From Terminal Velocity to Elasticity

From Terminal Velocity to Elasticity

1. Viscous Force

• The force that opposes the relative motion between different layers of liquid or gases is called the viscous force.

2. Viscosity

Definition

• Viscosity is the property of a liquid by virtue of which it opposes the relative motion between its different layers.

General Information

• Viscosity is the property of liquids and gases both.

• The viscosity of a liquid is due to cohesive force between its molecules.

• The viscosity of a gas is due to the diffusion of its molecules from one layer to another.

• The viscosity of gases is much less than that of liquids.

• There is no viscosity in solids.

• Viscosity of an ideal fluid is zero.

Temperature Dependence

• With a rise in temperature, the viscosity of liquids decreases and that of gases increases.

Measurement

Viscosity of a fluid is measured by its coefficient of viscosity. Its SI unit is decapoise (kg/ms) or pascal second. It is generally denoted by η.

3. Terminal Velocity

When a body falls in a viscous medium, its velocity first increases and finally becomes constant. This constant velocity is called terminal velocity.

• In this situation, the weight of the body is equal to the sum of viscous force and force of buoyancy, i.e., the net force on the body is zero.

• The terminal velocity of a spherical body falling in a viscous medium is proportional to the square of the radius of the body.

4. Streamline Flow

If a fluid is flowing in such a way that the velocity of all the fluid particles reaching a particular point is the same at all times, then the flow of fluid is said to be streamline flow.

• In streamline flow, each particle follows the same path as followed by a previous particle passing through that point.

5. Critical Velocity

The maximum velocity up to which fluid motion is streamlined is called critical velocity.

• If the velocity of flow is below critical velocity, flow is streamlined.

• If the velocity of flow is above critical velocity, flow is turbulent.

• If the velocity of flow is less than critical velocity, the rate of flow of fluid depends basically on the viscosity of the fluid.

• If the velocity of flow is more than critical velocity, the rate of flow depends on the density of the fluid and not on viscosity.

Example: Due to this reason, on eruption of the volcano, the lava coming out of it flows very swiftly although it is very dense, having large viscosity.

6. Bernoulli's Theorem

According to Bernoulli's theorem, in the case of streamline flow of incompressible and non-viscous fluid (ideal fluid) through a tube, total energy (sum of pressure energy, potential energy, and kinetic energy) per unit volume of fluid is the same at all points.

• This theorem is simply the principle of conservation of energy.

• A venturimeter, a device used to measure the rate of flow of fluid, works on Bernoulli's theorem.

Elasticity

Definition

• Elasticity is the property of a material of a body by virtue of which the body acquires its original shape and size after the removal of a deforming force.

Elastic Limit

• The elastic limit is the maximum value of deforming force up to which a material shows elastic property and above which the material loses its elastic property.

Stress

• The restoring force per unit area set up inside the body subjected to deforming force is called stress.

Strain

The relative change in dimension or shape of a body that is subjected to stress is called strain.

• It is measured by the ratio of change in length to the original length (longitudinal strain) and change in volume to original volume (volume strain).

Hooke's Law

Under elastic limit, stress is proportional to strain

i.e., stress ∝ strain or = E (constant)

• E is called the elastic constant or modulus of elasticity. Its value is different for different materials. Its SI unit is Nm⁻², also called pascal.

Types of Elastic Constants

1. Young’s modulus of elasticity

2. Bulk modulus of elasticity

3. Rigidity modulus

Final Thoughts

Viscosity slows down the motion between layers of liquids or gases, and viscosity measures this resistance.

Liquids are more viscous than gases, and their flow changes with temperature. When an object falls through a viscous fluid, it eventually reaches terminal velocity, where forces balance. Fluids can flow smoothly in streamline flow, but at higher speeds, they become turbulent, exceeding the critical velocity. Bernoulli's theorem explains energy conservation in flowing fluids, used in devices like venturimeters.

Elasticity lets materials regain their shape after stress, following Hooke’s law, up to the elastic limit. These concepts appear in lava flow, candle wicks, and floating needles in everyday life.