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What is the absolute pressure on the bottom of a swimming pool 24.0 m by 7.20 m whose uniform depth is 2.24 m?

What is the total force on the bottom of that swimming pool?

What will be the pressure against the side of the pool near the bottom?

Added Thu, 02 Jul '15

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find the mass of the water:

V = 24 * 7.2 * 2.24

V = 387.07 m^3

m = V * ?

m = 387.07 * 1000

m = 387070 kg

From this we can find the weight of the water:

weight = mg

weight = 387070 * 9.81

weight = 3797156.7 N

We need to add this to the force of the atmosphere pressing down on the pool too:

A = 24 * 7.20

A = 172.8 m^2

F = P * A

F = 101325 * 172.8

F = 17508960 N

So the total force on the bottom of the pool is:

Force = 3797156.7 + 17508960

Force = 21306117 N

Force = 21,310,000 N to three significant figures.

From this, and using the area calculated earlier, it is possible to calculate the pressure on the bottom:

P = F / A

P = 21306117 / 172.8

P = 123299.2 Pa

P = 124 kPa to three significant figures.

The pressure on the side near the bottom will be very nearly equal to the pressure on the bottom, so also 124 kPa.

Added Thu, 02 Jul '15

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