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

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SUMMARY

This discussion focuses on calculating the width in hydrostatic force problems involving varying depths, specifically in the context of integration techniques used in Calculus 2. Participants emphasize the importance of understanding how pressure varies with depth and the implications for calculating forces on triangular plates submerged in fluid. The conversation highlights the need to clarify the specific forces being analyzed, particularly when considering the effects of water pressure against a wall. Key insights include the necessity of integrating over the exposed areas of the triangles to accurately determine the hydrostatic forces involved.

PREREQUISITES
  • Understanding of hydrostatic pressure principles
  • Familiarity with integration techniques in calculus
  • Knowledge of how to calculate area for triangular shapes
  • Concept of pressure variation with depth in fluids
NEXT STEPS
  • Study hydrostatic pressure calculations in fluid mechanics
  • Learn about integration methods for calculating areas under curves
  • Explore applications of hydrostatic force in engineering problems
  • Investigate the relationship between pressure and depth in various fluids
USEFUL FOR

Students in calculus and physics courses, particularly those studying fluid mechanics, as well as engineers and professionals dealing with hydrostatic force calculations in practical applications.

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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