Evaluate the displacement thickness ( delta ) and the momentum thickness ( theta ) for a velocity profile given by ( frac u U sin left( frac pi y 2 delta ight) ) Plot the nondimensional velocity profile and show the thicknesses ( frac delta y ) and ( frac theta y ) on the plot Does this expression ...

The Answer is in the image, click to view ...

Evaluate the displacement thickness (delta^{*}) and the momentum thickness (theta) for a velocity profile given by (frac{u}{U}=sin

Question:

Evaluate the displacement thickness $\delta^{*}$ and the momentum thickness $\theta$ for a velocity profile given by $\frac{u}{U}=\sin \left(\frac{\pi y}{2 \delta}\right)$. Plot the nondimensional velocity profile and show the thicknesses $\frac{\delta^{*}}{y}$ and $\frac{\theta}{y}$ on the plot. Does this expression satisfy the boundary conditions applicable to a laminar boundary layer?