# Solving for the Force Exerted on a Dam by Water

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(Image of dam)

## Step 1: Why Do You Need to Know How to Solve for the Force Exerted on a Dam?

If you ever take a statics class for engineering or physics class, you will need to know how to solve for the force exerted on a dam.

## Step 2: What Is the Practical Application?

Outside of the classroom, engineers must know the forces acting on a dam so they can correctly build one. If the materials used are to weak or the dam was not built well enough to withstand the forces acting upon it, the dam could break leading to flooding and destroying of people’s homes and livelihoods.

## Step 3: Needed Material/knowledge:

Basic understanding of algebra

Pencil/pen

Calculator

## Step 4: What Is the Force Exerted on a Dam?

Have you ever been swimming in a pool and had your ears pop near the bottom? This occurs because the weight of the water above you increases causing the pressure to also increase as the depth of the pool increases.

The same principle can be applied on a dam. The pressure is drawn as a triangle of arrows increasing in size. These arrows represent the pressure, and the size of the arrows demonstrates how the magnitude (amount) of the pressure increases directly with depth.

## Step 5: Needed Formula:

Force on the dam= pressure of the water (x) area

The area refers to the surface of the dam that come into direct contact with the water.

## Step 6: Needed Formula Part 2:

Breaking this formula down even further, we can write:

F= (density of water)(acceleration of gravity)(height of the water/2)(width of the dam (x) height of the water)

The density of water and gravity indicate the weight of the water. (like how in a pool the weight of water above you affects the pressure)

The (h/2) refers to the centroid of the triangle, or in more basic terms, a location where the total weight of the water can be theoretically condensed to a particular point.

The (w (x) h) is the area in contact with the water.

## Step 7: Examining the Constants:

The density of water and the acceleration of gravity are constants. This means they have the same value no matter what problem you are presented with.

## Step 8: Addressing the Rest of the Variables:

The rest of the dimensions are given in a problem. The values just need to be placed into the appropriate variables before conducting simple algebra to solve for the answer.

## Step 9: Example Problem:

What is the force acting on a 25 meter width dam with the thickness of 1 meter and water with a depth of 15 meters? (Note: 1N= 1 kg m/s^2 and 1N=1000kN)

Notice how the units cancel out to leave (kg (x) m)/s^2.

## Step 10: Test What Your Have Learned:

What is the force acting on a 35 meter width dam with the thickness of 1 meter and water with a depth of 15 meters?

(finish this step before moving onto the next slide)