QUESTION $2$

Derive the equation for displacement thickness in a boundary layer. The velocity profle

for a fluid flow over a flat plate is given as $\frac{u}{U}=(4\frac{y}{7})$ where $u$ is velocity at a distance of

$"Y\text{'}$ from the plate and $u=U$ at $y=,$ where $$ is the boundary layer thickness. Determine

the displacement thickness and the momentum thickness for the above velocity profile:

$[12$ Marks$]$