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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 7.41 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.

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Complete Question

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Answer:

The gauge pressure that water has at the House A
P_A = 257020.68 Pa

The gauge pressure that water has at the House B
P_B = 188454 \ Pa

Step-by-step explanation:

From the question we are told that

The mass of water when full is
m_f = 7.41* 10^(5) kg

Generally the volume of water in this tank is mathematically represented as


V = (m )/(\rho)

Where
\rho is the density of water with a value of with a value of
\rho = 1000 kg /m^3

substituting values


V = (7.41 *10^5)/(10^3)


V = 741 m^3

This volume is the volume of a sphere since the tank is spherical so


V = (4 \pi ^3)/(3)

making r the subject of the formula


r =\sqrt[3]{ (741 *3 )/(4\pi) }


r = 5.6134 m

Now we can use this parameter to obtain the diameter

So


d = 2 * r

substituting values


d = 2 * 5.6134


d = 11.23m

The pressure the water has at faucet in House A is mathematically evaluated as


P_A = \rho g h_A

This height is obtained as follows


h_A = d+ 15

The value 15 is gotten from the diagram

so


h_A = 15 + 11.23


h_A = 26.22 m

Now substituting values


P_A = 26.23 * 9.8 * 1000


P_A = 257020.68 Pa

The pressure the water has at faucet in House B is mathematically evaluated as


P_B = \rho g h_B

This height is obtained as follows


h_B = d+ 15

The value 15 is gotten from the diagram

so


h_B = d + 15 -h

substituting values


h_B =11.23 + 15 -7


h_A = 19.23 m

Now substituting values


P_B = 19.23 * 9.8 * 1000


P_B = 188454 \ Pa

A water tower is a familiar sight in many towns. The purpose of such a tower is to-example-1
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