Physics final prep, question about force under water at depth h

In summary, the conversation discusses a question about finding the magnitude of the frictional force between a plug and a horizontal pipe passing through a reservoir dam. The question involves determining the pressure and force equations, with the use of the circular pipe's radius. The solutions manual uses a different equation, ρgh * πr^2, which takes into account the atmospheric pressure on the "dry" side of the plug. This helps to determine the net pressure on the plug, which explains the difference in the two equations.
  • #1
09jlk
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Homework Statement



The question states: The fresh water behind a reservoir dam has depth D=15 meters. A horizontal pipe 4.0cm in diameter passes through the dam at depth d=6.0m. A plug secures the pipe opening. (a) Find the magnitude of the frictional force between plug and pipe wall.

Initially when I did this problem I found the pressure at this point with p = p(atm) + ρgh, where h = 6.0 meters. I then used the Force equation F=pA and used the area of the circular pipe with radius .02 meters. So my friction force, which is in equilibrium, should be equal to the force pushing from the water, F= (p(atm) + ρgh) * πr^2.

However, when I look at the solutions manual, they have F = ρgh * πr^2. I'm not sure I understand why this is the case -- it seems to me that they are using the gauge pressure here to determine the force of the water. Why would we use the pressure as ρgh and not p(atm) + ρgh?
 
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  • #2
That's because there is atmopherisc pressure on the 'dry' side of the plug...'canceling' out the P_atm force part of the absolute water pressure...such that the net pressure on the plug is just the gauge pressure
 
  • #3
Ahh, pressing on the other side of the plug. Thank you!
 

What is the relationship between depth and force under water?

The force under water at a given depth is directly proportional to the depth. This means that as the depth increases, the force also increases.

How does the density of water affect the force under water at a certain depth?

The density of water is a factor in determining the force under water at a certain depth. The higher the density of water, the greater the force will be at a given depth.

What is the formula for calculating force under water at a depth h?

The formula for calculating force under water at a depth h is F = ρghA, where ρ is the density of water, g is the acceleration due to gravity, h is the depth, and A is the area of the object.

How does the shape and size of an object affect the force under water at a certain depth?

The shape and size of an object can affect the force under water at a certain depth. Objects with a larger surface area will experience a greater force under water compared to smaller objects of the same shape at the same depth.

What other factors can influence the force under water at a certain depth?

Other factors that can influence the force under water at a certain depth include the density and temperature of the water, as well as the shape and orientation of the object in relation to the direction of flow of the water.

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