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 5.50 105 kg of water when full. (h = 8.50 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.

Find:

House A = ? Pa

House B = ? Pa

Explanation / Answer

(a)

The pressure at the level of house A is given by Equation P A = P atm + gh A .

Now the height h A consists of the 15.0 m plus the diameter of the tank.

We first calculate the radius of the tank, from which we can infer d.

Since the tank is spherical, its full mass is given by

M = V = [(4/3) pi r^3 ]

Therefore

r^3 = 3M / * 4 pi

r^3 = 3*( 5.50* 10^5 ) / 1000 * 4 pi
r = 5.08 m

Therefore, the diameter of the tank is 10.16 m, and the height is given

h A = 10.16 + 15 = 25.16 m

According to Equation, the gauge pressure in house A is, therefore,

P A - P atm = gh A .

P A - P atm = 1000*9.8*25.16 .

P A - P atm = 2.466*10^5 Pa .

(b)

The pressure in house B is, P B = P atm + gh B.

Where h B = 15 + 10.16 – 8.5 = 16.66 m

According to Equation, the gauge pressure in house B is, therefore,

P B - P atm = gh B .

P B - P atm = 1000*9.8*16.66 .

P B - P atm = 1.63*10^5 Pa .

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