Help please -- Problem of hydrostatics force in flat surfaces

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SUMMARY

The discussion focuses on calculating hydrostatic forces acting on flat surfaces submerged in a fluid. A key approach involves integrating pressure over sloping surfaces to determine vertical forces, as pressure varies with depth. A simplified method is proposed, where the net upward force on an object resting on the bottom of a tank is analyzed, considering fluid seepage beneath the object. This method aids in understanding the contributions of forces from different compartments in hydrostatic scenarios.

PREREQUISITES
  • Understanding of hydrostatic pressure principles
  • Knowledge of fluid density and its impact on pressure
  • Familiarity with integration techniques for varying pressure calculations
  • Basic concepts of force equilibrium in fluid mechanics
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  • Study hydrostatic pressure calculations in varying fluid depths
  • Learn about fluid dynamics and pressure distribution in tanks
  • Explore the concept of buoyancy and its relation to hydrostatic forces
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Students studying fluid mechanics, engineers working with hydrostatic systems, and anyone involved in designing or analyzing fluid containers and their interactions with submerged objects.

Queren Suriano
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Homework Statement



upload_2015-3-26_14-17-21.png

Homework Equations

The Attempt at a Solution


I could know the pressure in point B

upload_2015-3-26_14-18-23.png


If I calculate the heigh of pressure I got:
upload_2015-3-26_14-19-0.png
But I don't know where is my free surface in the container 3, is it down??

I don't know how to keep doing it...
 
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On the face of it, you need to integrate over the sloping surfaces to get the vertical force (because the pressure varies with depth).
Let me suggest a simpler approach.
Consider an object of known volume sitting at the bottom of a tank of fluid of known density and depth. The shape is arbitrary, except that the base is flat and sits squarely on the flat bottom of the tank. The contact surfaces are not perfectly smooth, though, so fluid can readily seep under the object.
What is the net upward force on the object from the fluid?
What is the upward force on the object arising only from the fluid that seeps under the object?
What can you conclude about the downward force on the object only arising from the fluid elsewhere?

Can you see how this would help you figure out the force contribution from each compartment in your problem?
 

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