X Most towns use o water tower to store water and provide pressure in the pipes
ID: 1554167 • Letter: X
Question
X Most towns use o 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 5.00 times 10^5 kg of water when full. Note that the tank is vented to the atmosphere at the tap and that the pipe delivering water to customer Smith is a height h= 7.75 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 if full. Jones house What is the proper height of the fluid to use for the Jones house? See if you call determine an expression for the diameter of the tank in terms of fluid required to fill the tank and the mass density of the fluid. pa (b) Smith house paExplanation / Answer
The volume of the reservoir can be found from the mass of stored water and water's density:
V = m/rho
And from this water volume, you can find the diameter, since it is spherical:
V = 4/3*Pi*(d/2)^3
V = Pi*d^3/6
d = cube root(6*V/Pi)
In terms of mass:
d = cube root(6*m/(Pi*rho))
At location A(smith's house), the faucet is a distance d + H from the top of the water surface. To find gauge pressure
there, simply
use the hydrostatics equation for pressure variation with depth. Neglect flow effects.
P_gaugeA = rho*g*(H + d)
At location B(john's house), the faucet is a distance d + H - h from the top of the water surface. To find gauge
pressure there, simply use the hydrostatics equation for pressure variation with depth. Neglect flow effects.
P_gaugeB = rho*g*(H + d - h)
P_gaugeA = rho*g*(H + cbrt(6*m/(Pi*rho)))
P_gaugeB = rho*g*(H + cbrt(6*m/(Pi*rho)) - h)
Given :-
m = 5 x 10^5 kg;
rho = 1000 kg/m^3;
H = 18 m;
h = 7.75 m;
g = 9.81 N/kg
d = cube root(6*m/(Pi*rho))
d = 9.849
P_gaugeA = 273.2 kPa
P_gaugeB = 197.17 kPa
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