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 5.30 105 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 = 9.25 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.

(a) Jones house Incorrect: Pa

(b) Smith house Pa

Explanation / Answer

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 5.30 105 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 = 9.75 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 is full.

here,

mass of water in sphere = 5.30*10^5 kg
Rho of Water = 1000 kg/m^3

Volume of Sphere = (4/3)*pi*r^3
m/rho = (4/3)*pi*r^3

r = cuberoot(3m/4*rho*pi)
r = cuberoot((3*5.30*10^5)/(4*1000*3.14))
r = cuberoot(126.592)
r = 5.021 m

For House A
The effective Head = 18 + 5.021 = 23.021 m

Pressure = Rho * g * H
Pa = 1000 * 23.021 * 9.8
Pa = 225605.8 pa = 225.60 Kpa

For House B
The effective Head = 18 + 5.021 - 9.75 = 13.271 m
Pressure = Rho * g * H
Pb = 1000 * 13.271 * 9.8
Pb = 130055.8 pa = 130.05 Kpa

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

here,

mass of water in sphere = 5.30*10^5 kg
Rho of Water = 1000 kg/m^3

Volume of Sphere = (4/3)*pi*r^3
m/rho = (4/3)*pi*r^3

r = cuberoot(3m/4*rho*pi)
r = cuberoot((3*5.30*10^5)/(4*1000*3.14))
r = cuberoot(126.592)
r = 5.021 m

For House A
The effective Head = 18 + 5.021 = 23.021 m

Pressure = Rho * g * H
Pa = 1000 * 23.021 * 9.8
Pa = 225605.8 pa = 225.60 Kpa

For House B
The effective Head = 18 + 5.021 - 9.25 = 13.771 m
Pressure = Rho * g * H
Pb = 1000 * 13.771 * 9.8
Pb = 134955.8 pa = 134.95 Kpa

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