How Do You Calculate Width in Hydrostatic Force Problems with Varying Depths?

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Calculating width in hydrostatic force problems with varying depths involves understanding how pressure changes with depth and how it affects the force on submerged surfaces. The integration process requires dividing the area into infinitesimally small rectangles to accurately compute the total force. It's essential to clarify which specific force is being referenced, especially if the plate is sealed against a wall, as this affects the pressure calculations. The exposed area of each triangle should be analyzed to determine which has more area subjected to higher pressures. Understanding these concepts is crucial for solving hydrostatic force problems effectively.
Virang807
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Hello! I am currently in Calculus 2 and we are dealing with hydrostatic force. I get the integration that happens but I always seem to have trouble with solving the word problems. With this problem, I realize that I use integrate by making an infinite number of rectangles on the 2 triangles. I want to know the differences in solving both of them and trying to find the width formula with respect to x. Thank you!
 

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The question is unclear. Which force are they asking about? If the plate is sealed against the wall so that there is no water between the plate and the wall, there will be a force pushing the plate against the wall, arising from water pressure. Do you think that's the force they mean?
 
From the question : ' try to anticipate the answer ' .

Ask yourself :

How does pressure vary with depth ?

For each triangle which has the more area exposed to the higher pressures ?
 

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