Most towns use a water tower to store water and provide pressure in the pipes th

Question

Most towns use a water tower to store water and provide pressure in the pipes that deliver water to customers. The figure below shows a spherical water tank that holds 5.60 105 kg of water when full. Note that the tank is vented to the atmosphere at the top and that the pipe delivering water to customer Smith is a height h = 3.25 m above the level of the pipe delivering water to customer Jones. Determine the gauge pressure of the water at the faucet of each house when the tank if full.

Explanation / Answer

Volume:

V= m/density= 5.6×10^5 /1000 = 5.6×10^2 m^3

The radius of the container is

V=(4/3)R^3

R=[3V/4]^1/3

= [3*5.6*10^2/4*3.14]^1/3

= 10.9663 m

Diameter:

d= 2R=21.9326 m

Gauge pressure at A is

P-Po= density*g(d+H)

= 1000*9.8*(21.9327+18)

= 3.91×10^5 Pa

Gauge pressure at B is

P-Po= density*g(d+H-h)

= 1000*9.8*(21.9327+18-3.25)

= 3.59×10^5 Pa

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