Understanding Viscous Force in Physics

Viscous force is the resistive force that arises when layers of a fluid move past each other, causing internal friction within the liquid or gas. This concept is essential in JEE Main Physics, as it explains why substances like honey pour slowly while water flows easily, connecting real-world experiences to the physics syllabus.

For JEE aspirants, mastering viscous force builds a foundation for fluid mechanics problems, from the motion of objects in fluids to the calculation of terminal velocity. Imagine stirring thick oil versus stirring water—the difference is due to viscosity and the forces produced by it.

Understanding Viscous Force in Fluids

Whenever any fluid moves, its adjacent layers rub against each other, generating internal friction known as viscosity. The force responsible for this opposition is called viscous force. In everyday terms, this is why a swimmer feels resistance as they glide through water.

The bigger the difference in speed between layers, the stronger the viscous force that acts to minimise that difference. In fluids like glycerine or oil, where flow is slow, viscosity (and thus viscous force) is higher. In contrast, air and water have much lower viscosity.

Formula and Units for Viscous Force

The mathematical expression for viscous force between fluid layers comes from Newton’s law of viscosity:

F = ηA (dv/dx)
Where:
F = viscous force (N)
η = coefficient of viscosity (Pa·s)
A = area of contact (m²)
dv/dx = velocity gradient perpendicular to flow (s⁻¹)

Here, η (eta) measures the “stickiness” or internal resistance of the fluid. This coefficient varies with temperature and the type of fluid. Questions in JEE Main often use this equation to relate flow patterns to fluid properties.

Stokes’ Law and Motion in Fluids

When an object moves through a viscous fluid, it experiences a drag force. For a small sphere with radius r moving at speed v in a fluid of viscosity η, Stokes’ law gives:

F = 6π η r v
This formula:
Is accurate for slow-moving spheres in laminar flow (low Reynolds number, Re < 1).
Explains the balance of forces when objects reach terminal velocity.

For example, raindrops stop accelerating and fall at constant speed because the upward viscous force balances their weight—a classic exam concept. See this viscosity overview for practical solved examples.

Dependence on Temperature and Fluid Type

In liquids, the coefficient of viscosity (η) decreases when temperature rises; fluid layers slide past more easily. In gases, the opposite happens since hotter gas molecules collide more and transfer momentum better, so viscosity increases with temperature.

• Honey’s viscosity drops when heated, so it flows faster
• Engine oil thins out at high temperature
• Air’s resistance (viscosity) grows with temperature

For JEE, remember: Liquid viscosity drops with heat, while gas viscosity rises. Questions often test your memory with real-life examples and graphs.

Viscous Force vs Frictional Force

It’s easy to mix up viscous and frictional forces. However, they act in different contexts:

• Viscous force acts inside fluids between moving layers
• Frictional force acts at the interface of two solids
• Viscous force depends on fluid’s viscosity and velocity gradient
• Friction depends on surface roughness and normal force
• Both always oppose relative motion

Exploring the difference in detail helps in solving complex problems. For more clarity, see this explanation on friction types.

Laminar Flow, Pipe Flow and Reynolds Number

The strength of viscous force directly affects the type of flow. Slow, steady movement leads to smooth “laminar” flow, while fast movement causes “turbulent” patterns.

A key tool here is the Reynolds number (Re):

Re = (ρ v d) / η
Where:
ρ = fluid density
v = mean speed
d = pipe diameter
η = viscosity

• If Re < 2000: Flow is laminar (viscous effects dominate)
• If Re > 4000: Flow is turbulent (inertia dominates)

In real-world applications—from laboratory pipes to blood flow—calculating the Reynolds number helps determine which kind of force is more important. For more insight, read about fluid pressure and flow.

Practical Significance in the JEE Syllabus

Understanding viscous force is essential for solving problems on:
• Terminal velocity calculations
• Pipe flow rates (Poiseuille’s law and laminar flow)
• Forces on moving spheres or plates
• Distinguishing laminar and turbulent flows

This knowledge even connects to biology and technology—blood flow, lubrication, and the design of vehicles. Vedantu’s JEE mentors regularly emphasise these applications in live classes and revision material, helping students target high-frequency exam questions.

Whether analysing a falling particle or the forces at work in a water pipe, mastering viscous force lets you tackle some of the most scored topics in JEE Main Physics—combining formula skills with direct real-world understanding.