Fluid

1.0What is a Fluid?

A fluid is any substance that can flow and take the shape of its container. Fluids have the ability to deform continuously under the application of external force. They do not have a fixed shape but possess a definite volume.
Both liquids and gases are considered fluids.

Examples of Fluids:

• Water
• Air
• Oil
• Alcohol
• Mercury

In simple words, a fluid is a substance that flows. It can be easily poured and moves freely under pressure.

2.0Types of Fluids

Fluids are classified based on their physical and flow characteristics:

1. Ideal Fluid: An ideal fluid is a hypothetical fluid that cannot be compressed and has no viscosity. It does not exist in reality but helps in theoretical study.

Examples (theoretical): Perfect water flow without resistance.

2. Real Fluid: A real fluid is a fluid that exists in the real world and has viscosity.

Examples: Water, air, oil.

3. Newtonian Fluid: A fluid whose viscosity remains constant at a given temperature, regardless of the rate of shear strain.

Example: Water, air.

4. Non-Newtonian Fluid: A fluid whose viscosity changes with the applied force or shear rate.

Examples: Toothpaste, blood, paint, ketchup.

5. Compressible and Incompressible Fluids

• Compressible Fluids: Density changes with pressure (e.g., air, gases).
• Incompressible Fluids: Density remains constant (e.g., water, oil).

3.0Properties of Fluids

Fluids exhibit unique physical properties that determine how they behave in different conditions.

1. Density (ρ): It is the mass per unit volume of a fluid.

$\rho =\frac{m}{V}$
SI Unit: kg/m³

2. Pressure (P): Pressure is defined as the force exerted per unit area on the surface of a fluid.

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

SI Unit: Pascal (Pa)

3. Viscosity (η): Viscosity is the property of a fluid that resists its motion or flow. It measures the internal friction between fluid layers.

4. Surface Tension: It is the force acting along the surface of a liquid, making it behave like a stretched elastic sheet. Surface tension allows insects to walk on water.

5. Temperature: The flow properties of fluids such as viscosity and density vary with temperature. When temperature increases, viscosity of liquids decreases while that of gases increases.

4.0Pressure in Fluids

Fluid pressure is one of the most important concepts in science. It determines how forces act in liquids and gases.

1. Definition

Fluid pressure is the force exerted by a fluid per unit area on the walls of its container or on any object immersed in it.

$P=\rho gh$

where:

• ρ = density of fluid
• g = acceleration due to gravity
• h = height (depth) of the fluid column

2. Pascal’s Law: According to Pascal’s Law, when pressure is applied to a fluid in a closed container, it is transmitted equally in all directions.

Applications:

• Hydraulic brakes
• Hydraulic lifts
• Hydraulic presses

5.0Buoyancy and Archimedes’ Principle

1. Buoyant Force: When an object is partially or completely immersed in a fluid, the fluid exerts an upward force called the buoyant force.

2. Archimedes’ Principle: It states that a body immersed in a fluid experiences an upward force equal to the weight of the fluid displaced by it.

$F_b=\rho ,g,V$

Applications:

• Designing ships and submarines
• Measuring purity of metals
• Determining fluid density

6.0Fluid Flow and Streamlines

1. Steady Flow: If the velocity of the fluid particles at a point remains constant over time, it is a steady flow.

2. Turbulent Flow: When the fluid moves irregularly with random motion of particles, it is a turbulent flow.

3. Streamlines: Imaginary lines drawn in the direction of flow are called streamlines. They help visualize how fluid particles move.

7.0Equation of Continuity

For an incompressible fluid, the mass flow rate remains constant throughout the pipe.

$A_1{v}_1=A_2{v}_2$

where:

• A = cross-sectional area
• v = velocity of fluid

This means that if the pipe becomes narrower, the fluid speed increases.

8.0Bernoulli’s Theorem

Statement:

For a steady, incompressible, and non-viscous fluid flow, the total energy per unit volume remains constant along a streamline.

$P+\frac{1}{2}\rho v^2+\rho gh=\text{constant}$

where:

• ( P ) = pressure energy
• ($\frac{1}{2}\rho v^2$) = kinetic energy per unit volume
• ( $\rho gh$ ) = potential energy per unit volume

Applications of Bernoulli’s Principle:

• Airplane wings (lift)
• Atomizers and spray guns
• Flow of blood in arteries
• Carburetors in engines

9.0Viscosity and Stokes’ Law

When a small spherical object moves through a fluid, it experiences a viscous drag force given by Stokes’ Law.

$F=6\pi \eta rv$

where:

• η = coefficient of viscosity
• r = radius of sphere
• v = velocity of sphere

Applications:

• Raindrop motion
• Oil drop experiment
• Sedimentation analysis

10.0Viscosity and Flow of Fluids

What is Viscosity?

Viscosity is the internal friction between layers of a fluid moving at different velocities.

Newton’s Law of Viscosity:

Where:

• τ = Shear stress
• η = Coefficient of viscosity
• dv/dy = Velocity gradient

Factors Affecting Viscosity

1. Temperature: In liquids, viscosity decreases with rise in temperature.
2. Pressure: In gases, viscosity increases with rise in pressure.
3. Nature of Fluid: Depends on intermolecular attraction.

Measurement of Viscosity

• Devices used: Viscometer and Stoke’s Law method.

11.0Surface Tension and Capillarity

Surface Tension: The property of liquid surfaces that allows them to resist an external force. It causes the formation of spherical droplets.

Capillary Action: The rise or fall of a liquid in a narrow tube due to surface tension.

Examples:

• Water rises in a thin glass tube.
• Ink moves up a paper towel.

12.0Applications of Fluids in Daily Life