Q$(5)$ A smooth flat plate $1\mathrm{.}5$ m wide and $4$ m long is subjected to flow of water along its length with a velocity of $\backslash (2\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash ).$ The flow in the boundary layer is laminar at the leading edge of the plate. The laminar boundary layer undergoes a transition $\backslash (\backslash$left$($R e$\_\{$c r$\}=5\backslash$times $10^\{5\}\backslash$right$)\backslash )$ to turbulent boundary layer as the flow proceeds in the downstream. It is observed that a cubic laminar profile is finally changed into a $\backslash (1/7\backslash )$ th power law velocity profile in the turbulent regime. Answer the following questions:

$($a$)$ The distance from the leading edge where the boundary layer flow changes from laminar to turbulent flow.

$($b$)$ The thickness of the boundary layer at the edge of the laminar boundary layer and at the trailing edge.

$($c$)$ The shear stress at the trailing edge.

$($d$)$ The portion of frictional drag due to turbulent boundary layer.

$($e$)$ The ratio of drag forces created due to turbulent boundary layer flow to laminar boundary layer flow i$.$e$.\backslash ($ F$\_\{\backslash$text $\{$turb $\}\}/$ F$\_\{\backslash$text $\{$lam $\}\}\backslash )$