Hello everyone in previous article we have studied about the basic definition of pressure and derivation pressure exerted by liquid column along with the atmospheric pressure. The formulae for the pressure is given as,
∴ P = F/A
And the gauge pressure is given as,
∴ P – Pa = ρhg
In this article we are going to discuss the most essential law in fluid mechanics known as Pascal’s law.
Let’s discuss the Pascal’s law in detail……………!
Statement:
The pressure applied to any part of fluid at rest is transmitted equally and undiminished to every part of fluid and to the wall of container.
Consider the vessel containing fluid at rest and the pressure gauge meter are fixed at different points as shown in fig below,
In the figure according to Pascal’s law, the pressure reading in all the gauge meter will be same so that,
P1 = P2 = P3 = P4 = ⋯….
The magnitude of force acting on the given areas may be different from point to point but the magnitude of pressure always remains same.
Let’s study some applications of Pascal’s law……!
1.) Hydraulic press which is used to press cotton bales, extract oil from oil seed is based on Pascal’s law. It contains the tank of water with two openings of different cross sectional areas A1 and A2 such that A1>A2. Opening A2 has one piston termed as input piston. Thick metal and movable plate is fixed at opening A1 taken as output piston and then allowed to strike on another plate(wall) as shown in fig below,
Force of magnitude F2 is applied on input piston of area A2, which exerts pressure P2 on the liquid in the tank. This pressure is transmitted to the output piston of area A1 exerts force F1.
The pressures on the pistons can be written as,
∴P1 = F1/A1 ( output piston)
∴P2 = (F2 )/A2 ( input piston)
By Pascal’s law
P1 = P2
∴F1/A1 =(F2 )/A2
∴F1 = A1 × (F2 )/A2
as A1 > A2, then
∴F1 > F2
Hence force on output piston is greater that the force on input piston which helps to press or crush the things kept on metal plate.
2.) Hydraulic brakes are used to stop the running vehicle instantly which also works on the principle of Pascal’s law.
3.) Hydraulic lift used to lift heavy objects, heavy vehicles also works on Pascal’s law.
4.) Injection given by doctor through needle and syringe uses Pascal’s law.