# Calculating Force On A Dam, Using Pressure, Area, and other Known Values

• Beginner@Phys
In summary, the conversation discusses the calculation of the force on a horizontal layer of a dam wall located above a reservoir floor, and the torque on the dam caused by the water in the reservoir. The force is expressed in terms of water density, acceleration due to gravity, and other quantities from the problem introduction. Similarly, the torque is expressed in terms of these quantities and the distance from the point of rotation. The picture provided is a cross-section of the dam, and the desired force is the force on a thin layer of the dam.
Beginner@Phys

## Homework Statement

Part A
Consider a horizontal layer of the dam wall of thickness dx located a distance x above the reservoir floor. What is the magnitude of the force on this layer due to the water in the reservoir?

Express your answer in terms of , x, dx, the magnitude of the acceleration due to gravity , g and any quantities from the problem introduction: dw(water density), L(width of the dam), h (depth of the water). For more info: See image attached.

Part B
The force of the water produces a torque on the dam. In a simple model, if the torque due to the water were enough to cause the dam to break free from its foundation, the dam would pivot about its base (point P). What is the magnitude of the torque T about the point P due to the water in the reservoir?

Express your answer in terms of quantities given in the problem introduction and the magnitude of the acceleration due to gravity .

## Homework Equations

(1)P=P_o+ rho*g*h
(2)P=F/A

## The Attempt at a Solution

Part A: rho_w*g*x=F/A Therefore, F=rho_w*g*x (A). But what is the area equal to?
Part B: Use the equation for Torque T=r*F?

What they want is the force on a layer. The picture is a cross-section of the dam.

But a layer of "area" is a skinny ribbon Δx high and L wide.

## 1. How do you calculate the force on a dam?

To calculate the force on a dam, you can use the formula F = P x A, where F represents the force, P represents the pressure, and A represents the area. This formula can be used as long as you have the values for pressure and area.

## 2. What is the relationship between pressure and force?

The relationship between pressure and force is directly proportional. This means that as pressure increases, the force will also increase. This can be seen in the formula F = P x A, where F and P are directly proportional to each other.

## 3. What are some common units of measurement for pressure and force?

Some common units of measurement for pressure include pounds per square inch (psi), pascals (Pa), and atmospheres (atm). Common units of measurement for force include newtons (N), pounds (lb), and dynes (dyn).

## 4. Can you calculate the force on a dam using only pressure and area?

Yes, it is possible to calculate the force on a dam using only pressure and area. As mentioned earlier, the formula F = P x A can be used for this calculation. However, it is important to note that this formula assumes that the pressure is evenly distributed over the entire area of the dam.

## 5. How can calculating the force on a dam be useful?

Calculating the force on a dam can be useful for engineers and scientists who are involved in the design and maintenance of dams. By knowing the force acting on a dam, they can ensure that the structure is strong enough to withstand the pressure and prevent potential disasters. Additionally, this calculation can also be used to determine the amount of force that can be exerted on the dam before it reaches its breaking point.

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