Calculating Pressure & Force in a Swimming Pool

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In summary: For the second equation, you can use the standard atmosphere as the pressure of the air and then multiply it by the density of water to find the pressure at the bottom of the pool. For b), you will need to use calculus to integrate the pressure along the length of the pool. The force on the long side will be greater than the force on the bottom because the pressure is increasing as you go down the side of the pool. In summary, the force on the bottom of the pool can be calculated by multiplying the pressure at the bottom (using the second equation with the standard atmosphere as the pressure of the air) by the area of the bottom (50m x 20m). For the long side, calculus will need to be used
  • #1
roman15
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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
 
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  • #2
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.
 
  • #3
so what i thought of doing for a) is correct then?
 
  • #4
roman15 said:
so what i thought of doing for a) is correct then?

Sure.
 
  • #5


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.
 

1. What is pressure in a swimming pool?

Pressure in a swimming pool refers to the force exerted by the water on the walls and bottom of the pool. It is measured in units of force per unit area, such as pounds per square inch (psi) or newtons per square meter (N/m²).

2. How is pressure calculated in a swimming pool?

Pressure in a swimming pool can be calculated using the formula P = F/A, where P is pressure, F is the force exerted by the water, and A is the area over which the force is distributed. The force can be calculated by multiplying the weight of the water by the acceleration due to gravity, and the area can be calculated by multiplying the length and width of the pool.

3. How does pressure change with depth in a swimming pool?

Pressure in a swimming pool increases with depth because there is more water above pushing down on the lower layers. This is due to the weight of the water and the force of gravity acting on it. For every 10 feet of depth, the pressure increases by about 4.3 psi.

4. What is the impact of pressure on swimmers in a swimming pool?

The impact of pressure on swimmers in a swimming pool can vary depending on the depth and size of the pool. Generally, the deeper the pool, the greater the pressure, which can make it more difficult for swimmers to move and can increase the risk of injury. However, the pressure in most swimming pools is not significant enough to cause any major impacts on swimmers.

5. Can pressure in a swimming pool be controlled or changed?

Yes, pressure in a swimming pool can be controlled and changed by adjusting the water level or the size of the pool. Increasing the water level will increase the pressure, while decreasing the water level will decrease the pressure. Changing the size of the pool, either by adding or removing water, will also impact the pressure. Additionally, the use of pool pumps and filters can help regulate pressure levels in a swimming pool.

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