Engineering Statics: pressure on dam question

In summary, the force P on the body of water CDE is calculated using the average hydrostatic pressure multiplied by the area covered by the water, which in this case is 18 sq. ft. The average pressure is found by multiplying the weight density of the water (62.4 lb/ft^3) by the depth (18 ft). This is because the pressure varies with depth in the dam. The force per length on a distributed load due to pressure will always have a 1:1 ratio between height and width, as seen in this calculation where the height is 18 ft and the width is 1 ft.
  • #1
thepatient
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I just had a question regarding the determination of force P on the body of water CDE. For weight P, they used 1/2(18ft)(1ft)(18ft)(62.4lb/ft^3). I understand that this is because we are using volume*specific weight to find net weight P on body CDE. What I don't understand is why did they use 18ft as the base of the triangle? Is this because the pressure varies with the depth in the dam? Will this always be the case where there is a 1:1 ratio between height and width when considering the force per length on a distributed load due to pressure? Thanks. :]
 
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  • #2
P, according to problem statement, is the force due to pressure. To go from pressure to force you must multiply by area. They calculate the average pressure by .5*18*62.4. That must be multiplied by an area to get force P. The area is 1.0*18.
 
  • #3
The pressure at the bottom of the water is the depth * weight density of the water or
p = 18 * 62.4 = 1123.2 lbs / sq.ft.

Since the pressure of the water varies with depth, the average pressure is
0.5 p = 0.5 * 1123.2 = 561.6 lbs / sq. ft.

In order to calculate the total hydrostatic force acting on a 1-foot slice of the dam,
the average hydrostatic pressure must be multiplied by the area covered by the water.
The area is 18 feet deep by 1 foot wide,
so A = 18 x 1 = 18 sq. ft.

The hydrostatic force is equal to avg. pressure * area or
P = (p avg) * area = 561.6 * 18 = 10,108.8 lbs. or 10,109 lbs.
 

1. What is Engineering Statics and why is it important for dams?

Engineering Statics is a branch of mechanics that deals with the study of forces acting on stationary structures. It is important for dams because it helps engineers analyze and predict how external forces, such as water pressure, will affect the stability and integrity of the dam.

2. How is pressure calculated on a dam?

Pressure on a dam is calculated by multiplying the height of the water by the density of the water and the acceleration due to gravity. This is known as the hydrostatic pressure formula (P = ρgh).

3. What factors can affect the pressure on a dam?

The pressure on a dam can be affected by various factors such as the height of the water, the density of the water, the shape and size of the dam, and the type of material used to construct the dam.

4. How do engineers ensure that a dam can withstand the pressure from water?

Engineers use various techniques and calculations to ensure that a dam can withstand the pressure from water. This includes analyzing the design of the dam, conducting simulations and tests, and using safety factors to account for uncertainties.

5. What are the consequences of not considering pressure in dam engineering?

If pressure is not properly considered in dam engineering, it can lead to catastrophic failures such as dam collapses and floods. This can result in loss of life, property damage, and environmental damage. Therefore, it is crucial for engineers to carefully consider pressure when designing and constructing dams.

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