Question $2$: Similitude of a model plane

A full$-$size airplane will fly in air at $15$ degrees Celsius at a speed of $\backslash (50\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash ).$ Its Reynolds number is calculated using a representative length scale of $2\mathrm{.}3$ m $.$ A model of an airplane will be tested in water at $20$ degrees Celsius flowing at $10\backslash (\backslash$mathrm$\{$m$\}/\backslash$mathrm$\{$s$\}\backslash ).$ Calculate the representative length scale $\backslash ($ L$\_\{$m$\}\backslash )$ with which the model should be built in order to achieve similitude $($i$.$e$.$ the same Reynolds number for both model and prototype$).$

$\backslash ($ L$\_\{$m$\}=\backslash )$

$0\mathrm{.}6375$

m