Fluid Mechanics, influence of the speed of sound AND drag on a sphere. Design a

Question

Fluid Mechanics, influence of the speed of sound AND drag on a sphere.

Design a set of experiments^1 to investigate the influence of speed of sound on the drag of a rotating sphere (i.e you must isolate the influence of compressibility effects from other factors). Specifically design five experiments where spin parameter and Reynolds number will be held constant, while the dimensionless group containing the speed of sound term can be altered. Choose a Reynolds number for this set of tests of around Re = 4,000,000 and attempt to keep the diameter of the sphere the same in every experiment. Explain any potential difficulties / expense / safety issues with your designed set of experiments.

Explanation / Answer

Spin paramemter = WD/V = constant

Drag coefficient Cd = F/D^2V^2P

Reynolds No. = VPD/u = constant

a = sqrt(rRT.M)

Fd = -0.5 rhoa AV^2 Cd

the set of 5 speeds , corrrspnds to Re = inertial force/Viscous force = Vd/u

3 mm dispeher = speed = 400 m/s

Re = 8 e 4 to 200 m/s

Re = 2 e4

Viscoscity = 1.5 e 5 m/s^2 @20 deg C

Subsonic below 0.5 mach

transoic = 0.5m -1.4 m Cd directly prop to V

Higher supersonic velcoity > 1,4 m

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