# Pressure exerted on the end of a pool

• JCL
In summary, the conversation discusses calculating the force exerted by water against one of the triangular ends of a trough with specific dimensions and filled with water of a given weight density. The equation F=pgxa is used to calculate the force, but there is a discrepancy in the expression for "a" and the integration limits. The correct setup is 624g integral (4-x)(5-1.25x) dx, with x representing the distance from the top of the trough.
JCL

## Homework Statement

Consider a
trough with triangular ends, as pictured below, where the tank is 10 feet long, the top is 5
feet wide, and the tank is 4 feet deep. Say that the trough is full to within 1 foot of the top with water
of weight density 62.4 pounds/ft^3. How much force does the water exert against one of the triangular
ends?

## Homework Equations

F=pgxa The given picture has the axis rotated 90 degrees clockwise

## The Attempt at a Solution

I took the integral from 0 to 3 of p * g * x * a dx
so I got integral of 0 to 3 of (62.4 lbs/ft^3)(g)(4-x)(10(5-1.25x) dx
which can be written as 624g integral (4-x)(5-1.25x) dx
is this set up correct?

Pressure depends on ...?
So force is ρgha as you say. So where does the length of trough creep into your calculation?

I think it's your expression for a that is wrong, (10(5-1.25x) , as well as the missing bracket.

JCL said:
integral from 0 to 3 of p * g * x * a dx
so I got integral of 0 to 3 of (62.4 lbs/ft^3)(g)(4-x)(10(5-1.25x) dx
How exactly are you defining x? The above is not consistent.

## 1. What exactly is the pressure exerted on the end of a pool?

The pressure exerted on the end of a pool is the force per unit area that is applied to the surface of the pool at the end. This pressure is typically caused by the weight of the water in the pool and any additional external forces, such as the weight of a person standing on the end of the pool.

## 2. How is the pressure exerted on the end of a pool calculated?

The pressure exerted on the end of a pool can be calculated using the formula P = F/A, where P is pressure, F is force, and A is the area on which the force is applied. In the case of a pool, the force is the weight of the water and any additional external forces, and the area is the surface of the pool at the end.

## 3. How does the depth of the water affect the pressure at the end of a pool?

The depth of the water in a pool does not directly affect the pressure at the end of the pool. However, the depth of the water can indirectly affect the pressure by adding to the weight of the water and increasing the overall force exerted on the end of the pool.

## 4. Does the shape of the pool affect the pressure at the end?

Yes, the shape of the pool can affect the pressure at the end. A circular or oval-shaped pool will evenly distribute the pressure around the end, while a rectangular or square-shaped pool may have higher pressure at the corners due to the weight of the water being concentrated in those areas.

## 5. How does the pressure at the end of a pool change with an increase in water level?

An increase in water level will result in an increase in the pressure at the end of a pool. This is because there is more weight of water being exerted on the end, which increases the force and therefore the pressure. However, the rate at which the pressure increases will depend on the shape and size of the pool.

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