Calculating Pressure & Force in a Swimming Pool

[roman15]

Homework Statement

A swimming pool in 50m long, 20m wide and 3m deep. Its filled to the top
a)what is the force of the water on the bottom (50m x 20m) of the pool?
b)what is the force on the long side (50m x 3m) of the pool?

Homework Equations

force=pressure*area

p(d)=(pressure of the air) +(density of the fluid)*g*d where d is the distance from the top to bottom of the pool

The Attempt at a Solution

not exactly sure, but for a) do i use the second equation to find the pressure at the bottom of the pool and then just multiple it by its area? but then what is the pressure of the air?

for b) I am not really sure what to do

 

[gneill]

For the pressure of the air you can use one standard atmosphere (look it up).

The bottom is all at one depth so that it's all at one pressure. You're not so lucky with the sides. Looks like a touch of calculus will come in handy.

 

[roman15]

so what i thought of doing for a) is correct then?

 

[gneill]

so what i thought of doing for a) is correct then?

Sure.

 

[rwisz]

I can provide a response to the questions in the following manner:

a) To calculate the force of the water on the bottom of the pool, we can use the equation force = pressure * area. In this case, the pressure is equal to the sum of the pressure of the air and the pressure due to the weight of the water. The pressure of the air can be assumed to be equal to atmospheric pressure (1 atm). The pressure due to the weight of the water can be calculated using the equation p(d) = p(a) + ρgd, where p(a) is the pressure of the air, ρ is the density of the fluid (in this case, water), g is the acceleration due to gravity, and d is the distance from the top to the bottom of the pool. In this case, d = 3m. Therefore, the pressure at the bottom of the pool would be equal to 1 atm + (1000 kg/m^3 * 9.8 m/s^2 * 3m) = 29,400 Pa. Multiplying this pressure by the area of the bottom of the pool (50m * 20m = 1000 m^2), we can calculate the force of the water on the bottom of the pool to be 29,400 * 1000 = 29,400,000 N.

b) To calculate the force on the long side of the pool, we can use the same equation, force = pressure * area. In this case, the pressure is determined by the depth of the water on the long side. Since the depth is 3m, the pressure at this side of the pool would be equal to 1 atm + (1000 kg/m^3 * 9.8 m/s^2 * 3m) = 29,400 Pa. Multiplying this pressure by the area of the long side (50m * 3m = 150 m^2), we can calculate the force on the long side of the pool to be 29,400 * 150 = 4,410,000 N.

I hope this explanation helps. If you have any further questions, please let me know.