Class 9 > Unit # 05: Forces and Matter > Pascal's Law and Hydraulic Machines

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Forces and Matter - Pascal's Law and Hydraulic Machines

State Pascal’s Law and explain it with an example.

Pascal’s Law

The liquid pressure at the surface of a liquid increases when an external force is applied. This increase in pressure is transmitted equally in all directions and uniformly to the walls of the enclosing container. This fundamental principle is known as Pascal's law.

"The pressure applied externally at any point of a liquid enclosed in a container is transmitted equally and undiminished to all parts of the liquid."

Figure: Demonstration of Pascal's Law using a perforated glass vessel and piston.

Example & Demonstration

Pascal's law can be demonstrated using a water-filled glass vessel with multiple small holes distributed across its surface. When a force is applied via a piston, water rushes out of all the holes with equal speed and force. The force on the piston exerts pressure on the liquid, which is transmitted equally throughout in all directions. In general, this law holds true for all fluids (both liquids and gases).

Define Hydraulic Machine and explain working of Hydraulic press according to Pascal’s Law.

Hydraulic Machine

"A machine in which mechanical force is transmitted by means of liquids under pressure is known as a hydraulic machine. By applying a relatively small force, they can produce a much larger output force."

Hydraulic Press

A hydraulic press consists of two interconnected pistons of different surface areas joined by a liquid-filled pipe:

• A smaller input force of magnitude $F_1$ is applied to a piston of smaller surface area $A_1$.
• The resulting pressure $P = \frac{F_1}{A_1}$ is transmitted undiminished through the incompressible liquid to a larger piston of surface area $A_2$.

Since the pressure must remain identical on both sides according to Pascal's law:

$P_1 = P_2 \implies \frac{F_1}{A_1} = \frac{F_2}{A_2}$

Solving for the output force $F_2$:

$F_2 = \left(\frac{A_2}{A_1}\right) F_1$

Because the area ratio $\frac{A_2}{A_1}$ is greater than 1, the output force $F_2$ is significantly larger than the input force $F_1$. By carefully designing a hydraulic press with appropriate piston areas, heavy loads can be easily lifted or pressed using minimal input effort.

Figure: Hydraulic Press.

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