A cylinder of diameter and span stands in an air stream of speed ( , )

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Viscous flow and dynamical similarity · Viscous flow and dynamical similarity

Fluid Dynamics, Ch Separation, wakes, jets and free shear flows

Problem

A cylinder of diameter d=0.10 md = 0.10\,\mathrm{m} and span 1.0 m1.0\,\mathrm{m} stands in an air stream of speed U=20 m s−1U = 20\,\mathrm{m\,s^{-1}} (ρ=1.20 kg m−3\rho = 1.20\,\mathrm{kg\,m^{-3}}, ν=1.51×10−5 m2 s−1\nu = 1.51\times10^{-5}\,\mathrm{m^2\,s^{-1}}). Someone argues: "Treat each half of the cylinder's surface as a flat plate of length equal to half the circumference, L=πd/2=0.157 mL = \pi d/2 = 0.157\,\mathrm{m}. The Reynolds number based on this length is ReL=UL/ν=20×0.157/1.51×10−5≈2.08×105Re_L = UL/\nu = 20\times0.157/1.51\times10^{-5} \approx 2.08\times10^5, so the Blasius drag coefficient is CD=1.328/ReL≈2.91×10−3C_D = 1.328/\sqrt{Re_L} \approx 2.91\times10^{-3}. The drag per unit span on both surfaces is D′/span=CD (12ρU2) (2L)≈0.00291×240×0.314≈0.22 N m−1D'/\mathrm{span} = C_D\,(\tfrac12\rho U^2)\,(2L) \approx 0.00291\times240\times0.314 \approx 0.22\,\mathrm{N\,m^{-1}}. So the total drag on the whole cylinder is about 0.22 N0.22\,\mathrm{N}." ((a)) Find the error in this reasoning. ((b)) Give a corrected estimate of the drag per unit span, using a measured drag coefficient appropriate to this Reynolds number, and compare the two numbers.

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