Pressure

Pressure is a fundamental concept in physics that describes how force is distributed over an area. It plays an essential role in everyday life and engineering, affecting everything from how we walk on soft surfaces to how submarines function under extreme water pressure.

Definition

Pressure is defined as the amount of force exerted per unit area. It determines how a force is spread over a surface.

Equation for Pressure:

• Pressure is the amount of force exerted per unit area.

• Equation for Pressure: 

Where:

• p = pressure (in pascals, Pa)

• F = force (in newtons, N)

• A = area (in square meters, m²)

Example:

A person applies a force of 500 N on a surface with an area of 2 m². Find the pressure exerted.

p = 500/2 

p= 250 Pa

A larger force or a smaller area results in higher pressure, while a smaller force or a larger area results in lower pressure.

How pressure varies with force and area

1. Increasing Force → Higher Pressure

• If the force increases while the area remains the same, the pressure increases.

• Example:

  • Pushing harder on a table increases the pressure exerted on the surface.

  • A person standing on one foot exerts more pressure on the ground than when standing on two feet.

2. Increasing Area → Lower Pressure

• If the same force is spread over a larger area, the pressure decreases.

• Examples:

  • Snowshoes distribute weight over a large surface area, reducing pressure, so you don’t sink into the snow.

  • A sharp knife has a small cutting edge, which concentrates the force and creates high pressure, making it easier to cut.

  • A wide tire distributes the weight of a vehicle over a larger area, reducing pressure on the road and improving grip.

Pressure beneath the surface of a liquid

How Pressure Changes in Liquids

• As depth increases, pressure increases.

• Denser liquids exert greater pressure than less dense liquids.

Why Does Pressure Increase with Depth?

• The deeper you go in a liquid, the greater the weight of the liquid pressing down on you.

• Since liquids have mass, they exert force due to gravity on any object submerged in them.

Why Do Denser Liquids Exert Greater Pressure?

• Density is the mass per unit volume of a substance.

• Denser liquids (e.g., mercury) have more mass in the same volume compared to less dense liquids (e.g., water).

• Since pressure depends on weight, denser liquids exert higher pressure at the same depth.

Examples of Pressure in Liquids:

1. Deep-Sea Diving:

   • The deeper a diver goes, the more water is above them, increasing the pressure on their body.

   • Special diving suits are required to withstand the immense pressure at great depths.

2. Dams Are Thicker at the Bottom:

   • Water pressure is higher at greater depths, so dams are built with thicker bases to withstand the pressure.

3. A Plastic Bottle Experiment:

   • If you poke holes at different heights in a water-filled bottle, water from the bottom hole will squirt out with greater force because the pressure is higher at greater depths.

Equation for pressure change in a liquid

The increase in pressure with depth in a liquid can be calculated using the equation:

Where:

• Δp = change in pressure (Pa)

• ρ = density of the liquid (kg/m³)

• g = gravitational field strength (≈ 9.8 m/s²)

• Δh = change in depth (m)

Example Calculation:

A diver descends 10 meters underwater in the ocean. The density of seawater is 1025 kg/m³. Find the increase in pressure.

Δp = 1025 × 9.8 × 10

Δp = 100,450 Pa (or 100.45 kPa)

Applications of pressure