Solving Fluid Statics Problem: Accounting for Atmospheric Pressure

In summary, the problem asks for the resultant force exerted by the water on the dam, which can be calculated by taking the pressure at the bottom and the average of the pressure at the top and the pressure at the bottom.
  • #1
member 731016
Hi!

For this fluid statics problem,
1669440301598.png


One of the answers is:
1669440335829.png

However, why did they assume the pressure at the top was zero? I thought the pressure at the top would be 1 atm?

So tried to take atmospheric pressure into account putting 1 atm at the top,
p02BmFMz8bsEq6v6b6YrLD4C2XVxcmjDIvK6DND5Ijn6d5RGSw.png

Do you please know how to get P_0A/2 so that the P_0A/2 terms can cancel to get their hydrostatic force? I assume that the atmospheric pressure is the same at the top and bottom since the height of the dam is negligible to the scale of the atmosphere.

Many thanks!
 
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  • #2
Callumnc1 said:
However, why did they assume the pressure at the top was zero? I thought the pressure at the top would be 1 atm?
That one atmosphere is present above the water, through the water column, and also against the dry face of the dam wall. Those two atmospheric forces on the two sides of the dam wall oppose each other, and so can be cancelled.
 
  • #3
Moderator's note: Thread moved to introductory physics homework forum.
 
  • #4
How did you calculate Pavg?
 
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  • #5
Baluncore said:
That one atmosphere is present above the water, through the water column, and also against the dry face of the dam wall. Those two atmospheric forces on the two sides of the dam wall oppose each other, and so can be cancelled.
But the problem does not ask for the total net force on the dam. It asks for the resultant force exerted by the water on the dam. While the problem author likely intended to ask for the total net force, it is not what they wrote.
 
  • #6
haruspex said:
How did you calculate Pavg?
Thanks for your reply. I found P_avg by assuming the pressure at the top was 1 atm, and the pressure at the bottom was pgH then took the average (divided by 2). Many thanks,
Callum
 
  • #7
Baluncore said:
That one atmosphere is present above the water, through the water column, and also against the dry face of the dam wall. Those two atmospheric forces on the two sides of the dam wall oppose each other, and so can be cancelled.
Thanks, yes, I agree. I just wanted to solve the problem by taking the atmosphere into account then cancelling with Newton's Second Law.
 
  • #8
Callumnc1 said:
and the pressure at the bottom was pgH
Is it though?
 
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  • #9
Orodruin said:
Is it though?
Thanks for your reply, yeah true the pressure is p_0 + pgH which solves my confusion. Thank you very much for pointing that out!
 
  • #10
Orodruin said:
But the problem does not ask for the total net force on the dam. It asks for the resultant force exerted by the water on the dam. While the problem author likely intended to ask for the total net force, it is not what they wrote.
Ok thank you for pointing that out!
 

Related to Solving Fluid Statics Problem: Accounting for Atmospheric Pressure

1. What is fluid statics and why is it important?

Fluid statics is the study of fluids at rest and the forces acting on them. It is important because it helps us understand the behavior of fluids in various systems, such as in pipes, tanks, and dams, and allows us to make accurate predictions and calculations for engineering and scientific applications.

2. How does atmospheric pressure affect fluid statics problems?

Atmospheric pressure is the pressure exerted by the weight of the Earth's atmosphere on a given area. In fluid statics problems, atmospheric pressure must be taken into account because it acts on the surface of the fluid and can affect the pressure and forces within the fluid system.

3. What is the formula for calculating atmospheric pressure?

The formula for calculating atmospheric pressure is P = ρgh, where P is the atmospheric pressure, ρ is the density of air, g is the acceleration due to gravity, and h is the height of the column of air above the given point.

4. How do you incorporate atmospheric pressure into calculations for fluid statics problems?

To incorporate atmospheric pressure into calculations for fluid statics problems, you must add the atmospheric pressure to the pressure at the surface of the fluid. This will give you the total pressure at that point, which can then be used in various equations and calculations.

5. What are some real-world applications of solving fluid statics problems and accounting for atmospheric pressure?

Fluid statics and accounting for atmospheric pressure are important in a wide range of real-world applications, such as designing and analyzing water distribution systems, calculating buoyant forces on ships and submarines, and understanding the behavior of fluids in weather patterns. They are also crucial in industries such as oil and gas, where accurate calculations of pressure are necessary for drilling and extracting resources.

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