![]() ![]() A material (dyed) volume is a collection of designated fluid particles. ![]() Df 0 means f is constant for a fluid particle but it can differ between different Dt ![]() 0 means f is constant along a streamline but it can vary between different y x y, x,0 x y įor steady flow: Df f u f u s f u Dt s where s ss is the tangent vector to a streamline. f f dx f dy f dz t x dt y dt z dtĪcceleration: Du u ( u )u Dt t Uniform rotation: u ( y, x,0) Material derivative, or, rate of change “following the fluid”: Df d rc f Dt dt fvv Streak photographs: illuminated polystyrene beads of neutral buoyancy. Let curve be: x x ( s ), y y ( s ), z z ( s ) Then Streamline: Curve with tangent equal to u everywhere. Experiment: Aerofoil & Starting Vortex Applications: Waves (§3.1) Flow Instability (§9.1) Hydraulic Jumps (§3.10) Smoke Ring Interactions (§5.4) Atmospheric Jet Stream (§9.8) Quantum Vortices (§5.8) Sperm Movement (§7.5) Spindown of Stirred Tea (§8.5) ![]() Elementary Fluid Dynamics D.J.Acheson, Clarendon Press (90) Notes by CKWongġ Introduction Sources: D.J.Acheson, “Elementary Fluid Dynamics”, Clarendon Press (90) R.E.Meyer, ”Introduction to Mathematical Fluid Dynamics”, Wiley (71). ![]()
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