Expert-level fluid mechanics covering fluid statics, continuity, Bernoulli, Navier-Stokes, boundary layers, turbulence, pipe flow, and external aerodynamics.
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Pressure variation: dP over dz = negative rho g, increases with depth. Hydrostatic force: F = rho g h_c times A on submerged surface. Center of pressure: below centroid for inclined submerged surface. Buoyancy: upward force equals weight of displaced fluid.
Continuity: rho A V = constant for steady 1D flow. Bernoulli: P plus half rho V squared plus rho g z = constant along streamline. Momentum equation: sum of forces equals rate of change of momentum. Energy equation: adds shaft work and heat transfer to Bernoulli equation.
Reynolds number: Re = rho V L over mu, ratio of inertia to viscous forces. Laminar pipe flow: Poiseuille flow, parabolic velocity profile, f = 64 over Re. Turbulent pipe flow: Moody chart relates friction factor to Re and roughness. Navier-Stokes: governing equations for viscous flow, nonlinear, difficult to solve.
Boundary layer: thin region near wall where viscous effects important. Displacement thickness: effective thickness of zero velocity region. Transition: Re_x around 500,000 for flat plate boundary layer transition. Separation: adverse pressure gradient causes reverse flow and wake.
Reynolds averaging: separate mean and fluctuating components. Reynolds stresses: additional apparent stresses from turbulent fluctuations. k-epsilon model: two transport equations for turbulent kinetic energy and dissipation. DNS: direct numerical simulation resolves all scales, prohibitively expensive.
| Pitfall | Fix |
|---|---|
| Applying Bernoulli across streamlines | Bernoulli valid only along a streamline |
| Ignoring minor losses in pipe systems | Include entrance, exit, fittings in head loss |
| Wrong turbulence model for separated flow | Use more advanced model or LES for separated regions |
| Incorrect Reynolds number scaling | Ensure dynamic similarity in experimental scaling |
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日本語の概要は準備中です。原文の説明を表示しています。