Viscosity: Definition, Formula, Types & Examples | Famous Books for UPSC Exam (Summary & Tests) PDF Download

Introduction

Viscous force is the force that opposes the relative motion of adjacent layers of a fluid as they move past each other. It arises due to the internal friction between fluid particles. When a solid object moves through a fluid or when layers of a fluid move with different velocities, the viscous force acts to resist this motion. It depends on the viscosity of the fluid and the velocity gradient within the fluid.

Viscosity

Viscosity is a measure of a fluid's resistance to flow. It is a property of the fluid that determines how easily it can be deformed or how resistant it is to shear forces. The higher the viscosity of a fluid, the more resistant it is to flow. Viscosity is often referred to as the "thickness" or "stickiness" of a fluid. It is measured in units of poise or pascal-seconds (Pa·s).

Viscosity can be classified into two types

• Dynamic viscosity (η): It is the measure of a fluid's resistance to shearing or flow. It is defined as the ratio of the shear stress (force per unit area) to the velocity gradient perpendicular to the direction of flow. The unit of dynamic viscosity is poise or pascal-seconds (Pa·s).
• Kinematic viscosity (ν): It is the ratio of dynamic viscosity to the density of the fluid. It represents the fluid's resistance to flow under the influence of gravity. The unit of kinematic viscosity is stokes or square meters per second (m²/s).

Terminal Velocity

• Terminal velocity is the maximum velocity attained by a falling object when the drag force acting on it is equal in magnitude and opposite in direction to the gravitational force. In the context of fluid dynamics, it refers to the constant velocity reached by an object falling through a viscous fluid, such as air or water. At terminal velocity, the net force on the object becomes zero, resulting in no further acceleration.
• Terminal velocity depends on several factors, including the mass and shape of the object, the density and viscosity of the fluid, and the gravitational acceleration. For example, a more streamlined object will have a higher terminal velocity compared to a less streamlined object.

Streamline Flow

• Streamline flow, also known as laminar flow, is a type of fluid flow where the fluid particles move along smooth paths called streamlines, without crossing or mixing with each other. In streamline flow, the fluid flows in parallel layers, and there is no turbulence or eddies present.
• In streamline flow, the velocity of the fluid is constant at any point within the flow, and there is no lateral mixing. It is characterized by smooth, well-defined flow patterns. Streamline flow usually occurs at low velocities and with fluids of low viscosity.

Critical Velocity

• The critical velocity is the minimum velocity required for a fluid to transition from streamline flow to turbulent flow. When the velocity of a fluid exceeds the critical velocity, the flow becomes turbulent, characterized by irregular fluctuations in velocity and the formation of eddies.
• The critical velocity depends on factors such as the viscosity and density of the fluid, as well as the diameter and roughness of the pipe or channel through which the fluid flows. Rough surfaces or high-viscosity fluids generally have lower critical velocities.

Bernoulli's Theorem

• Bernoulli's theorem states that in a fluid flow, the total mechanical energy (sum of pressure energy, kinetic energy, and potential energy per unit volume) remains constant along a streamline. It is based on the principle of conservation of energy.
• Mathematically, Bernoulli's theorem can be stated as: P + (1/2)ρv² + ρgh = constant
• where P is the pressure, ρ is the density of the fluid, v is the velocity of the fluid, g is the acceleration due to gravity, and h is the height of the fluid above a reference point.
• Bernoulli's theorem is often applied to analyze the flow of fluids through pipes, nozzles, and other devices. It helps explain phenomena such as lift in airfoils, the working of a Venturi meter, and the flow of blood in arteries.