FLD-00 · laboratory
Bernoulli, Navier–Stokes snapshot, Reynolds, Stokes drag and Strouhal.
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25 governing sheets
A₁ v₁ = A₂ v₂. Volume flux is conserved for steady incompressible flow.
FluidsRe = ρ v D / μ. Laminar below ~2300 in a pipe, turbulent above.
FluidsF = 6π μ r v. Linear drag on a slow sphere, Re ≪ 1.
FluidsQ = π r⁴ Δp / (8 μ L). Laminar flow in a circular tube.
FluidsΔp = 32 μ L v / D². The mean-speed form of Hagen–Poiseuille.
Fluidsn = v² / r. Normal acceleration on a curved streamline.
Fluidsv = √(2 g h). Ideal speed from an orifice under a head h.
FluidsM = v / c. Subsonic, transonic, supersonic as M crosses 1.
FluidsFr = v / √(g L). Inertia versus gravity on a free surface.
FluidsWe = ρ v² L / σ. Inertia versus surface tension.
FluidsSt = f L / v. Shedding frequency of a bluff body.
FluidsL = ½ ρ v² S C_L. The aerodynamic lift equation.
FluidsD = ½ ρ v² S C_D. Quadratic drag on a bluff or streamlined body.
Fluidsp = ρ g h. Gauge pressure under a free surface.
FluidsK = − Δp / (ΔV/V). How hard a fluid is to compress.
Fluidsc = √(K/ρ). Newton–Laplace speed in a compressible fluid.
FluidsRe = ρ U L / μ compares ρ(u·∇)u with μ ∇²u. The local inertial-to-viscous ratio.
Fluidsh = 2 σ cosθ / (ρ g r). Jurin's law in a circular tube.
Fluidsω = 2 Ω. For rigid-body rotation the vorticity is twice the angular velocity.
Fluidsc_f = 0.664 / √Re_x on a laminar flat plate. Local skin-friction coefficient.
FluidsΔp = f (L/D) (ρ v² / 2). The Darcy–Weisbach pipe formula in pascals.
FluidsQ = A₂ √(2 Δp / ρ (1 − β⁴)), β = d/D. Bernoulli plus continuity.
FluidsF = ρ g V. The buoyant force equals the weight of displaced fluid.
FluidsΔp = σ (1/R₁ + 1/R₂). Pressure jump across a curved interface.
Fluidsp/ρg + v²/2g + z = H along a streamline of an ideal fluid.
Fluids