Problem $1$: The following figure shows a stream$-$tube$/$actuator disc model of a wind turbine. Assume that the actuator disc has a radius of $3$ m $,$ and a freestream wind speed of $\backslash ($ V$\_\{\backslash$infty$\}=7\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash ).$

$-$ Estimate the maximum power that can be extracted by the idealized wind turbine.

$-$ Determine the velocity at the actuator disc and in the wake.

$-$ Determine the areas, $\backslash ($ A$\_\{\backslash$infty$\}\backslash )$ and $\backslash ($ A$\_\{$w$\}\backslash ).$