Problem $1(20$ Points$)$

A one$-$twelfth$-$scale model of a large commercial aircraft is tested in a wind tunnel at $20$ C and $1$ atm $.$ The model chord length is $27$ cm $,$ and its total wing area is $\backslash (0\mathrm{.}63\backslash$mathrm$\{$~m$\}^\{2\}\backslash ).$ The test results for the drag of the model area as follows:

Use the following for the properties of air for the model and the prototype:

Use the drag coefficient, $\backslash ($ C$\_\{$D$\}\backslash ),$ and Reynolds number, $\backslash ($ R e $\backslash ),$ to estimate the drag of the full$-$scale aircraft when flying at $\backslash (550\backslash$mathrm$\{$mi$\}/\backslash$mathrm$\{$h$\}\backslash )(=246$ m$/$s$),$ for the same angle of attack, at $32,800$ ft standard altitude. Neglect Mach number differences between the model and prototype. $($Hint: Plot $\backslash (\backslash$log $(\backslash$mathrm$\{$Cd$\})\backslash )$ vs $\backslash (\backslash$log $(\backslash$mathrm$\{$Re$\})\backslash ).$