Unformatted text preview: Reynolds Numbers & Hydrodynamics Fluids: Gas or Liquid Fluids resist moving Fluids = viscosity viscosity No Slip Condition No All movement with fluids No movement at boundary with solid => Velocity Gradients Boundary Layer Newtonian fluids Newtonian Have no memory of previous shape Properties are the same at different velocities (we will talk later about some (we biological non-Newtonian fluids) biological Never act like solids Boundary Layer Distance from a solid surface until in main-stream velocity of the fluid Water Flow Regimes: Velocity Gradient on a flat plate put a plate into the flow LAMINAR - regular, smooth, orderly TURBULENT - irregular, erratic Osborne Reynolds (1842 - 1912) Osborne Interested in flow of fluids through pipes Pipe flow Pipe 1) fluid viscosity, fluid density 2) pipe diameter 3) flow speed 3) Laminar - e.g. pouring honey nice, orderly flow 1 Flow visualization Turbulence Laminar Turbulent Transition from Laminar to Turbulent abrupt Transition occurs when a dimensionless composite of these three factors about equal to 2000. about 2000. This dimensionless composite = The Reynolds number (Re) Single Best Index of Flow Character Re is an indicator of the Relative importance of Re Relative Intertial Forces and Viscous Forces Forces Viscous Favors Turbulence Prevents Turbulence Equality of the Re for two flows ==> The physical character of the flows will be the same Examples: See attached end page with equations it would not print with equations in the ppt Whale (10 m / s) Tuna (10 m / s) Squid (jetting) Dragon Fly (7 m / s) Fruit Fly in flight Smallest insect in flight Copepod in pulse (20 cm / s) Invert. larva (1 mm / s) Sea Urchin sperm (0.2 mm / s) Bacterium swimming Human swimming Re 300,000,000 30,000,000 1,000,000 30,000 100 30 300 0.3 0.03 0.000001 10,000 2 At Re greater than 100 At Low Re (Less than or equal to 10) Laminar Gentle velocity gradients Drag proportional to U (velocity) Not affected by shape Turbulent Steep velocity gradients Drag proportional to U2 Very dependent on shape What is life like at Low Re? 1) Viscosity Dominates 2) Reversibility (no inertia) 3) Laminar Flow 4) Thick Boundary Layer Swimming or moving : Asymmetric strokes Bristles and spines - act like paddles Bristles Viscous drag (skin friction) can escape to higher Re - e.g., copepods can with sudden high velocities 3 Re less than 0.5 2 less than Re less than 20 slightly higher 40 less than Re less than 70 Re less than 90 Streamlines around a symmetric object in flow Streamlines compress as they move around the object - continuity of fluids velocity higher Low pressure above generates lift 4 ...
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This note was uploaded on 01/27/2010 for the course BIO 37282 taught by Professor Padilla during the Fall '10 term at SUNY Stony Brook.
- Fall '10