The velocity profile inside the boundary layer for flow over a flat plate is given as $\dfrac{u}{U_{\infty }}= \sin \left ( \dfrac{\Pi }{2}\dfrac{y}{\delta } \right )$, where $U_{\infty}$ is the free stream velocity and $\delta$ is the local boundary layer thickness. If $\delta^{*}$ is the local displacement thickness, the value of $\dfrac{\delta ^{*}}{\delta }$ is
- $\dfrac{2}{\Pi } \\$
- $1-\dfrac{2}{\Pi } \\$
- $1+\dfrac{2}{\Pi } \\$
- $0$