Fluid Mechanics

Concept overview

Fluid mechanics for JEE splits into statics (fluids at rest) and dynamics (fluids in motion). In statics, the pressure at depth h below a fluid surface is P = P₀ + ρgh — this is the hydrostatic equation. Pascal's law extends this: pressure applied to an enclosed fluid transmits undiminished in all directions, the principle behind hydraulic lifts.

Archimedes' principle gives the buoyant force on any submerged object: F_B = ρ_fluid × V_displaced × g. If F_B > weight, the object floats; if less, it sinks. For a floating object, F_B = weight, and the volume submerged adjusts to make this true.

For fluid dynamics, JEE requires ideal-fluid assumptions — incompressible, non-viscous, streamline (laminar) flow. Under these assumptions, Bernoulli's equation applies: P + ½ρv² + ρgh = constant along a streamline. This is energy conservation per unit volume of fluid — pressure + kinetic + potential energy densities sum to a constant.

Viscosity introduces friction between fluid layers. Stokes' law gives the drag on a sphere moving through a viscous fluid: F = 6πηrv. Surface tension arises from the imbalance of intermolecular forces at a liquid surface — the capillary rise h = 2T cosθ / (ρgr) predicts how high a liquid climbs a narrow tube.

Key formulas & concepts

• Hydrostatic pressure: P = P₀ + ρgh
• Pascal's law: Applied pressure transmits undiminished throughout an enclosed fluid
• Archimedes / buoyancy: F_B = ρ_fluid × V_submerged × g
• Continuity equation: A₁v₁ = A₂v₂ (for incompressible fluids)
• Bernoulli's equation: P + ½ρv² + ρgh = constant along streamline
• Stokes' law: F_drag = 6π η r v (small sphere in viscous fluid)
• Capillary rise: h = 2T cosθ / (ρgr)

Common mistakes to avoid

• Applying Bernoulli's equation across a pump or valve — it only holds along a streamline in ideal-fluid flow.
• Forgetting that buoyancy depends on the submerged volume, not the total volume — floating objects use only the underwater part.
• Using gauge pressure vs absolute pressure inconsistently — Bernoulli works with either, but be consistent throughout the equation.
• Assuming capillary rise is a universal formula — it depends on the contact angle θ; for non-wetting liquids (mercury) capillary depression occurs.

JEE Main relevance

JEE Main asks 1 fluid problem every paper — usually either a Bernoulli application (Venturi meter, water flow) or a buoyancy/pressure numerical.

JEE Advanced relevance

Advanced fluid problems combine multiple concepts — for instance, a floating object with a hole letting water in, or a Venturi meter connected to a manometer. Terminal-velocity problems using Stokes' law are also standard.

Previous-year questions (PYQ)

Fluid PYQs favour Bernoulli-based flow problems and buoyancy. Drill 15 problems of each in a dedicated session.