$6.$ The combined velocity potential function for a flow over an airfoil is expressed as $\backslash (\backslash$phi $\backslash ).$ At an arbitrary point A on the surface of an airfoil, normal and tangential to the surface unit vector is denoted as $\backslash (\backslash$overrightarrow$\{\backslash$mathrm$\{$n$\}\}\backslash )$ and $\backslash (\backslash$vec$\{$s$\}\backslash )$

$($a$)$ Write down the mathematical equation for the boundary condition that the velocity velocity potential function $\backslash (\backslash$phi $\backslash )$ should satisfy on the airfoil surface. $(\backslash (10\backslash \%\backslash ))$

$($b$)$ Express mathematical equation for the pressure coefficient $(\backslash ($ C p $\backslash ))$ on the airfoil surface in terms of velocity potential function $\backslash (\backslash$phi $\backslash ).(\backslash (10\backslash \%\backslash ))$