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 7.02 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.

Answer 1

The student's question involves calculating the gauge pressure of water at different heights in a water distribution system, which is a concept related to hydrostatic pressure in physics.

Step-by-step explanation:

The question pertains to the concept of hydrostatic pressure in physics.

Hydrostatic pressure is the pressure that is exerted by a fluid at equilibrium at any given point within the fluid due to the force of gravity and is calculated using the formula p = ρgh, where p is the hydrostatic pressure, ρ is the fluid density, g is acceleration due to gravity (9.81 m/s2), and h is the height of the fluid column above the point in question.

The gauge pressure, which is the pressure relative to the ambient atmospheric pressure, can be determined based on this formula.

For example, in the student's homework question above, the pressure that the water has at the faucet in house A or B would depend on the vertical height difference between the water level in the spherical reservoir or city water tower and the faucet location, while ignoring pipe diameter as mentioned in the question.

Answer 2

Note: The drawing referred to in the question is attached below

Answer:

gauge pressure that the water has at the faucet in house A = 254878.4 Pa

gauge pressure that the water has at the faucet in house B = 186278.4 Pa

Step-by-step explanation:

Mass of water,
`m = 7.02 * 10^5 kg`

Calculate the volume of water in the reservoir:

`V = m/\rho`

Where
`\rho` = density of water = 10³ kg/
`m^3`

`V = (7.02 * 10^5)/(10^3) \\V = 702 m^3`

Since the reservoir is spherical in shape, the volume of a sphere is given by the equation:

`V = (4)/(3) \pi r^(3) \\702 = (4)/(3) \pi * r^(3) \\r = 5.504 m`

By observing the diagram shown, the height of the tower to house A:

h = 2r + 15 = 2(5.504) + 15 = 26.008 m

The gauge pressure in house A can be given by the formula:

`P_A = \rho gh\\P_A = 1000 * 9.8 *26.008\\P_A = 254878.4 Pa`

By observing the diagram shown, the height of the tower to house B:

h = 2r + 15 - 7 = 2(5.504) + 15 - 7

h= 19.008 m

`P_B = \rho gh\\P_A = 1000 * 9.8 *19.008\\P_B = 186278.4 Pa`