# GATE2017 ME-1: 30

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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