Question

Only for great moderator like Edweena, shirley, rahul.
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prove that pressure is same at all the direction in a fluid at rest.​

Answer 1

Pascal's law states that

"Whenever external pressure is applied on any part of fluid contained in a vessel and at rest, the change in pressure is transmitted undiminished in all the directions".

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TO PROVE : The pressure is same at all the directions in a fluid at rest.

~consider a liquid at rest in a container and assume a right angled prism shape(ABC-DFE) of liquid part in it.

The Force acting on different surfaces are,

• On ADFC is Fb
• On ADFB is Fc
• On BECF is Fa

As fluid is at rest all the three force should cancel to give out the net force zero for that from figure.

• Fc=Fbcos¤ ....(1)
• Fa=Fbsin¤ ....(2)

Similarly, if Ab is the area of ADFC, Aa is area of BEFC and Ac is the area of ABED, from geometry,

• Aa=Absin¤ ....(3)
• Ac= Abcos¤ ....(4)

Dividing above equation (1),(2),(3)&(4) suitably we get

$\dfrac{Fa}{Aa} = \dfrac{Fb}{Ab} = \dfrac{Fc}{Ac}$

.°. Pa=Pb=Pc.

Therefore, we can conclude that pressure is same in all directions.

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Note:-

assume ¤ = theta.