Fluid mechanics problem, need explanation please

[Bassel]

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.

 

[tiny-tim]

Hi Bassel! Welcome to PF!

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

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

(so it's the same on both sides, and you can ignore it)

 

[Bassel]

by the other side you mean from outside ??

 

[tiny-tim]

yes, the plug has two sides