Understanding Viscosity and Viscous Force

Viscosity and Viscous Force are essential physical properties that describe how fluids resist internal motion and flow. In JEE Main Physics, these concepts help explain why different liquids and gases behave so differently in tubes, machines, and even the human body. For example, when you try to pour honey and water, honey flows much slower—a direct result of its much greater viscosity. Mastering these ideas makes it easier to solve complicated fluid mechanics questions in the exam.

How to Understand Viscosity and Viscous Force

Viscosity is a measure of a fluid’s internal resistance to flow or deformation under applied force. Whenever one fluid layer slides past another, a tangential force arises—this is called the viscous force. It always acts opposite to the relative motion and is crucial for predicting flow rates, energy losses, and mechanical efficiency in both natural and engineered systems.

To see viscous force in action, think of a raindrop drifting through air versus in oil. The drop moves faster in air and much slower in thick oil—showing how viscosity determines the drag acting on moving objects. This drag manifests as a viscous force that must be considered in practical calculations.

Formulas and Derivation: Viscosity in Mathematics

The fundamental formula linking viscous force, often denoted as F, to a fluid’s properties is:

Step 1: Assume two parallel fluid layers separated by a small distance dx and moving with velocity difference dv.
Step 2: The viscous force F is proportional to area A and velocity gradient (dv/dx):
$$F \propto A \frac{dv}{dx}$$
Step 3: Introducing coefficient of viscosity η, the equation becomes:
F = -\eta A \frac{dv}{dx}
The negative sign shows opposition to velocity difference direction.
Step 4: From here, if velocity gradient is 1 and area is 1, η measures the viscous force per unit area.
Final expression: F = -\eta A \frac{dv}{dx}

The SI unit for viscosity is pascal-second (Pa·s), and its dimensional formula is [ML^-1T^-1]. These appear in almost every JEE formula sheet—memorise them for exam calculations!

Types, Examples, and Exam Significance

Two forms of viscosity are tested in JEE Main: Dynamic (absolute) viscosity η and kinematic viscosity ν. Dynamic viscosity relates shear stress to velocity gradient, while kinematic viscosity measures the ratio of dynamic viscosity to fluid density, ν = η/ρ. Understanding their difference is often essential when tackling problems involving different fluids or flow conditions.

Everyday examples clarify these types. When oil is used as a lubricant, it must have high dynamic viscosity to reduce machinery wear. Blood’s viscosity affects its circulation, while viscosity changes with temperature are essential in the food industry and engineering.

• Water has low viscosity, so it flows easily in pipes
• Honey’s high viscosity makes it pour slowly
• Lubricating oils must balance viscosity for engine parts
• Kinematic viscosity is key for designing drainage systems
• Stokes’ law uses dynamic viscosity for drag on spheres

Newton’s Law of Viscosity and Exam Application

Newton’s law of viscosity states: “For a Newtonian fluid, the shear stress between adjacent layers is proportional to the velocity gradient perpendicular to the layers.” In other words, the ratio of shear stress (τ) to velocity gradient is constant and equals η:

τ = η (dv/dx)

This works for most real-world fluids at JEE level; only some complex liquids and slow-moving flows show non-Newtonian behaviour. Exam questions may also ask you to calculate forces using typical values, predict flow types, or compare viscosities of different fluids under changing temperatures. Be ready for derivations, plug-and-play calculations, and concept questions.

Stokes’ Law and Falling Spheres: Key Example

One classic JEE problem is the viscous force acting on a falling sphere, where Stokes’ Law applies. For a sphere of radius r moving at velocity v through a fluid of viscosity η:

F = 6π η r v

This relation allows calculation of terminal velocity, where the net force on the sphere becomes zero. Make sure you recall when this law holds—only in laminar (non-turbulent) flows and small velocity conditions.

If you want to see more practical use of these ideas, you can read detailed notes on fluid properties and behaviors on Vedantu.

Temperature Effects and JEE Tips

Viscosity is always influenced by temperature. For liquids, viscosity decreases as temperature increases—honey becomes runnier when warm. In gases, however, viscosity increases with temperature. JEE Main often asks you to compare these trends and apply them to predict fluid behaviour.

• Higher temperature lowers liquid viscosity
• In gases, viscosity goes up with heating
• Material choice for lubrication depends on operating temperature
• Common exam errors include mixing up these trends

Why Viscosity and Viscous Force Matter for JEE

Questions on viscosity and viscous force test your understanding of both fundamentals and real-life relevance. You may encounter problems on pipe flow, falling drops, or motion through viscous media. Mastery of definitions, formulas, and the ability to reason about examples is crucial. Vedantu’s resources are designed with these needs in mind and offer solved examples to help you connect theory and practice for top scores on exam day.