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Advanced Physics — Fluid Mechanics

Fluid statics, dynamics, and classical fluid equations

T
turbulent_flow 22 terms Dec 24, 2025
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Terms 22

1
Fluid
Substance that deforms continuously under applied shear stress; liquids and gases
2
Density (ρ)
Mass per unit volume; ρ = m/V; water ≈ 1000 kg/m³; air ≈ 1.2 kg/m³
3
Pressure
Force per unit area; P = F/A; hydrostatic: P = P₀ + ρgh
4
Pascal's Principle
Pressure applied to enclosed fluid transmitted equally throughout; basis of hydraulics
5
Archimedes' Principle
Buoyant force = weight of displaced fluid; object floats if ρ_object < ρ_fluid
6
Continuity Equation
A₁v₁ = A₂v₂ for incompressible flow; conservation of mass; narrower pipe = faster flow
7
Bernoulli's Equation
P + ½ρv² + ρgh = constant along streamline; speed↑ → pressure↓; conservation of energy
8
Viscosity (η)
Resistance to flow; internal friction; τ = η(dv/dy); Pa·s; water < honey
9
Laminar Flow
Smooth, ordered flow in parallel layers; low Reynolds number; predictable
10
Turbulent Flow
Chaotic, mixed flow with eddies; high Reynolds number; difficult to model exactly
11
Reynolds Number (Re)
Re = ρvL/η; ratio of inertial to viscous forces; Re < 2300 laminar; > 4000 turbulent
12
Poiseuille's Law
Q = πr⁴ΔP/(8ηL); flow rate ∝ r⁴; small radius greatly reduces flow; blood flow, IVs
13
Stokes' Law
Drag on sphere: F = 6πηrv; used for sedimentation rate, viscosity measurement
14
Terminal Velocity
Constant velocity when drag = gravity + buoyancy; v_t = 2r²(ρ−ρ_f)g/9η (Stokes)
15
Navier-Stokes Equations
Governing equations of viscous fluid flow; ρ(∂v/∂t + v·∇v) = −∇P + η∇²v + ρg; generally unsolvable analytically
16
Euler Equations
Navier-Stokes without viscosity; governs ideal fluid flow; simpler but less realistic
17
Streamline
Curve tangent to velocity vector at every point; no flow across streamlines in steady flow
18
Vorticity
ω = ∇×v; local rotation of fluid element; curl of velocity field
19
Potential Flow
Irrotational, inviscid flow; velocity = gradient of potential; analytically tractable
20
Boundary Layer
Thin region near wall where viscosity is important; velocity goes from zero (no-slip) to free-stream
21
No-Slip Condition
Fluid velocity equals wall velocity at boundary; basis of viscous drag
22
Drag Coefficient (Cd)
F_drag = ½ρv²ACd; depends on geometry and Re; streamlined shapes have lower Cd