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Dynamic Similarity

Dynamic Similarity. Dimensionless Science. http://www.typefreediabetes.com/Articles.asp?ID=150. http://www.eosnap.com/?tag=strait-of-gibraltar. Ideas needed to perform Dimensional Analysis. All terms in equation must have same dimensions.

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Dynamic Similarity

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  1. Dynamic Similarity Dimensionless Science http://www.typefreediabetes.com/Articles.asp?ID=150 http://www.eosnap.com/?tag=strait-of-gibraltar

  2. Ideas needed to perform Dimensional Analysis All terms in equation must have same dimensions Terms in equation can be expressed with 3 basic dimensions: Mass, Length, Time Dimensions of these variables can be arranged in “Dimensional Matrix”

  3. Dimensional Matrix The rank r of a matrix is the size of the largest square submatrix with non-zero determinant r = 3 Most problems in fluid mechanics Buckingham’s PI theorem: “n variables can be combined to form exactly (n-r) independent non-dimensional variables.”

  4. inertial vs viscous Reynolds Number

  5. Flow is laminar when Re < 1000 Flow is in transition to turbulence when 100 < Re < 105 to 106 Flow is turbulent when Re > 106, unless the fluid is stratified Low Re High Re

  6. Consider an oceanic flow where U = 0.1 m/s; L = 10 km; kinematic viscosity = 10-6 m2/s Is friction negligible in the ocean?

  7. Froude Number inertial vs pressure

  8. http://www.yourlocalweb.co.uk/greater-manchester/city-of-manchester/higher-blackley/pictures/http://www.yourlocalweb.co.uk/greater-manchester/city-of-manchester/higher-blackley/pictures/

  9. Euler Number pressure vs inertial

  10. Great Fountain Geyser, Yellowstone National Park, USA http://www.freefoto.com/browse/1222-02-0?ffid=1222-02-0

  11. http://ya.astroleague.org/?p=1445

  12. Strouhal Number local vs inertial f = frequency of motion; A = amplitude of motion – for flying or swimming organisms (fin or wing)

  13. Taylor at al. (2003, Nature 425, 707-711(16 ) doi:10.1038/nature02000) “Left panels, root-flapping motion; right panels, heaving motion. Amplitude, twice wing chord; static angle of attack, 15°; flow speed, 1.5 ms-1; smoke wire visualizations made at end of downstroke. a, For St < 0.10, flow separates at the sharp leading-edge, but no discrete vortex forms. b, For 0.10 < St < 0.25, a leading-edge vortex forms but is shed before the downstroke ends. c, For 0.25 < St < 0.45, the leading-edge vortex is shed as the downstroke ends. d, For St > 0.45, trailing edge separation produces a characteristic mushroom-shaped wake. At higher St, the wing collides with shed vorticity on the upstroke, giving an energetically inefficient mode.” http://www.nature.com/nature/journal/v425/n6959/fig_tab/nature02000_F1.html#figure-title

  14. Dynamic Similarity http://www.typefreediabetes.com/Articles.asp?ID=150 http://www.eosnap.com/?tag=strait-of-gibraltar

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