Pascal’s Law

A fluid is said to be confined when it is enclosed in a container so that it cannot escape. Any pressure applied at one point spreads instantly throughout the fluid.

Pressure applied at one part of the fluid affects every other part equally. This is because fluid particles move freely and push against surrounding particles uniformly.

If pressure \(P\) is applied on a confined fluid, every point in the fluid experiences the same pressure:

\( P = \dfrac{F}{A} \)

This pressure acts in all directions — upward, downward, and sideways.

Hydraulic machines use Pascal’s law to multiply force. A small force applied on a small piston creates equal pressure in the fluid, which produces a large force on a larger piston.

This allows lifting heavy loads with relatively small effort.

In hydraulic systems:

\( \dfrac{F_1}{A_1} = \dfrac{F_2}{A_2} \)

Where:

• \(F_1, A_1\): force and area of small piston
• \(F_2, A_2\): force and area of large piston

If \(A_2\) is much larger than \(A_1\), the output force \(F_2\) becomes much larger than the applied force \(F_1\).

Fluid molecules are constantly moving and colliding. When pressure is applied at one point, the motion and collisions transmit it in every direction without loss.

Fluids cannot resist shear stress. As a result, they spread the applied pressure evenly instead of holding it in one location.

Used in garages to lift vehicles. A small force applied on the small piston results in a large upward force on the big piston, lifting heavy loads easily.

In vehicles, pressing the brake pedal applies pressure to brake fluid, which spreads equally to all wheels, applying uniform braking force.

Used for shaping metals, compressing materials, or printing. The machine applies huge force over a large area using Pascal’s principle.

When the plunger is pressed, pressure is applied to the liquid inside. The liquid transmits this pressure uniformly, pushing out the fluid from the nozzle.

If a ball filled with water is squeezed at one point, water pushes out equally in all directions. This shows the equal transmission of pressure.

Pressing a sealed plastic bottle at one point makes other parts bulge out slightly. The internal air transmits pressure uniformly.