Show me the steps to solve Problem $3(3$ marks$)$

If the resultant force on an airfoil, $R,$ can be expressed as

$R=f({}_{},V_{},c,{}_{},a_{}),inML{T}^{-2}$

where $c$ is the chord length in units of $[L],V_{}$ is the free stream velocity in units of $L{T}^{-1},{}_{}$ is the free stream air density in units of $[M{L}^{-3}],{}_{}$ is the free stream viscosity in units of $M{L}^{-1}{T}^{-1},$ and $a_{}$ is the speed of sound of the free stream in units of $L{T}^{-1}.$

Use the Buckingham$-$Pi theorem to determine a suitable set of dimensionless parameters.

Hence show that

$C_R=g(Re,M_{})$

where $C_R$ is a resultant force coefficient, $Re$ is the Reynolds number, and $M_{}$ is the Mach number of the free stream air.