# Calculating Force Exerted by Water on Container Bottom

• jayced
In summary, the container has a lower part holding 12.5 m3 of water with a surface area of 4.68 m2 and a height of 3.30 m. The neck contains a column of water with a volume of 0.200 m3 and a height of 8.20 m. The total force exerted by the water on the bottom of the container is 527440.68N, taking into account the density of water, acceleration due to gravity, and height of the water column. The formula for this calculation is F = PA, with units in Newtons. However, the question may also include the force exerted by the air above, which would change the calculation.
jayced

## Homework Statement

A container has a large cylindrical lower part with a long thin cylindrical neck. The lower part of the container holds 12.5 m3 of water and the surface area of the bottom of the container is 4.68 m2. The height of the lower part of the container is h1 = 3.30 m and the neck contains a column of water h2 = 8.20 m high. The total volume of the column of water in the neck is 0.200 m3. What is the magnitude of the force exerted by the water on the bottom of the container?

## Homework Equations

F = PA
= (ρgh + P0)(4.68 m²)
ρ = density of water=1000kg/m^3
g = acceleration due to gravity = 9.8 m/sec²
h = height of water column = 3.30m + 8.20m = 11.50 m
P0 = air pressure at top of column = 1 atmosphere.

## The Attempt at a Solution

F = PA
= (ρgh + P0)(4.68 m²)
= (1000kg/m^3)(9.8m/s^2)(11.50m) + 1 atm.)(4.65 m²)=527440.68N need to convert to MN

Is my formula correct?
Are my units for force correct that it comes out in Newtons?

It's correct, but the question asks for the pressure the water exerts. The pressure exerted by the air above is not usually taken into consideration.

I think the contribution of force exerting on bottom of container includes force by neck and force by lower part.

F = F_neck + F_low

## 1. What is the formula for calculating force exerted by water on a container bottom?

The formula for calculating force exerted by water on a container bottom is F = ρghA, where F is the force in Newtons, ρ is the density of water in kg/m^3, g is the gravitational acceleration in m/s^2, h is the height of the water column in meters, and A is the area of the container bottom in square meters.

## 2. How do I determine the density of water for the calculation?

The density of water is typically given in scientific units as 1000 kg/m^3. However, this value can vary slightly depending on temperature and impurities. It is best to consult a reliable source, such as a scientific textbook or online database, for the most accurate density value for your specific situation.

## 3. Can this formula be used for any container shape?

Yes, this formula can be used for any container shape as long as the container bottom is flat and the height of the water column is measured from the bottom of the container to the surface of the water. If the container has a non-flat bottom or the water level is measured from a different reference point, the formula may need to be modified.

## 4. What units should be used for the variables in the formula?

The units used for the variables in the formula should be consistent. For example, if the density of water is given in kg/m^3, then the height of the water column should be given in meters and the area of the container bottom should be given in square meters. This will ensure that the final result is in Newtons, the unit for force.

## 5. How can I use this calculation to determine the stability of a container?

By calculating the force exerted by water on the container bottom, you can compare it to the weight of the container and its contents. If the force exerted by the water is greater than the weight, the container will likely tip over. This information can be useful for determining the stability of a container and making adjustments to prevent accidents or damage.

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