Fluid dynamics (hydrodynamics) studies fluids in motion. Continuity equation: mass conservation (A₁v₁ = A₂v₂). Bernoulli's equation: energy conservation (P + ½ρv² + ρgh = constant). Viscosity resists flow. Reynolds number determines flow type (laminar vs turbulent).
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Continuity, Bernoulli, viscosity, flow, Reynolds
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| Concept | Formula | Notes / Units / Conditions |
|---|---|---|
| Continuity Equation | A₁ v₁ = A₂ v₂ | Incompressible fluid → A v = constant |
| Bernoulli's Equation | P + ½ ρ v² + ρ g h = constant | Along a streamline; ideal fluid (no viscosity) |
| Torricelli's theorem | v = √(2 g h) | Speed of efflux from hole at depth h |
| Viscosity (Newtonian) | F = η A (dv/dx) | η = coefficient of viscosity (Pa·s) |
| Stokes' Law | F_d = 6πη r v | Laminar flow, small sphere |
| Poiseuille's Law | Q = (π r⁴ ΔP) / (8 η L) | Volume flow rate; laminar flow |
| Reynolds number | Re = ρ v D / η | Re < 2000 → laminar; Re > 4000 → turbulent |
About Fluid Dynamics
Fluid dynamics (hydrodynamics) studies fluids in motion. Key principles include mass conservation (continuity), energy conservation (Bernoulli), and flow resistance (viscosity).
Continuity Equation
Continuity equation: A₁v₁ = A₂v₂ for incompressible fluids. Mass conservation: flow rate is constant. Narrow pipe → faster flow; wide pipe → slower flow.
Bernoulli's Equation
Bernoulli's equation: P + ½ρv² + ρgh = constant along a streamline. High speed → low pressure (Venturi effect). Used for lift, flow measurement, and pressure calculations.
Viscosity and Flow
Viscosity (η) measures fluid resistance to flow. Stokes' law: F_d = 6πηrv for drag on sphere. Poiseuille's law: Q = (πr⁴ΔP)/(8ηL) for flow through tube.
Reynolds Number
Reynolds number Re = ρvD/η determines flow type. Re < 2000 → laminar (smooth), Re > 4000 → turbulent (chaotic). Dimensionless parameter for flow characterization.