Fluid mechanics problem, need explanation please

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SUMMARY

The discussion centers on a fluid mechanics problem regarding the forces acting on a plug in a fluid system. The participants clarify that the integral of pressure times area was correctly applied, with the simplification that the height can be treated as a constant due to the small size of the plug. Additionally, it is established that the atmospheric pressure force is present on both sides of the plug and can be ignored for the purposes of this analysis.

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  • Understanding of fluid mechanics principles, specifically hydrostatic pressure.
  • Familiarity with integral calculus as applied to pressure calculations.
  • Knowledge of atmospheric pressure effects in fluid systems.
  • Experience with analyzing forces in static fluids.
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  • Study hydrostatic pressure calculations in detail.
  • Learn about the implications of atmospheric pressure in fluid mechanics.
  • Explore integral calculus applications in engineering problems.
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Bassel
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Hi please check the highlighted question in the attachment and the solution and see the problem, i need help please. I have two questions about it:

1- why didn't we take the plug as a vertical wall and thus the force would be integral of pressure x area?

2-WHERE DID THE FORCE DUE TO ATMOSPHERIC PRESSURE GO?

Thnx for your help.
 

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Hi Bassel! Welcome to PF! :smile:
Bassel said:
1- why didn't we take the plug as a vertical wall and thus the force would be integral of pressure x area?

You did.

You did ∫ ρgA(H+h) dh, but the plug is so small that you can take H+h to be a constant, H …

so that integral is just ∫ ρgAH dh :wink:
2-WHERE DID THE FORCE DUE TO ATMOSPHERIC PRESSURE GO?

it nipped round the other side when you weren't looking, and started pushing back :smile:

(so it's the same on both sides, and you can ignore it)
 
by the other side you mean from outside ??
 
yes, the plug has two sides :smile:
 

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