Applications of Pascal’s law :
1. Hydraulic car lift and hydraulic press
2. Hydraulic brakes.
All the above applications work on the principle of multiplication of thrust by transmission of fluid pressure.
(1) Working of a hydraulic lift : Two hydraulically connected cylinders, one of cross section a and the other A, are such that A is many times larger than a : A = na. If a force Fa is exerted on the smaller piston, a pressure p = \(\frac{F_a}a\) is produced and transmitted
undiminished throughout the liquid. Then, the thrust FA on the larger piston
FA = pA = \(\frac{A}a\)Fa = nFa
is n times greater than that on the smaller piston. A platform attached to the larger piston can lift a car (as in a hydraulic car lift), or press bales of cotton or paper against a fixed rigid frame (as in Brahma’s.)
(2) Working of hydraulic brakes in a car: Brakes which are operated by means of hydraulic pressure are called hydraulic brakes. An automobile hydraulic brake system, shown schematically in below figure, has fluid-filled master and slave cylinders connected by pipes. When the brake pedal is pushed, it depresses the piston of the pedal or master cylinder through a lever. The change in pressure in the master cylinder is transmitted to the four wheel or slave cylinders. Since the brake fluid is incompressible, the pistons of the slave cylinders are pushed out, pressing braking pads onto the braking discs on the wheels. Note that we can add as many wheel cylinders as we wish.
The master cylinder has a much smaller area of cross section Am compared to the combined area As
FW : Front wheel slave cylinder, RW : Rear whel slave cylinder Hydraulic brakes system in an automobile (Schematic)
of the slave cylinders. Hence, with a small force Fm on the master cylinder, a force Fs
= \(\frac{A_s}{A_m}\) Fm which is greater than Fm is applied on each slave cylinder. Consequently, the master piston has to travel sev-eral inches to move the slave pistons the fraction of an inch it takes to apply the brakes. But the arrangement allows great force to be exerted at the brake pads.
[Note : (1) Pascal’s law laid the foundation for hydraulics, the use of a liquid under pressure to transfer force or motion, or to increase an applied force. It is one of the most important branches in modern engineering. (2) A hydraulic system, as an example of a simple machine, can increase force but cannot do more work than is done on it. Work being force times the distance moved, the piston in a wheel cylinder moves through a smaller distance than that in the pedal cylinder. Power brakes in modern automobiles have a motorized pump that does most of the work in the system.]
