Calculating Water Pressure Against a 120-Foot High Dam Using Symmetric Function

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In summary, the conversation discusses setting up an integral to find the total force on a 120 foot high dam shaped by a symmetric function. The water level is at the top of the dam and the integral is set up using the equation P = F / A. The teacher's answer is 120 S 62.5(120-y)*2(y/2)^(3/4)dy 0, where 62.5 represents the weight of water per cubic foot and 120-y gives the water pressure as a function of vertical position. The problem is asking for the total force against the dam, not the total pressure.
  • #1
beanryu
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A 120 foot high dam is shaped by the symmetric function y = 2x^(4/3). The water level is at the top of the dam. Set up an integral that gives the total water pressure against the dam. Water weights 62.5 lbs per cubic foot.

S = integral sign

P = F / A

but teacher's answer is

120
S 62.5(120-y)*2(y/2)^(3/4)dy
0

I understand the 2(y/2)^(3/4)dy part, its the area, but I don't get what is
62.4(120-y), its seems to me that the teacher is doing P = F * A, which is wrong... if I m not wrong... please help me clear this... Final coming!
 
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  • #2
What you are probably asked to find is the total force on the dam due to the water pressure. The teacher is doing F = P * A (not P = F * A, which would indeed make no sense). 62.4(120-y) gives the water pressure as a function of vertical position (measured from the bottom of the dam).
 
  • #3
There is no such thing as "total pressure". As Doc Al said, the problem clearly is asking for "total force" against the dam. And it is correct that F= P*A.
 

1. How is water pressure calculated against a 120-foot high dam?

The water pressure against a 120-foot high dam can be calculated using the formula P = ρgh, where P is the pressure, ρ is the density of water, g is the gravitational acceleration, and h is the height of the dam. In this case, the height of the dam would be 120 feet.

2. What is a symmetric function and how is it used in this calculation?

A symmetric function is a mathematical function that remains unchanged when its variables are interchanged. In this calculation, a symmetric function is used to represent the pressure on both sides of the dam, as the water pressure on one side is equal to the water pressure on the other side.

3. How does the density of water affect the water pressure against the dam?

The density of water plays a crucial role in calculating water pressure against a dam. The higher the density of water, the more mass it contains, resulting in higher pressure against the dam. The standard density of water is 1000 kg/m3, but it can vary slightly depending on temperature and salinity.

4. What is the significance of the gravitational acceleration in this calculation?

The gravitational acceleration (g) is a constant that represents the force of gravity on an object. In this case, it is used to calculate the weight of the water above the dam, which contributes to the overall water pressure against the dam. The higher the gravitational acceleration, the higher the water pressure against the dam.

5. Can this calculation be used for dams of different heights?

Yes, this calculation can be used for dams of different heights by simply adjusting the value of h in the formula. However, it is important to note that this calculation assumes a symmetrical dam and uniform water density, and may not be accurate for more complex situations.

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