Q$1$: The mixed boundary layer over a flat plate may be approximated by the velocity

profiles $(\frac{u}{U_{}}=A(\frac{y}{})-B(\frac{y}{}{)}^3)$ for the laminar boundary layer and $(\frac{u}{U_{}}=(\frac{y}{}{)}^{\frac{1}{7}})$

for the turbulent boundary layer respectively. Find the following :$-$

$1-$ The boundary conditions at the wall surface and at the outer edge of the laminar

boundary layer.

$2-$The magnitude of constants $(A)$ and $($B$)$ for the laminar boundary layer.

$3-$ The equivalent length of the turbulent layer at the transition region, if the transition

occurs at a distance $(AB)$ from the leading edge of the plate.

$4-$ The drag coefficient for the mixed boundary layer in terms of the transition distance

$(AB).$