Fluid mechanics problem, need explanation please

AI Thread Summary
The discussion focuses on a fluid mechanics problem where the user seeks clarification on two points regarding the forces acting on a plug. The first question addresses why the plug is not treated as a vertical wall for calculating force, to which the response explains that the integral can be simplified due to the small size of the plug. The second question concerns the atmospheric pressure force, which is noted to be equal on both sides of the plug, allowing it to be ignored in calculations. The conversation emphasizes understanding the simplifications made in fluid mechanics problems. Overall, the exchange highlights the nuances of pressure forces in fluid dynamics.
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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