EXAMPLE $5\mathrm{.}9$

A prototype airplane, with a chord length of $1\mathrm{.}6$ m $,$ is to fly at $\backslash (\backslash$mathrm$\{$Ma$\}=2\backslash )$ at $10$ km standard altitude. A one$-$eighth scale model is to be tested in a helium wind tunnel at $\backslash (100^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and $1$ atm $.$ Find the helium test section velocity that will match $($a$)$ the Mach number or $($b$)$ the Reynolds number of the prototype. In each case criticize the lack of dynamic similarity. $($c$)$ What high pressure in the helium tunnel will match both the Mach and Reynolds numbers? $($d$)$ Why does part $($c$)$ still not achieve dynamic similarity?