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10 Cards in this Set

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Reynolds number formula and meaning

Re < 1 laminar flow (η, viscosity, greater)
Re > 1 turbulent flow (velocity greater)

Re < 1 laminar flow (η, viscosity, greater)


Re > 1 turbulent flow (velocity greater)

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.

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.

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)





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)

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)

drag coefficients for 10^2 < Re < 10^5:

for aerodynamic shapes: CD = 0.1


for spheres: CD = 0.5


for blunt shapes: CD = 1

drag force for turbulent flow

Fd = 1/16 π ρf v^2 d^2

terminal velocity in turbulent flow

v = sqrt[ 8/3 (ρs - ρf)/ρf g d ]

graph to show change in variation of CD to Re

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)