Chapter 6, Problem 6.26P

Experiments have shown that the transition from laminar to turbulent conditions for flow normal to the axis of a long cylinder occurs at a critical Reynolds number of ${\mathrm{Re}}_{D,c}\approx 2\times {10}^5,$ where D is the cylinder diameter. Moreover, the transition from incompressible to compressible flow occurs at a critical Mach number of $M{a}_c\approx \mathrm{0.3.}$ For air at a pressure of $p=1$ atm and temperature $T=27°\text{C,}$ determine the critical cylinder diameter $D_c$ below which, if the flow is turbulent, compressibility effects are likely to be important.