Fluid Mechanics (the NCERT "Mechanical Properties of Fluids" chapter) is a quiet over-performer: in JEE Main it is a 1–2 question, mostly formula-direct scorer, but in JEE Advanced it punches well above its question count. Advanced typically asks just one fluids question, yet it is frequently conceptual and fused — a floating body executing SHM, Bernoulli combined with continuity, or viscous/terminal-velocity reasoning. So the Main strategy is "drill the standard formulas for speed," while the Advanced strategy is "understand the concept well enough to handle it inside another chapter."

How to Study Fluid Mechanics — In Order

1. Pressure and Pascal's law. Hydrostatic pressure P = P₀ + ρgh, the difference between gauge and absolute pressure, and Pascal's law (hydraulic lift). Getting gauge-vs-absolute straight here prevents a whole class of later errors.
2. Buoyancy and floatation. Archimedes' principle: upthrust = weight of displaced fluid. For a floating body the fraction submerged = ρ_body / ρ_fluid. This single ratio answers most floatation questions in one line.
3. Continuity and Bernoulli. A₁v₁ = A₂v₂ (continuity) and P + ½ρv² + ρgh = constant (Bernoulli). Always pair them — most Bernoulli questions need continuity to eliminate one velocity. Remember Bernoulli holds only for non-viscous, incompressible, streamline flow.
4. Applications: Venturi and Torricelli. Venturi meter (flow rate from a pressure difference) and Torricelli's law for efflux, v = √(2gh). These are direct consequences of Bernoulli and recur as Main numericals.
5. Viscosity and Stokes' law. Viscous drag F = 6πηrv and terminal velocity v_t = 2r²(ρ − σ)g/9η for a sphere falling through a fluid. The dependence v_t ∝ r² (not r) is the most-tested point.
6. Surface tension and capillarity. Excess pressure inside a drop (2T/r) versus a soap bubble (4T/r, two surfaces), and capillary rise h = 2T cosθ/ρgr. The drop-vs-bubble factor and the 1/r dependence of capillary rise are the recurring questions.

High-Yield Sub-Topics (most-asked first)

1. Bernoulli's theorem with continuity. The most-tested fluids theme. Combine P + ½ρv² + ρgh = constant with A₁v₁ = A₂v₂ to solve flow-speed and pressure-difference problems (aerofoil lift, Venturi, a tank emptying through a hole). Torricelli's v = √(2gh) is just Bernoulli applied to efflux.
2. Floatation: fraction submerged. A body floating in a fluid has fraction submerged = ρ_body / ρ_fluid. Iceberg-in-water and block-in-two-liquids questions reduce to this ratio. If the body is pushed down and released, it executes SHM about the floating position.
3. Terminal velocity (Stokes' law). v_t = 2r²(ρ − σ)g/9η. The key exam point is v_t ∝ r² — doubling the radius quadruples the terminal velocity. Used for raindrops, ball-bearing-in-glycerine and Millikan-style setups.
4. Surface tension: excess pressure and capillary rise. Excess pressure = 2T/r for a liquid drop and 4T/r for a soap bubble (two surfaces). Capillary rise h = 2T cosθ/ρgr, so a narrower tube gives a higher rise. The drop-vs-bubble factor of 2 is a classic single-correct trap.

Mistakes Students Repeatedly Make

• Applying Bernoulli's equation to viscous or turbulent flow. It is valid only for an ideal fluid in steady, streamline, incompressible flow — viscous-flow questions need Stokes' law or Poiseuille reasoning instead.
• Using excess pressure 2T/r for a soap bubble. A bubble has two surfaces, so its excess pressure is 4T/r; a liquid drop (one surface) is 2T/r.
• Mixing up gauge and absolute pressure. P = P₀ + ρgh is the absolute pressure; the gauge pressure is just ρgh. Bernoulli and force problems must use a consistent choice.
• Thinking terminal velocity scales with radius. Stokes' law gives v_t ∝ r², so a drop of twice the radius falls four times as fast at terminal velocity.