8.8 - Pressure

Pressure is defined as the force applied per unit area. It is a scalar quantity and is commonly measured in pascals (Pa). The concept of pressure helps us understand how force is distributed over a surface. For example, a sharp object like a nail applies more pressure on a surface than a blunt object of the same weight, as the force is concentrated on a smaller area.

Formula for Pressure:

The formula for pressure is given by:

Pressure (P) = $\dfrac{Force (F)}{Area (A)}$

Where:

• P is the pressure applied,
• F is the force applied,
• A is the area over which the force is applied.

Pressure is measured in pascals (Pa), where 1 Pa = 1 N/m². This means that one pascal is the pressure exerted by a force of 1 newton on an area of 1 square meter.

Units of Pressure:

• Pascals (Pa): The SI unit of pressure. 1 Pa = 1 N/m² (newton per square meter).
• Atmospheres (atm): Often used in atmospheric pressure measurements. 1 atm = 101325 Pa.
• Millimeters of Mercury (mmHg): A unit used in measuring blood pressure and atmospheric pressure. 1 mmHg = 133.322 Pa.

Types of Pressure:

• Atmospheric Pressure: The pressure exerted by the weight of the air above us. It is approximately 101325 Pa at sea level and decreases with altitude.
• Hydrostatic Pressure: The pressure exerted by a fluid at rest due to the force of gravity. It depends on the height of the fluid column and its density. The formula for hydrostatic pressure is:

Hydrostatic Pressure (P) = $\rho g h$

Where:

• $\rho$ is the density of the fluid,
• g is the acceleration due to gravity,
• h is the height of the fluid column.

Effect of Pressure:

Pressure affects various phenomena, such as:

• Behavior of Liquids: Fluids exert pressure in all directions, which is why water in a container applies pressure on the sides and the bottom. This pressure increases with depth.
• Weather Patterns: Differences in atmospheric pressure create wind and weather systems. High-pressure areas lead to clear skies, while low-pressure areas are associated with clouds and storms.
• Compressibility of Gases: The volume of a gas decreases as pressure increases, according to Boyle's Law. The relationship between pressure and volume of a gas is given by:

Boyle’s Law: $P_1 V_1 = P_2 V_2$

Where:

• $P_1$ and $V_1$ are the initial pressure and volume,
• $P_2$ and $V_2$ are the final pressure and volume.

Factors Affecting Pressure:

• Force: The greater the force applied to a surface, the higher the pressure. For example, a heavier object exerts more pressure than a lighter one.
• Area: The pressure is inversely proportional to the area. That is, the larger the area over which a force is applied, the less the pressure. For example, a person lying flat on the ground exerts less pressure than when standing on the same surface.

Applications of Pressure:

• In daily life: The design of shoes with wide soles helps distribute weight and reduces the pressure on the ground. Similarly, snowshoes distribute a person's weight over a larger area to prevent sinking into the snow.
• In engineering: Hydraulic systems use the principle of pressure to lift heavy objects. The pressure exerted on a confined fluid is transmitted equally in all directions, as described by Pascal's Law:

Pascal’s Law: $F_1 / A_1 = F_2 / A_2$

Where:

• $F_1$ and $A_1$ are the force and area in one part of the system,
• $F_2$ and $A_2$ are the force and area in the other part.

Hydraulic brakes and lifts are based on this principle, allowing small forces to generate larger forces on a different area.