# Buoyant force of pool (fluids)

• Clark Smith
In summary, to find the total outward force exerted on the vertical wall of the above-ground backyard swimming pool, we need to calculate the average water pressure and the surface area of the pool wall. Using the given diameter and depth of the pool, we can calculate the volume and use the density of water to find the buoyant force. However, since this is not a buoyant force problem, we need to consider the force exerted by the water on the sides of the pool wall. By calculating the average water pressure and multiplying it by the surface area of the pool wall, we can find the total outward force exerted on the wall. The answer, according to the back of the book, is 160kN.
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

## 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

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?

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.

## What is the buoyant force of pool fluids?

The buoyant force of pool fluids is the upward force exerted by a fluid on an object immersed in it. It is a result of the pressure difference between the top and bottom of the object, and is equal to the weight of the fluid displaced by the object.

## How is the buoyant force of pool fluids calculated?

The buoyant force of pool fluids is calculated using Archimedes' principle, which states that the buoyant force is equal to the weight of the fluid displaced by the object. This can be calculated by multiplying the density of the fluid, the volume of the fluid displaced, and the acceleration due to gravity.

## Does the shape and size of an object affect the buoyant force of pool fluids?

Yes, the shape and size of an object do affect the buoyant force of pool fluids. Objects with a larger volume will displace more fluid, resulting in a greater buoyant force. Additionally, objects with a greater surface area will experience more pressure from the fluid, resulting in a larger buoyant force.

## How does the density of an object affect the buoyant force of pool fluids?

The density of an object does not directly affect the buoyant force of pool fluids. However, the density of the fluid and the density of the object do play a role. An object with a lower density than the fluid will experience a greater buoyant force and will float, while an object with a higher density will experience a smaller buoyant force and will sink.

## Can the buoyant force of pool fluids be greater than the weight of an object?

Yes, the buoyant force of pool fluids can be greater than the weight of an object. This is known as "floatation" and occurs when the buoyant force is strong enough to keep the entire object afloat. In this case, the object will not sink and will remain at the surface of the fluid.

• Introductory Physics Homework Help
Replies
9
Views
1K
• Introductory Physics Homework Help
Replies
13
Views
2K
• Introductory Physics Homework Help
Replies
10
Views
3K
• Introductory Physics Homework Help
Replies
7
Views
3K
• Introductory Physics Homework Help
Replies
8
Views
1K
• Introductory Physics Homework Help
Replies
4
Views
3K
• Introductory Physics Homework Help
Replies
7
Views
6K
• Introductory Physics Homework Help
Replies
18
Views
3K
• Introductory Physics Homework Help
Replies
5
Views
2K
• Introductory Physics Homework Help
Replies
4
Views
2K