2.4.1 Pascal’s Principle
Pascal’s Principle
- Pascal’s principle states that in a confined fluid, an externally applied pressure is transmitted uniformly in all directions.
- Pascal’s principle is also known as the principle of transmission of pressure in a liquid.
Q & A
Q: Suggest an experiment to prove Pascal’s Principle.
A:
- When the plunger is pushed in, the water squirts equally from all the holes.
- This shows that the pressure applied to the plunger has been transmitted uniformly throughout the water.
Hydraulic System
- A hydraulic system applies Pascal’s principle in its working mechanism. It can be used as a force multiplier.
- In this hydraulic system, a small force, Fl is applied to the small piston X results in a large force, F2 at the large piston Y. The pressure, due to the force, F1, is transmitted by the liquid to the large piston.
- According to Pascal’s principle,
F1A1 = F2A2
Change of Oil Level in a Hydraulic System
In the diagram to the left, when piston-X is pressed down, piston-Y will be push up. The change of the piston levels of the 2 pistons is given by the following equation:
h1A1 = h2A2
Example 1:
In a hydraulic system the large piston has a cross-sectional area A2 = 200 cm² and the small piston has cross-sectional area A1 = 5 cm². If a force of 250 N is applied to the small piston, what is
a. the pressure exerted on the small piston
b. the force F, produced on the large piston?
Answer:
a. Pressure exerted on the small piston
b. Pressure exerted on the large piston = Pressure exerted on the small piston
Example 2:
A hydraulic lift is to be used to lift a truck masses 5000 kg. If the diameter of the small piston and large piston of the lift is 5cm and 1 m respectively,
- what gauge pressure in Pa must be applied to the oil?
- What is the magnitude of the force required on the small piston to lift the truck?
Answer:
a. Weight of the truck,
W = mg
W = (5000)(10) = 50,000N
Area of the big piston
A2 =πr2
=π(1)2
=πm2
Pressure of the oil
b.
Area of the small piston
A1 =πr2
=π (0.05)2
=0.0025π m2
According to Pascal’s Principle, 
Example 3:
Figure above shows a hydraulic system. The area of surface X is 5 cm² and the area of surface Y is 100 cm². Piston X has been pushed down 10cm. what is the change of liquid level, h, at Piston Y?
Answer:
Distance move by the piston-X, h1 = 10cm
Distance move by the piston-Y, h2 = h
Area of piston-X, A1 = 5 cm²
Area of Piston-Y, A2 = 100 cm²