PhysicsFluid Dynamics

Effective Study Strategies

• Understand viscosity conceptually: Internal friction between fluid layers. High viscosity = flows slowly (honey), low viscosity = flows easily (water).
• Master Stoke’s law: F_D = 6πηrv for spherical objects in viscous fluids. Drag force ∝ velocity and radius.
• Learn terminal velocity derivation: When weight = drag force + buoyancy, acceleration = 0, velocity constant. V_t ∝ r² for constant density.
• Differentiate flow types: Streamline/laminar (smooth, parallel layers) vs turbulent (chaotic, mixing).
• Apply equation of continuity: A₁v₁ = A₂v₂ for incompressible fluids. Narrower pipe → faster flow.
• Master Bernoulli’s theorem: P + ½ρv² + ρgh = constant. Pressure low where speed high (and vice versa).
• Understand applications: Venturi meter, airplane lift, spinning ball swing, carburetor, blood flow.
• Learn Torricelli’s theorem: v = √(2gh) for fluid exiting hole at depth h.

Exam Preparation Tips

• Memorize key formulas: η = F/(A·dv/dx), F_D = 6πηrv, V_t = (2r²g(ρ_s-ρ_f))/(9η), A₁v₁ = A₂v₂.
• Practice unit conversions: Viscosity: Poise (P) to Pa·s (1 P = 0.1 Pa·s). Pressure: Torr to Pa (1 Torr ≈ 133 Pa).
• Solve terminal velocity problems: Remember V_t ∝ r² if density constant, V_t ∝ 1/r if mass constant.
• Work with Bernoulli’s equation: For horizontal flow: P + ½ρv² = constant. For static fluid: P + ρgh = constant.
• Analyze Venturi effect problems: P₁ – P₂ = ½ρ(v₂² – v₁²). Pressure difference measured by height difference.
• Practice blood pressure concepts: Normal: 120/80 mmHg. Systolic (max), diastolic (min). Increases with age/narrow arteries.
• Understand ideal fluid assumptions: Incompressible, non-viscous, steady flow.

Common Pitfalls to Avoid

• Confusing viscosity (internal friction) with density (mass/volume)
• Forgetting buoyancy force in terminal velocity calculations
• Applying Stoke’s law to non-spherical objects or turbulent flow
• Mixing up equation of continuity (mass conservation) with Bernoulli’s (energy conservation)
• Assuming pressure always increases with speed (opposite is true in horizontal pipes)
• Forgetting that terminal velocity means acceleration = 0, not velocity = 0
• Confusing blood pressure units (mmHg/Torr vs Pa)
• Applying Bernoulli’s equation to viscous fluids without correction