How to Solve Hydrostatics Problems with Curved Surfaces?

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Discussion Overview

The discussion revolves around solving hydrostatics problems involving curved surfaces, specifically in the context of a dam. Participants explore the application of pressure distribution, integration techniques, and the implications of geometry on force calculations.

Discussion Character

  • Homework-related
  • Exploratory
  • Debate/contested

Main Points Raised

  • One participant expresses difficulty in calculating the force on a curved dam, suggesting that integration could be used if the dam were straight.
  • Another participant clarifies that the force at each point on the dam is normal to the surface and that pressure acts uniformly in all directions at a point.
  • A participant questions whether the overturning moment about a point is independent of the dam's cross-sectional shape, proposing to use a vertical pressure distribution.
  • Another participant counters that the angle of the dam does matter since pressure is always perpendicular to the surface.
  • A participant notes a potential missing angle in the analysis, indicating the need for a more complete free-body diagram to set up the integral correctly.
  • One participant acknowledges a mistake in their earlier post, indicating a willingness to correct their understanding.

Areas of Agreement / Disagreement

Participants express differing views on the relevance of the dam's shape to the pressure distribution and the calculation of moments. The discussion remains unresolved with multiple competing perspectives on how to approach the problem.

Contextual Notes

Participants have not fully resolved the implications of the dam's curvature on force calculations, and there are indications of missing assumptions regarding the geometry involved.

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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