Find force when given air pressure and volume

AI Thread Summary
To determine the total force acting on the dam's surface, the average pressure must be calculated, as pressure varies linearly with depth. The average pressure is found by taking the midpoint between the pressure at the water surface and the pressure at the bottom of the dam. Given the dimensions of the dam (170 m wide and 10 m high), the average pressure can be used to calculate the total force using the formula Force = Pressure x Area. The discussion highlights the importance of understanding pressure variation in fluid mechanics. The correct application of these principles leads to the solution of the assignment problem.
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The vertical surface of a reservoir dam that is in contact with the water is 170 m wide and 10 m high. The air pressure is one atmosphere. Find the magnitude of the total force acting on this surface in a completely filled reservoir. (Hint: The pressure varies linearly with depth, so you must use an average pressure.)

Could anyone please help me with this. Its part of an assignment due. The question comes from "Physics 7th edition by Cutnell" Chapter 11 problem 26.

I know that Pressure=Force/Area but no idea how to solve this problem. I also know the p2=p1+pgh equation but don't know if i need this.:rolleyes:
 
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The hint shows you the way. What's the average pressure? (What's the pressure at the water surface? At the bottom of the dam?)
 
OK. Thanks. I got the right answer.
 
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Since pressure varies linearly with height, the average pressure will be smack in the middle between the two extremes.
 

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