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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Expert-level abstract algebra knowledge. Use when working with groups, rings, fields, modules, Galois theory, representation theory, or algebraic structures. Also use when the user mentions 'group', 'ring', 'field', 'homomorphism', 'isomorphism', 'normal subgroup', 'quotient group', 'Sylow theorem', 'Galois theory', 'polynomial ring', 'ideal', 'module', 'vector space', or 'representation theory'.
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Expert-level acoustics knowledge. Use when working with sound waves, acoustic propagation, resonance, standing waves, Doppler effect, room acoustics, ultrasound, noise control, musical acoustics, or architectural acoustics. Also use when the user mentions 'sound wave', 'decibel', 'frequency', 'resonance', 'standing wave', 'Doppler effect', 'acoustic impedance', 'reverberation', 'ultrasound', 'noise control', 'harmonics', or 'sound intensity'.
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Expert-level aerodynamics covering subsonic and supersonic flow, lift and drag, airfoil theory, boundary layers, compressible flow, and CFD methods.
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Expert-level air quality engineering covering pollutant sources, atmospheric dispersion, air quality standards, emission controls, and air quality modeling.
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Expert-level aircraft structures covering structural design philosophy, wing and fuselage analysis, fatigue and damage tolerance, composite structures, and certification.
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Expert-level algorithms and complexity theory covering sorting, searching, graph algorithms, dynamic programming, greedy algorithms, NP-completeness, and algorithm design paradigms.
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