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Fluids

Drag coefficient and Reynolds number

The drag coefficient depends on the Reynolds number. However not in a very simpel way. It has to be measured for each different shape.
Below we show the measaured relation between the drag coefficient and the Reynolds number for a spherical object in a graph which we have borrowed from aerospaceweb.org.



For small values of the Reynolds constant Re<1 one may use the approximation

C_d ≅ 24/Re = 12μ/ρvr

Hence, using the previous expression for the resistive force, we find (S=πr²)

F_res = C_d ρv²S/2 = 6πμrv

which is Stoke's law for the resistant force of a fluid on small spheres.

For Reynold constants from Re≅10³ up to Re≅3×10⁵ we read that the drag coefficient is almost constant. Previously we used C_d=0.47.

Laminar flow patterns