Q$3$:

$($a$)$ For the velocity profile given below $(=$ boundary layer thickness, $U_{}=$ free$-$stream velocity$),$ state whether the boundary layer has separated or on the verge of separation or will remain attached with the surface:

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

$($ii$)\frac{u}{U_{}}=-2(\frac{y}{})+\frac{1}{2}(\frac{y}{}{)}^3$

$($iii$)\frac{u}{U_x}=\frac{3}{2}(\frac{y}{}{)}^2+\frac{1}{2}(\frac{y}{}{)}^3$