Pressure

Pressure is defined as the perpendicular force per unit area acting on a surface. It is a scalar quantity measured in Newton per square meter (N/m²) or Pascal (Pa).

Pressure can also be expressed as the force per unit area, calculated by dividing the total force by the area over which the force is applied:

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

Although force and pressure are related, they are distinct concepts. A small pressure applied over a large area can generate a significant total force.

Example

Problem: A force of 40 N acts on an area of 5 m². What is the pressure exerted on the surface?

Solution:

• Force, F = 40 N
• Area, A = 5 m²
• Pressure, P = F / A = 40 / 5 = 8 Pa

Pressure in Liquids

The pressure in a liquid has the following properties:

• Pressure increases with depth.
• Pressure depends on the density of the liquid.
• Pressure at any point in the liquid acts equally in all directions.
• Pressure at the same depth within a liquid is uniform.
• Pressure is independent of the liquid’s cross-sectional area.

The formula for pressure in a liquid is:

$$ P = hρg $$

• P = Pressure (Pa)
• h = Height (m)
• ρ = Density of the liquid (kg/m³)
• g = Acceleration due to gravity (9.8 m/s²)

Pascal's Principle

Pascal’s principle states that pressure applied to an enclosed fluid is transmitted equally and undiminished to every part of the fluid and to the walls of the container.

This principle is the basis for the operation of hydraulic systems such as hydraulic presses and car braking systems.

Measurement of Pressure

Pressure Gauge

A pressure gauge is a device used to measure and display pressure in a gas or liquid. It is also known as a vacuum gauge.

Barometer

A barometer is a scientific instrument used to measure atmospheric pressure.

Simple Mercury Barometer

The mercury barometer was invented by Evangelista Torricelli in 1643. It consists of a glass tube marked in inches, with one end sealed and the other resting in a small container of mercury called a cistern. The column of mercury inside the tube measures atmospheric pressure. Mercury barometers are commonly used in physics classes.

Aneroid Barometer

An aneroid barometer does not use liquid. Instead, it contains a small, flexible metal box called an aneroid capsule, made from an alloy of beryllium and copper. The box is tightly sealed, and changes in atmospheric pressure cause it to expand or contract, moving internal levers and springs to display the pressure.

Manometer

A manometer is a scientific instrument used to measure pressure in liquids or gases. An open manometer measures gas pressure relative to atmospheric pressure, while a mercury or oil manometer determines gas pressure based on the height of a fluid column supported by the gas.