Pressure in a Fluid

This section explains pressure in a fluid covering, pressure exerted on a surface by a fluid, pressure exerted by a column of liquid, upthrust (buoyancy) and atmospheric pressure.

Fluids

A fluid is a substance that can flow and take the shape of its container. Fluids can be either liquids or gases, and they can exert pressure on surfaces they come into contact with.

• Liquids have a fixed volume but can change shape to fit the container.
• Gases have neither a fixed shape nor a fixed volume, and they expand to fill any container.

The pressure in fluids plays a key role in various phenomena, such as buoyancy, the operation of hydraulic systems, and the behaviour of gases.

Pressure Exerted on a Surface by a Fluid

The pressure exerted by a fluid on a surface is the force that the fluid applies per unit area of the surface. The pressure in a fluid depends on the depth of the fluid and the density of the fluid. The formula to calculate the pressure exerted by a fluid on a surface is:

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

Where:

• P is the pressure in Pascals (Pa).
• F is the force applied in Newtons (N).
• A is the area over which the force is applied in square metres (m²).

Example:

If a force of 100 N is exerted on an area of 2 m², the pressure can be calculated as follows:

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

$$P = \frac{100 \, \text{N}}{2 \, \text{m}^2}$$

$$P = 50 \, \text{Pa}$$ 

So, the pressure exerted on the surface is 50 Pascals (Pa).

Pressure Exerted by a Column of Liquid

When a liquid is in a column (such as in a tall container), the pressure exerted at the bottom of the column depends on the height of the liquid, the density of the liquid, and the gravitational field strength.

The formula to calculate the pressure exerted by a column of liquid is:

$$P = \rho \times g \times h$$

Where:

• P is the pressure at the bottom of the liquid column in Pascals (Pa).
• ρ is the density of the liquid in kilograms per cubic metre (kg/m³).
• g is the acceleration due to gravity, approximately 9.8 m/s².
• h is the height of the liquid column in metres (m).

Example:

Consider a column of water with a height of 5 m. The density of water is approximately 1000 kg/m³. The pressure at the bottom of the column can be calculated as follows:

$$P = \rho \times g \times h$$

$$P = 1000 \, \text{kg/m}^3 \times 9.8 \, \text{m/s}^2 \times 5 \, \text{m}$$

$$P = 49,000 \, \text{Pa}$$ 

So, the pressure at the bottom of the column is 49,000 Pascals (Pa), or 49 kPa.

Upthrust (Buoyancy)

Upthrust (also known as buoyancy) is the upward force exerted by a fluid on an object immersed in it. This force is equal to the weight of the fluid displaced by the object, and it is what makes objects float or sink in liquids or gases.

• If the upthrust (buoyant force) is greater than the weight of the object, the object will rise or float.
• If the upthrust is less than the weight of the object, the object will sink.

The principle of flotation states that an object will float if it displaces a volume of fluid whose weight is equal to the weight of the object.

The formula for upthrust is:

$$\text{Upthrust} = \text{Weight of displaced fluid} = \rho \times V \times g$$ 

Where:

• ρ is the density of the fluid in kg/m³.
• V is the volume of the displaced fluid in m³.
• g is the acceleration due to gravity in m/s².

Atmospheric Pressure

Atmospheric pressure is the pressure exerted by the Earth's atmosphere on all objects within it. This pressure is due to the weight of the air molecules above us and is the result of the Earth's gravity pulling the air towards the surface. Atmospheric pressure decreases with altitude, as there is less air above at higher altitudes.

At sea level, atmospheric pressure is approximately 101,325 Pascals (Pa), or 101.3 kPa. It can be measured using a barometer.

Atmospheric pressure is important in many situations, including weather systems, breathing, and the operation of various devices like pressure cookers.

Pressure in fluids is the force exerted per unit area and can be calculated using the formula $P = \frac{F}{A}$​. The pressure exerted by a column of liquid depends on the height, density, and gravity, and is calculated using $P = \rho \times g \times h$. Upthrust or buoyancy is the upward force exerted by a fluid on an object, causing it to float or sink. Atmospheric pressure is the pressure exerted by the Earth's atmosphere, and it decreases with altitude. Understanding fluid pressure is essential for explaining many natural phenomena and technological applications.