Fluid Mechanics JEE Main: Pressure, Bernoulli & Flow

Fluid mechanics consistently delivers one to two questions per JEE Main session. The topics are self-contained and reward systematic study: hydrostatics, fluid dynamics through Bernoulli's equation, viscosity, and surface tension each have a small set of core ideas that cover virtually every question the exam asks. Most JEE Main fluid problems follow recognizable templates once you understand the underlying principles.

Hydrostatics: Pressure and Archimedes' Principle

Pressure in a static fluid increases with depth. This principle underpins problems about connected vessels, U-tubes with different fluids, and pressure at specific points in fluid systems. JEE Main frequently combines two or three fluids in a U-tube and asks for the height difference or the unknown density. The key skill is identifying the datum and applying the pressure increase formula correctly at every point.

Archimedes' principle states that any object fully or partially submerged in a fluid experiences an upward buoyant force equal to the weight of the displaced fluid. The condition for floating and the relationship between the fraction submerged and the ratio of densities are the two numerical results JEE Main uses most often. Connect this to mechanics fundamentals for free-body diagram analysis of submerged objects.

Bernoulli's Equation and Fluid Dynamics

Bernoulli's equation states that the sum of pressure, kinetic energy per unit volume, and gravitational potential energy per unit volume remains constant along a streamline in ideal fluid flow. The equation explains the Venturi effect and underlies applications including the Venturi meter, Pitot tube, and lift on aircraft wings. JEE Main tests all three applications numerically.

The continuity equation — that the product of cross-sectional area and flow velocity is constant for incompressible flow — is always used alongside Bernoulli's equation. Torricelli's theorem, giving the speed of efflux from a hole in a container, is a special case of Bernoulli's equation. Take a free mock test on fluid mechanics to practice these problem types.

Viscosity and Stokes' Law

Viscosity is the internal friction of a fluid. Poiseuille's equation gives the volume flow rate through a cylindrical tube as a function of pressure difference, radius, length, and viscosity. The flow rate is proportional to the fourth power of the radius — doubling the tube radius increases flow by a factor of sixteen.

Stokes' law gives the drag force on a sphere moving slowly through a viscous fluid. The terminal velocity of a sphere falling through a viscous medium follows from balancing drag force and buoyant force against gravity. The terminal velocity is proportional to the square of the radius and the difference in densities, and inversely proportional to the viscosity.

Surface Tension and Capillary Action

Surface tension can be expressed as force per unit length or energy per unit area. The excess pressure inside a bubble or droplet depends on surface tension and radius. Soap bubbles have two surfaces, so the excess pressure is twice that of a liquid droplet — a frequently tested distinction.

Capillary rise results from the competition between surface tension and gravity. The height to which a liquid rises in a narrow tube is inversely proportional to the tube's radius. The contact angle determines whether the liquid rises or is depressed. Reinforce with our waves guide and sign up free for daily practice problems.