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State Pascal's law and verify it with th...

State Pascal's law and verify it with the help of an experiment.

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Pascal's law: IT states that : the pressure in a fluid is the same at all points if they are at the same height".
Proof of Pascal's law: Consider an element in the interior of a fluid at rest as shown in the figure. The element ABC-DEF is in the form of a right-angled prism.
In principle, this prismatic element is very small so that every part of it can be considered at the same depth from the liquid surface and therefore, the effect of gravity is the same at all these points.
the forces on this element are those exerted by the rest of the fluid and they must be normal to the surfaces of the element.

Thus the fluid exerts pressures `P_a,P_b` and `P_c` on this element of area corresponding to the normal faces `F_a,F_b` and `F_c` as shown in fig. on the faces BEFC,ADFC and ADEB denoted by `A_a,A_b` and `A_c` respectively. Then,
`F_bsintheta_2=F_c`and `F_bcos theta_2=F_a`
`A_b sin theta_2=A_c` and `A_b cos theta_2=A_a`
(by geometry)
Thus, `(F_b)/(A_b)=(F_C)/(A_c)=(F_a)/(A_a)impliesP_b=P_c=P_a`
Hence, pressure exerted is same in all directions in a fluid at rest.
This proves that Pascal's law.
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