Fluid Mechanics — NEET Physics Notes

Fluid mechanics covers the behaviour of liquids and gases at rest (hydrostatics) and in motion (hydrodynamics) — an important topic with strong conceptual questions in NEET Physics.

Quick Revision

• Density: ρ = m/V (kg/m³)
• Pressure: P = F/A (N/m² = Pascal)
• Pascal’s Law: Pressure applied to an enclosed fluid is transmitted equally to every part of the fluid
• Buoyant Force: F_b = ρ_f × V_displaced × g (Archimedes’ Principle)
• Bernoulli’s Principle: P + ½ρv² + ρgh = constant (along a streamline)
• Surface Tension: γ = F/L (N/m)
• Viscosity: Internal friction in fluid flow — resists relative motion between layers
• Reynolds Number: Re = ρvd/η — predicts laminar or turbulent flow

Standard Study

Hydrostatics (Fluids at Rest)

Pressure in Fluids:

• P = ρgh (hydrostatic pressure at depth h)
• Absolute pressure at depth h: P = P₀ + ρgh (P₀ = atmospheric pressure)
• Pressure acts equally in all directions at a given depth

Pascal’s Law:

• A change in pressure at any point in an enclosed fluid causes the same change throughout the fluid
• Applications: Hydraulic press, hydraulic brakes, hydraulic lifts
• Mechanical advantage: F₂/F₁ = A₂/A₁

Archimedes’ Principle:

• Buoyant force = weight of fluid displaced
• F_b = ρ_f × V × g
• For floating body: weight = buoyant force → ρ_body × V_total × g = ρ_fluid × V_submerged × g
• For completely submerged body: apparent weight = actual weight − buoyant force

Floatation Conditions:

• Stable equilibrium: COG below CB (centre of buoyancy)
• Neutral equilibrium: COG at same height as CB

Surface Tension

• Surface tension γ = Work done / Area increase = F/L
• Excess pressure inside a soap bubble (2 surfaces): ΔP = 4γ/r
• Excess pressure inside an air bubble (1 surface): ΔP = 2γ/r
• Capillarity: Rise in a tube h = (2γ cosθ) / (ρgr)
• θ = contact angle (θ < 90° → liquid wets solid; θ > 90° → liquid does not wet solid)

Fluid Dynamics

Equation of Continuity:

• A₁v₁ = A₂v₂ (mass conservation in steady flow)
• For incompressible fluid: Av = constant
• v ∝ 1/A — fluid moves faster in narrower sections

Bernoulli’s Equation:

• P + ½ρv² + ρgh = constant along a streamline
• Applications:
  • Venturimeter (measure flow rate)
  • Atomiser (spray gun)
  • Airplane wing (lift)
  • Bunsen burner (mixing of gas with air)

Viscosity

• Viscous force: F = ηA(dv/dy) — Newton’s law of viscosity
• η = coefficient of viscosity (unit: poise or Pa·s)
• Streamlined flow (laminar): Re < 2000
• Turbulent flow: Re > 3000
• Terminal velocity: v_t = (2r²/9η)(ρ − σ)g (spherical body falling through fluid)

Stokes’ Law

• Viscous drag on sphere: F = 6πηrv
• Terminal velocity: v = (2/9) × (r²g(ρ − σ))/η
• Used in determining viscosity and for separating particles by centrifugation

Deep Study

Torricelli’s Theorem

• Speed of efflux (liquid flowing out of an orifice): v = √(2gh)
• Range of horizontal jet: R = 2√(h(H−h)) where H = total height of liquid

Venturimeter

• Measures flow rate of incompressible fluid
• Q = A₁A₂√(2(P₁−P₂)/(ρ(A₁²−A₂²)))

Surface Energy

• Surface energy = γ × Area
• Liquid drops minimise surface area → spherical shape (minimum surface for given volume)
• Coalescence of drops reduces surface area → releases energy

Capillarity Details

• Derivation: upward force = weight of liquid column
• 2πrγ cosθ = ρπr²h × g
• h = (2γ cosθ) / (ρgr)

Pressure Measurement

• Simple barometer: measures atmospheric pressure (~76 cm of Hg)
• Manometer: measures pressure difference (open tube)
• Bourdon pressure gauge: for high pressures

Exam Tips

1. Hydrostatic pressure P = ρgh — depth matters, not shape of container
2. Buoyant force depends on volume of fluid displaced, not weight of body
3. Bernoulli’s equation applies along a streamline — not between streamlines
4. Continuity equation: A₁v₁ = A₂v₂ — speeds up where pipe narrows
5. Surface tension formula ΔP = 2γ/r for single surface, 4γ/r for soap bubble
6. Terminal velocity reached when drag = net weight − buoyancy
7. Capillarity: ascent h ∝ 1/r — narrower tube, higher capillary rise

Common Pitfalls

• Confusing pressure with force — P = F/A, not F directly
• Applying Bernoulli incorrectly: it’s along a streamline, not across streamlines
• Forgetting atmospheric pressure in absolute pressure calculations
• Confusing surface tension with viscosity (both relate to fluid behaviour but different)
• Misapplying buoyant force — should be ρ_fluid × V_displaced × g, not body density
• Forgetting that viscosity produces drag opposite to direction of motion

Suggested Study Order

1. Pressure and Pascal’s law
2. Hydrostatic pressure formula
3. Archimedes’ principle and buoyancy
4. Surface tension and capillarity
5. Continuity equation and fluid dynamics
6. Bernoulli’s principle applications
7. Viscosity and Stokes’ law
8. Terminal velocity problems