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 7.86 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.

Answer 1

First we have find the height of the spherical reservoir, for that we can use basic hydrostatic equation, ie

where,

P = pressure

= density of the liquid

g= gravity of earth = 9.8 m/s2

h= height or depth of the liquid

Infact the pressure differential depends only on the height of the reservoir not the shape of the reservoir. So inorder to find the height,lets find the volume of the reservoir using the equation,

where M is the mass of the sphere and V is the volume

Given M= 7.86 105 kg,

  = density of water

Therefore,

= 786 m3

The volume of a sphere is (spherical reservoir)

where r is the radius of the sphere.

Therefore,

r = 5.76 m

Then, height of the reervoir will be, h= 2r + h1

= 2 5.76+ h1

Therefore,

(b) The extra height h2 reduces the pressure by

Then the gauge pressure at the elevated house,

Pa-pascal unit of pressure

h, h1 and h2  are marked in the figure. substitute the corresponding heights and find the answers in above equations.