Pascal's Law: The Foundation of Hydraulics

Pascal’s law is the single most important concept in fluid power. Formulated by French scientist Blaise Pascal in the 17th century, it states:

Pressure applied to a confined fluid is transmitted equally and undiminished in all directions.

The Principle Explained

When you apply pressure to a fluid trapped inside a closed container, that pressure acts with equal force on every surface in contact with the fluid — regardless of the shape of the container or the direction of the surface.

Mathematically, this is expressed as:

$P = \frac{F}{A}$

Where:

• P = pressure (Pa, MPa, or bar)
• F = force (N)
• A = area (m²)

Why It Matters in Hydraulics

Because pressure is transmitted equally, we can use a small piston to create pressure on a small area, and have that pressure act on a larger piston area to generate a much larger force. This is the principle of force multiplication.

$\frac{F_1}{A_1} = \frac{F_2}{A_2}$

This means the force ratio equals the area ratio:

$\frac{F_2}{F_1} = \frac{A_2}{A_1}$

💡 Practical Example: Lifting a Ton with 10 kg of Force

Consider a hydraulic jack with a small pump piston of area $10\ \text{cm}^2$ and a large lift piston of area $1000\ \text{cm}^2$.

Applying a force of $10\ \text{kg} \approx 98\ \text{N}$ on the small piston creates pressure:

$P = \frac{98\ \text{N}}{0.001\ \text{m}^2} = 98,000\ \text{Pa} = 0.098\ \text{MPa}$

This same pressure acts on the large piston of $0.1\ \text{m}^2$:

$F = P \times A = 98,000 \times 0.1 = 9800\ \text{N} \approx 1000\ \text{kg}$

A 10 kg input force becomes a 1-ton lifting force — force amplification of 100:1. This is how a small hydraulic jack can lift a car.

Key Takeaways

• Pressure is transmitted equally and undiminished through a confined fluid
• Hydraulic systems multiply force through the ratio of piston areas
• The work done (force × distance) remains conserved — a small force moves a long distance, a large force moves a short distance
• Pascal’s law is the basis of jacks, presses, brakes, and virtually all hydraulic machinery

Related Concepts

• Hydraulic vs Mechanical Transmission
• Basic System Components

Try It Yourself

Use our Cylinder Thrust Calculator to experiment with different bore sizes and pressures.