Revise: Fluid Dynamics
Laminar vs. turbulent flow, the continuity equation, Bernoulli's equation and its applications, viscosity, and surface tension.
Re = ρvd/η — below ~2000 laminar, above ~4000 turbulent.
Water at 0.5m/s in a 0.02m pipe → Re=10000, turbulent.
A₁v₁ = A₂v₂ — a narrower pipe means faster flow.
A₁=0.02m²,v₁=2m/s,A₂=0.005m² → v₂=8m/s.
P+½ρv²+ρgh = constant along a streamline.
Faster flow (v₂=8m/s) → lower pressure (P₂=170000Pa).
Faster flow ⟹ lower pressure — explains wing lift, atomizers.
v_top=250,v_bottom=200 → lift force 270000N on a 20m² wing.
F = ηA(v/d) — viscous drag between fluid layers.
η=0.001,A=0.5,v=0.3,d=0.002 → F=0.075N.
Re compares fluid inertia to viscosity.
Smoke: smooth column (laminar) breaking into swirls (turbulent).
Only valid for an incompressible fluid.
Covering a hose nozzle speeds up the water.
A statement of energy conservation for flowing fluid.
Assumes non-viscous, incompressible, steady streamline flow.
A wing's curved top forces air to move faster, not slower.
A perfume atomizer draws liquid up via low pressure.
Viscosity is independent of density.
Honey (high η) pours far slower than water.
Caused by unbalanced molecular attraction at the surface.
A water strider is supported by surface tension.
Rise stops when surface tension balances the risen weight.
A paper towel draws up liquid through capillary gaps.