Solving Hydrostatic Forces with Integral or Volume/Weight?

AI Thread Summary
The discussion centers on solving a fluid mechanics problem related to hydrostatic forces, specifically whether a vertical component of force acts upward on a dam. While integration is a viable method for solving the problem, there is uncertainty about the existence of this vertical component. It is noted that pressure acts normal to the surface, implying that if the surface has a vertical normal vector, the pressure force will also have a vertical component. A suggested approach is to express the normal vector as a function of x or y to facilitate integration. Overall, understanding the geometry of the problem is crucial for determining the appropriate method of solution.
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I am actually trying to solve a problem from fluid mechanics. The especifications of the problem are on the attachment.

I can solve the problem easily by integration, but I'm not so sure if there is a vertical component of a force in the "dam" acting upward. There is a vertical component of the force acting upward?
If there is, there is another method to solve the problem without integration, using properties such as volume, specific weight... to find that vertical component?
 

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I'm not sure what the various parts of your drawing represent. However, in general, pressure always acts normal to the surface. So if the normal vector of your surface at a given point has a vertical component then the pressure force will also have a vertical component. The easiest way to do something like this is to write an expression for the normal vector as a function of x (or y) and then use that in the integration.
 

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