Fluid Mechanics

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Fluid Mechanics — Key Facts Pressure: P = F/A = ρgh (hydrostatic); Pascal’s Law: pressure transmitted equally in all directions Archimedes’ Principle: Buoyant force B = ρVg (weight of displaced fluid) Continuity: A₁v₁ = A₂v₂ (incompressible fluid, conservation of mass) Bernoulli: P + ½ρv² + ρgh = constant (along a streamline) ⚡ Exam tip: Bernoulli is for horizontal flow OR when h is constant — use P + ½ρv² = constant

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🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

Fluid Mechanics — NEET/JEE Study Guide Archimedes: B = ρ_fluid × V_submerged × g; compare densities by weighing in fluid Floatation: fraction submerged = ρ_object/ρ_fluid; for ice floating in water: 9/10 submerged Continuity: Av = constant → v ∝ 1/A; for pipe narrowing, velocity increases Bernoulli application: Venturi meter (measure flow rate), Pitot tube (measure speed of aircraft), sprayer Surface tension: γ = F/L (force per unit length); excess pressure inside soap bubble = 4γ/r (2 surfaces) Capillarity: height h = 2γcosθ/(ρgr); rise if θ < 90° (water glass), fall if θ > 90° (mercury glass)

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🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Fluid Mechanics — Comprehensive Notes Navier-Stokes equation (terminal form): η ∇²v = ∇P - ρg for viscous flow at low Reynolds number Poiseuille’s law: volume flow rate Q = (πr⁴ΔP)/(8ηL); highly sensitive to radius (r⁴!) Stokes’ law: viscous drag F = 6πηrv; terminal velocity v_t = (2r²/9η)(ρ-σ)g for sphere Reynolds number: Re = ρvD/η; Re < 2000 → laminar; Re > 4000 → turbulent Venturi meter: Q = A₁A₂√(2gh/(A₁²-A₂²)) where h = difference in manometer levels Surface tension detailed: Laplace pressure ΔP = 2γ/r (sphere), ΔP = 4γ/r (soap bubble); drives capillary action Dimensional analysis: Buckingham Pi for drag force on sphere F = ηvD, Re = ρvD/η

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