Buoyant force of pool (fluids)

[Clark Smith]

Homework Statement

An above-ground backyard swimming pool is shaped like a large hockey puck, with a circular bottom and a vertical wall forming its perimeter. The diameter of the pool is 5.2m and its depth is 1.4m. Find the total outward force exerted on the vertical wall of the pool.
Density of air: 1.29 kg/mcubed
Density of water: 1000 km/mcubed
Answer: (back of book) 160kN

Homework Equations

Buoyant Force = density of external fluid x gravity x volume
Volume = radius squared x pi x height

The Attempt at a Solution

Volume = (5.2/2)squared (pi) (1.4) = 29.732 mcubed
Buoyant Force = (1.29) (9.8) (29.732) = 375.872 N

Attempt 2, using water's density
Buoyant Force= (1000) (9.8) (29.732) = 291373.922 N

 

[Doc Al]

water pressure

This isn't a buoyant force problem. Instead, consider the force exerted by the water on the sides of the pool wall. What's the average water pressure? What's the surface area of the pool wall?

 

[Moetasim]

The total outward force exerted on the vertical wall of the pool is the sum of the buoyant force and the weight of the water in the pool. Since the pool is filled with water, the weight of the water will be equal to the buoyant force. Therefore, the total outward force exerted on the vertical wall of the pool will be 2 x 291373.922 N = 582747.844 N or approximately 160 kN.

This calculation assumes that the pool is completely filled with water and that there is no air trapped in the pool. If there is air present, it will add a smaller amount to the buoyant force, but the overall answer will still be close to 160 kN. It is important to consider the buoyant force when designing structures that will be in contact with fluids, as it can significantly impact the forces acting on the structure.