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☻Give the experimental proof of Pascal's law with diagram☻
Answers
Answer:
Pascal's Law states,
" The intensity of pressure at any point in a fluid at rest, is the same in all direction."
Theorem Proof
Consider a very small right angled triangular element ABC of a liquid as shown in figure.
Let: = Intensity of horizontal pressure on the element of the liquid
= Intensity of vertical pressure on the element of the liquid
= Intensity of pressure on the diagonal of the triangular element of the liquid
= Angle of the triangular element of the liquid
Now total pressure on the vertical side AC of the liquid,
(1)
Similarly,total pressure on the horizontal side BC of the liquid,
(2)
and total pressure on the diagonal side AB of the liquid,
(3)
Since the element of the liquid is at rest, therefore sum of the horizontal and vertical components of the liquid pressure must be equal to zero.
Now using eqilibrium condition for horizontal pressure,
From the geometry of the figure, we find that,
(4)
Now using equilibrium condition for vertical pressure, i.e.,
(where W = Weight of the liquid)
As the triangular element is very small, the weight of the liquid W is neglected, so,
From the geometry of the figure, we find that
(5)
Now from equation (4) and (5), we find that
Thus the intensity of pressure at any point in a fluid, at rest, is the same in all direction.
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The liquid inside the cylinder is in equilibrium under the action of forces exerted by the liquid outside the cylinder. These forces are acting every where perpendicular to the surface of the cylinder. Thus force on the flat faces of the cylinder at C and D will perpendicular to the forces on the curved surface of the cylinder. Since the liquid is in equilibrium, therefore, the sum of forces acting on the curved surface of the cylinder must be zero. If P1 and P2 are the pressure at points C and D and F1 and F2 are the forces acting on the flat faces of the cylinder due to liquid.