram shown, the height of the tower to house A:

h = 2r + 15 = 2(5.504) + 15 = 26.008 m

The gauge pressure in house A can be given by the formula:

By observing the diagram shown, the height of the tower to house B:

h = 2r + 15 - 7 = 2(5.504) + 15 - 7

h= 19.008 m