Section 6.3: Pascal's Principle

Pascal’s Principle states that when pressure is applied to an enclosed fluid, the pressure is transmitted undiminished in all directions throughout the fluid. This is the basis for hydraulic systems.

Formula

\[ \frac{F_1}{A_1} = \frac{F_2}{A_2} \] where:
\( F_1, F_2 \) = forces applied on pistons (N)
\( A_1, A_2 \) = areas of pistons (m²)

Example 1: Hydraulic Lift

A small piston of area 0.02 m² is used to lift a car with a piston area of 1 m². If a force of 200 N is applied on the small piston, find the force exerted on the car.

Using Pascal's principle: \(\frac{F_1}{A_1} = \frac{F_2}{A_2}\)
\(\displaystyle F_2 = F_1 \frac{A_2}{A_1} = 200 \times \frac{1}{0.02} = 10{,}000 \, \text{N}\)
The hydraulic lift exerts 10,000 N on the car.

Example 2: Force Transmission

If a piston with area 0.05 m² has a force of 500 N applied, and it is connected to a piston of area 0.5 m², find the force on the larger piston.

\(\displaystyle F_2 = F_1 \frac{A_2}{A_1} = 500 \times \frac{0.5}{0.05} = 5{,}000 \, \text{N}\)
The larger piston experiences 5,000 N.

Practice Problems

  1. A hydraulic press has a small piston of area 0.01 m² and a large piston of area 0.8 m². If a force of 150 N is applied on the small piston, what force is exerted on the large piston?
  2. A hydraulic lift uses a piston of area 0.03 m² to apply a force of 250 N. The lift piston area is 0.6 m². Find the output force.
  3. If a piston of 0.04 m² lifts a 2,000 N load on a 0.8 m² piston, what force must be applied on the small piston?
  4. A small piston of area 0.05 m² is pushed with a force of 400 N. The larger piston area is 0.5 m². Determine the force on the larger piston.
  5. A hydraulic system uses a 0.02 m² piston to lift a 1,000 N weight on a 0.5 m² piston. What input force is needed?
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