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10 Cards in this Set
- Front
- Back
Reynolds number formula and meaning |
Re < 1 laminar flow (η, viscosity, greater) Re > 1 turbulent flow (velocity greater) |
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Coefficient of Drag to Reynolds Number relationship |
CD = f(Re) F(drag) = 1/2 ρf v^2 CD the important bit is using Re to discover what f(Re) CD is, and then using this to find F. |
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Stoke's Flow: |
for low Reynolds numbers (Re < 1, meaning small spherical particle moving slowly through high-viscosity fluids): CD = 24 / Re hence F = 6πηvr (can be derived) |
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formula for net force of a particle settling in laminar flow where particle is larger: |
F = 4/3 π r ^3 (ρs - ρf) g (gravitational force minus buoyancy) |
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terminal velocity formula of larger grain in laminar flow: |
v = 1/18 d^2 (ρs - ρf) g / η ( this is F = 4/3 π r ^3 (ρs - ρf) g combined with Stoke's Law) |
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drag coefficients for 10^2 < Re < 10^5: |
for aerodynamic shapes: CD = 0.1 for spheres: CD = 0.5 for blunt shapes: CD = 1 |
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drag force for turbulent flow |
Fd = 1/16 π ρf v^2 d^2 |
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terminal velocity in turbulent flow |
v = sqrt[ 8/3 (ρs - ρf)/ρf g d ] |
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graph to show change in variation of CD to Re |
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Reynolds number formula for general flows |
Re = ρf v l / η where l is a scale length ( some length that is characteristic of the problem) |