Lec.3 Pascal’s law

Pascal’s law:
Pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and the walls of the containing vessel.
Equation (6) shows that if we increase the pressure p0 at the top surface, possibly by using a piston that fits tightly inside the container to push down on the fluid surface, the pressure p at any depth increases by exactly the same amount. This fact was recognized in 1653 by the French scientist Blaise Pascal (1623–1662) and is called Pascal’s law.
The hydraulic lift shown schematically in (Fig. 6) illustrates Pascal’s law. A piston with small cross-sectional area (A1 ) exerts a force (F1 ) on the surface of a liquid such as oil. The applied pressure (p=F1/A1) is transmitted through the connecting pipe to a larger piston of area (A2).
The hydraulic lift is a force-multiplying device with a multiplication factor equal to the ratio of the areas of the two pistons. Dentist’s chairs, car lifts and jacks, many elevators, and hydraulic brakes all use this principle. For gases the assumption that the density ? is uniform is realistic only over short vertical distances.
Absolute Pressure and Gauge Pressure
If the pressure inside a car tire is equal to atmospheric pressure, the tire is flat. The pressure has to be greater than atmospheric to support the car, so the significant quantity is the difference between the inside and outside pressures.