State and prove Pascal's law in fluids.

Explanation

Statement of Pascal.s law: if the pressure in a liquid is changed at a particular point, the change is transmitted to the entire liquid without being diminished in magnitude.

Application of Pascal.s law: hydraulic lift: practical application of Pascal.s law is the hydraulic lift which is used to lift a heavy load with a small force. It is a force multiplier. In consists of two cylinders A and B connected to each other by a horizontal pipe, filled with a liquid. They are fitted with fractionaless pistons cross sectional area `A_1 and A_2 (A_2 > A_1)`. Suppose a downward force F is applied on the the smaller piston, the pressure of the liquid under this piston increase to P (where, `P = (F_1)/(A_1)`) . But according to Pascal.s law , this increased pressure P is transmitted undiminished in all directions. So a pressure is exerted on piston B. Upward force on piston B is
`F_2 = P xx A_2 = (F_1)/(A_1) xx A_2 implies F_2 = (A_2)/(A_1) xx F_1`
Therefore by changing the force on the smaller piston A, the force on the piston B has been increased by the factor `(A_2)/(A_1)` and this factor is called the mechanical advantage of the lift.