Glossary · Fluid Mechanics

Alphabetical reference for every technical term used in the PC316 wiki. Each entry links to the page where the idea lives.

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Absolute pressure — Pressure measured relative to perfect vacuum; always positive. → Pressure

Archimedes' principle — The buoyant force on a body equals the weight of fluid it displaces. → Buoyancy

Atwood number — \(\mathcal{A} = (\rho_1-\rho_2)/(\rho_1+\rho_2)\); sets the Rayleigh–Taylor growth rate. → Rayleigh–Taylor

Barometric formula — Pressure–height relation in a compressible atmosphere (isothermal, lapse-rate, or adiabatic variants). → Hydrostatic equilibrium

Bernoulli's equation — \(p + \frac12\rho v^2 + \rho gz\) constant along a streamline for steady inviscid incompressible flow. → Bernoulli

Buckingham Pi theorem — \(n\) variables with \(k\) dimensions reduce to \(n-k\) dimensionless groups. → Buckingham Pi

Buoyancy — Net upward pressure force on a submerged body. → Buoyancy

Center of pressure — Point where the resultant hydrostatic force acts; lies below the centroid. → Forces on surfaces

Characteristics — Curves \(dx/dt = u \pm c_s\) along which information propagates in compressible flow. → Shock waves

Closure problem — RANS averaging produces more unknowns (Reynolds stresses) than equations. → Reynolds averaging

Complex potential — \(F(z) = \phi + i\psi\), analytic for 2-D potential flow. → Conformal mapping

Conformal mapping — Analytic change of complex variable carrying potential-flow solutions between domains. → Conformal mapping

Continuity equation — Differential statement of mass conservation. → Continuity

Continuum hypothesis — Treating matter as smooth fields, valid when \(L \gg \lambda\). → What is a fluid?

Control volume — Fixed region of space used for conservation bookkeeping. → Reynolds transport theorem

Couette flow — Linear shear flow between a fixed and a moving plate. → Example

Dimensional analysis — Deducing functional forms by requiring unit consistency. → Dimensional analysis

Dynamic similarity — Model and prototype share all relevant dimensionless groups. → Buckingham Pi

Eddy viscosity — Modeled turbulent momentum diffusivity \(\nu_t\) (Boussinesq hypothesis). → Reynolds averaging

Energy cascade — Transfer of turbulent kinetic energy from large to small eddies. → Energy cascade

Eulerian description — Fields observed at fixed points in space. → Eulerian vs Lagrangian

Gauge pressure — Pressure relative to local atmosphere. → Pressure

Hagen–Poiseuille law — \(Q = \pi R^4 \Delta P / 8\mu L\) for laminar pipe flow. → Example

Hydrostatic equilibrium — Balance \(\nabla p = \rho\mathbf{g}\) in a fluid at rest. → Hydrostatic equilibrium

Incompressible flow — \(\nabla\cdot\mathbf{v} = 0\); volume-preserving fluid motion. → Continuity

Inertial range — Scales where energy cascades without dissipation; \(E(k)\sim k^{-5/3}\). → Energy cascade

Inviscid flow — Idealization with zero viscosity, governed by Euler's equation. → Euler's equation

Irrotational flow — \(\nabla\times\mathbf{v} = 0\); admits a velocity potential. → Potential flow

Isentropic flow — Adiabatic and reversible; \(P/\rho^\gamma\) constant. → Bernoulli

Joukowski transformation — \(w = z + c^2/z\); maps circles to airfoils. → Conformal mapping

Kelvin–Helmholtz instability — Shear-driven interface instability. → Kelvin–Helmholtz

Kinematic viscosity — \(\nu = \mu/\rho\); diffusivity of momentum (m²/s). → Viscosity

Knudsen number — \(\lambda/L\); gauges validity of the continuum hypothesis. → What is a fluid?

Kolmogorov microscale — \(\eta = (\nu^3/\varepsilon)^{1/4}\), where turbulence dissipates. → Energy cascade

Lagrangian description — Following individual fluid particles. → Eulerian vs Lagrangian

Laminar flow — Smooth, layered, low-Reynolds-number flow. → Reynolds number

Laplace's equation — \(\nabla^2\phi = 0\); governs potential flow. → Laplace

Mach number — \(M = u/c_s\); flow speed over sound speed. → Shock waves

Material derivative — \(D/Dt = \partial_t + \mathbf{v}\cdot\nabla\); rate of change following the fluid. → Material derivative

Method of images — Enforcing wall boundary conditions with mirror singularities. → Conformal mapping

Navier–Stokes equation — Momentum equation for viscous Newtonian fluids. → Navier–Stokes

Newtonian fluid — Shear stress proportional to shear rate; constant \(\mu\). → Viscosity

No-slip condition — Fluid velocity equals wall velocity at a solid boundary. → Viscosity

Pathline — Trajectory of an individual fluid particle. → Eulerian vs Lagrangian

Potential flow — Irrotational, incompressible flow described by \(\nabla^2\phi = 0\). → Potential flow

Rankine–Hugoniot conditions — Conservation-law jump relations across a shock. → Rankine–Hugoniot

Rayleigh–Taylor instability — Buoyancy-driven instability of heavy fluid over light. → Rayleigh–Taylor

Reynolds decomposition — Splitting fields into mean + fluctuation. → Reynolds averaging

Reynolds number — \(Re = UL/\nu\); inertia vs viscosity. → Reynolds number

Reynolds stress — \(\overline{u_i'u_j'}\); turbulent momentum flux appearing in RANS. → Reynolds averaging

Reynolds transport theorem — Converts material-volume rates to control-volume terms. → RTT

Riemann invariants — \(C_\pm = u \pm \frac{2}{\gamma-1}c_s\), constant along characteristics. → Shock waves

Sedov–Taylor solution — Self-similar strong blast wave, \(R \propto (Et^2/\rho)^{1/5}\). → Trinity example

Shock wave — Thin nonlinear front with abrupt jumps in \(\rho, p, T, u\). → Shock waves

Stream function — \(\psi\) with \(u = \partial_y\psi\), \(v = -\partial_x\psi\); contours are streamlines. → Potential flow

Streakline — Locus of particles that passed a fixed point (dye line). → Eulerian vs Lagrangian

Streamline — Curve everywhere tangent to the instantaneous velocity field. → Eulerian vs Lagrangian

Surface tension — Interface energy per area; stabilizes short-wavelength disturbances. → Interface dispersion relation

Turbulence — Chaotic, multi-scale, strongly mixing flow regime at high \(Re\). → Turbulence

Turbulent kinetic energy (TKE) — \(k = \frac12\overline{u_i'u_i'}\); budget governed by the TKE equation. → TKE equation

Velocity potential — Scalar \(\phi\) with \(\mathbf{v} = \nabla\phi\) in irrotational flow. → Potential flow

Venturi effect — Pressure drop where a flow accelerates through a constriction. → Pressure

Viscosity (dynamic) — \(\mu\); internal friction coefficient, Pa·s. → Viscosity

Vortex sheet — Surface of discontinuous tangential velocity; infinite vorticity. → Kelvin–Helmholtz

Vorticity — \(\boldsymbol{\omega} = \nabla\times\mathbf{v}\); local spin of fluid elements. → Potential flow