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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

  1. $\dfrac{2}{\Pi } \\$
  2. $1-\dfrac{2}{\Pi } \\$
  3. $1+\dfrac{2}{\Pi } \\$
  4. $0$
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