Find the $($i$)$ displacement thickness and the $($ii$)$ momentum thickness for the velocity distribution in the boundary layer given by

$\frac{u}{U}=2(\frac{y}{})-(\frac{y}{}{)}^2$

In the above, $U$ is the free stream velocity and $$ is the boundary layer thickness. $(2+3=5$ marks$)$

$4.$ For the velocity profile for the laminar boundary layer flow

$\frac{u}{U}=sin(\frac{}{2}\frac{y}{})$

Obtain an expression for $($i$)$ boundary layer thickness, $($ii$)$ shear stress, $($iii$)$ drag force on one side of the plate, and $($iv$)$ the coefficient of drag in terms of the Reynolds number. The symbols have their usual meanings solve question no $3$ and $4$ both