Understanding Viscous Force in Physics

In fluid mechanics, understanding the behaviour of liquids and gases often requires a deep look at internal resistive effects. Among these, the viscous force plays a central role in explaining phenomena ranging from the dripping of honey to the flight of aircraft. For JEE Main aspirants, mastery of this topic is crucial, as it connects molecular dynamics with observable macroscopic effects, forming a bridge between basic definitions and mathematical applications.

Understanding Viscous Force in Fluids

Viscous force is the internal frictional force that arises when layers of a fluid move relative to each other. This resistance originates from the molecular interactions and determines how easily a material flows. Substances like oil or glycerine, which flow slowly, have high viscosity, while water and air are characterised by low viscosity. The greater the difference in velocity between adjacent fluid layers, the larger the viscous force acting to minimise this difference.

Mathematical Formulation of Viscous Force

The viscous force is quantitatively described using Newton’s law of viscosity. According to this law, the tangential force F acting between two parallel layers of fluid with area A, separated by a distance dx and moving with velocity difference dv, is given by:

F = η A (dv/dx)

Here, η (Greek letter eta) denotes the coefficient of viscosity, which is a property specific to the fluid and depends on temperature. This formula is essential for solving various problems in the JEE Main syllabus, particularly those involving flow in pipes or around objects.

Dependence on Temperature and Fluid Type

In liquids, the value of η decreases as temperature increases, because the stronger molecular motion makes it easier for layers to slide over each other. For gases, the opposite is true: η increases with temperature due to higher molecular agitation leading to more momentum transfer across layers. This contrasting behaviour should be memorised and understood with examples for exam applications.

Stokes’ Law and Application of Viscous Force

A classic JEE Main question involves the viscous force experienced by a spherical object moving through a viscous medium. Stokes’ law provides the expression for the drag force on a sphere of radius r moving at velocity v in a fluid with viscosity η:

F = 6 π η r v

This law is valid for small, slowly moving spheres where the flow is laminar—that is, when the Reynolds number is much less than 1. This relationship underpins the concept of terminal velocity, where the viscous drag balances other forces like gravity and allows falling objects to reach constant speed.

Distinguishing Viscous and Frictional Forces

While both friction and viscous force resist relative motion, their sources and forms are distinct. Friction acts at solid surfaces due to surface roughness, while viscous force operates throughout the fluid, resisting internal motion. To explore further, see Static and Dynamic Friction for comprehensive differences.

• Viscous force exists between fluid layers in motion.
• Magnitude depends on velocity gradient and viscosity coefficient.
• Affects flow types: laminar versus turbulent flow regimes.
• Stokes’ law applies to slow motion of spheres in viscous fluids.
• Temperature change affects viscous force in liquids and gases differently.
• Plays a key role in determining terminal velocity of objects.

For a deeper dive into formulas and quick revision before your test, refer to our Viscous Force Revision Notes curated by Vedantu experts for JEE Main Physics.

Viscous Force in Pipe Flow and Reynolds Number

The impact of viscous force is dramatically observed in pipe or tube flows. According to Poiseuille’s law, the volumetric flow rate in a cylindrical tube depends on the viscosity of the liquid, tube dimensions, and pressure difference. Importantly, the balance between viscous and inertial forces is measured by the Reynolds number (Re):

Re = (ρ v d) / η

Here, ρ is fluid density, v is mean velocity, d is pipe diameter, and η is viscosity. When Re < 2000, flow is usually laminar (viscous effects dominate); at high Re, inertial forces become more significant, and turbulence sets in. Grasping this threshold is necessary for addressing typical JEE Main application problems.

You can further strengthen your foundation by studying Viscosity and Viscous Force where these concepts are explored with additional solved examples.

Significance for JEE Main and Real-World Technologies

The real-world relevance of understanding viscous force stretches from chemical processing industries to biological systems and everyday activities. Precise calculation of force helps in designing pipelines, predicting blood flow, or even controlling aerodynamic drag on vehicles and aircraft. In the JEE Main exam, expect numerical questions requiring the use of the above formulas, as well as conceptual questions that test your understanding of viscous versus other types of resistive forces.

Vedantu’s resources, including Physics Revision Notes, are tailored to address the typical pitfalls and focus points for JEE Main success. Practise regularly to build problem-solving speed and conceptual clarity on viscous force and associated phenomena.