Calculating Force on Swimming Pool Bottom and Short Sides | Fluid Statics

[whereisccguys]

A swimming pool has dimension 23.0 m by 8.0 m with a depth of 3.0 m. When it is filled with water, what is the force (resulting from the water alone) on the bottom?

When it is filled with water, what is the force (resulting from the water alone) on each short side?

i figured out part a already by finding the weight of the water in the swimming pool and multiplying it by gravity (which gave me 5.41E+06 N) but i cannot figure out part b... am i suppose to use the formula
Pressure = F/A?? (i tried with serveral different numbers and still got the wrong answer)

 

[Cyrus]

$$F=\rho g A d$$

 

[kyle8921]

I would approach this problem by first understanding the concept of fluid statics and how forces are calculated in this scenario. In fluid statics, the force on a surface is equal to the pressure exerted by the fluid multiplied by the surface area. Therefore, for part a, the force on the bottom of the swimming pool can be calculated by first finding the pressure exerted by the water and then multiplying it by the surface area of the bottom.

To find the pressure exerted by the water, we can use the formula P = ρgh, where ρ is the density of water (1000 kg/m^3), g is the gravitational acceleration (9.8 m/s^2), and h is the depth of the water (3.0 m). Plugging in these values, we get P = 1000 kg/m^3 * 9.8 m/s^2 * 3.0 m = 29400 Pa.

To find the surface area of the bottom of the pool, we can simply multiply the length and width dimensions, giving us 23.0 m * 8.0 m = 184 m^2.

Therefore, the force on the bottom of the swimming pool can be calculated as F = P * A = 29400 Pa * 184 m^2 = 5.41E+06 N, which is the same result you obtained.

For part b, we can use the same formula to calculate the force on each short side of the pool. However, the surface area will be different as the sides have a different length and depth compared to the bottom. The length of each short side is 8.0 m and the depth is 3.0 m. Therefore, the surface area of each short side would be 8.0 m * 3.0 m = 24 m^2.

Using this surface area in the formula, we get F = P * A = 29400 Pa * 24 m^2 = 705600 N. Therefore, the force on each short side of the swimming pool is 705600 N.

In summary, to calculate the force on the swimming pool bottom and short sides, we need to understand the concept of fluid statics and use the formula P = ρgh to find the pressure exerted by the water. Then, we can multiply this pressure by the surface area of each respective surface to get the force.