How to Solve Hydrostatics Problems with Curved Surfaces?

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SUMMARY

This discussion focuses on solving hydrostatics problems involving curved surfaces, specifically in the context of calculating forces on a curved dam. The primary equation referenced is the force equation f = pghA, where the challenge lies in expressing the area A in terms of height h due to the curvature. Participants emphasize the importance of using a free-body diagram (FBD) to set up the appropriate integral for calculating the force, while also noting that the pressure acts normal to the surface at all points, complicating the integration process.

PREREQUISITES
  • Understanding of hydrostatic pressure principles
  • Familiarity with integration techniques in calculus
  • Knowledge of free-body diagrams (FBD) in physics
  • Basic concepts of moments and force distribution
NEXT STEPS
  • Study the application of hydrostatic pressure on curved surfaces
  • Learn how to derive and use free-body diagrams for complex shapes
  • Explore integration methods for calculating areas under curves
  • Investigate the effects of pressure distribution on structural stability
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Students in engineering or physics, particularly those studying fluid mechanics and hydrostatics, as well as professionals involved in structural analysis of dams and other curved surfaces.

Fionn00
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Hi I am really stuck on this problem and would greatly appreciate some help.

Homework Statement



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Homework Equations


The Attempt at a Solution



I would be able to solve this if the dam wasn't curved. I would just use integration to find the magnitude of the force f = pghA. I would express a in h and integrate from 0 to 3. and then the direction would be at right angles to the wall but this is curved so I don't know how to find the force or how to express the area in h.

Thanks for help.
I know hot to calculate the moments and get the solution once I have the magnitude and position of the force.
 
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Hi Fionn00! :smile:

The force at each point of the dam is normal to the surface, and the force per area is pressure (which of course is the same in every direction at any particular point). :wink:
 
Can I postulate that the overturning moment about A is independent of the shape of the dam cross-section? In other words use pressure distribution as if the dam was vertical and use the projected (vertical) area.
 
but the pressure is always perpendicular to the dam, so surely the angle does matter?
 
Isn't the angle on strut BC missing?

Fionn00: Because you know how to do an integration, try drawing a free-body diagram (FBD), and set up an integral that is applicable to the situation at hand.
 
Sorry for post #3. I stand corrected.
 

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