Pascal’s law and its applications
The French scientist Blaise Pascal observed that the pressure in a fluid at rest is the same at all points if they are at the same height. Statement of Pascal’s law is 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.
A 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. It consists of two cylinders A and B connected to each other by a horizontal pipe, filled with a liquid (Figure 7.12). They are fitted with frictionless pistons of cross sectional areas A1 and A2 (A2 > A1). Suppose a downward force F is applied on the smaller piston, the pressure of the liquid under this piston increases to P(where, p=F1/A1).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
Therefore by changing the force on the smaller piston A, the force on the piston B has been increased by the factor A1/A2 and this factor is called the mechanical advantage of the lift.
Two pistons of a hydraulic lift have diameters of 60 cm and 5 cm. What is the force exerted by the larger piston when 50 N is placed on the smaller piston?
Since, the diameter of the pistons are given, we can calculate the radius of the piston
This means, with the force of 50 N, the force of 7200 N can be lifted.