Question $\backslash (3[20\backslash )$ marks$]$

As shown in Figure Q$3,$ a thin sharp$-$edged flat rectangular plate is $\backslash (0\mathrm{.}5\backslash$mathrm$\{$~m$\}\backslash$times $0\mathrm{.}5\backslash$mathrm$\{$~m$\}\backslash )$ in size. There is air flow past the plate at $1$ atm and $\backslash (20^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ The free$-$stream velocity of air is $\backslash (10\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash ).$ Assume the transition Reynolds number of the external flow problem is $\backslash (5\mathrm{.}0\backslash$times $10^\{5\}\backslash ).$

If the direction of air flow is parallel to the surface of the plate and parallel to one side of the plate as well as shown in Figure Q$3,$

$($a$)$ Calculate the percentage of the area of the plate that is covered by the laminar boundary layer of air.

$($b$)$ Calculate the drag coefficient of the plate.

$($c$)$ Calculate the drag force exerted by flowing air at one surface of the plate.

$($d$)$ If the length of the side of the plate that parallel to the direction of air flow becomes $1\mathrm{.}0$ m long, calculate the drag coefficient of the plate.

If the direction of air flow is normal to the surface of the plate, and the plate size remains $\backslash (0\mathrm{.}5\backslash$mathrm$\{$~m$\}\backslash$times $0\mathrm{.}5\backslash$mathrm$\{$~m$\}\backslash ),$

$($e$)$ Calculate the drag force that air exerts on the plate.

Direction of the free stream of flowing air corresponding to Question $3($a$,$ b$,$ c$,$ d$)$