Why use gauge pressure for plug friction in a submerged pipe

[09jlk]

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?

 

[PhanthomJay]

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

 

[09jlk]

Ahh, pressing on the other side of the plug. Thank you!