The velocity profile for laminar flow in the boundary layer of a flat plate is given by
$\frac{u}{U}=sin\left ( \frac{\pi }{2} \frac{y}{\delta }\right )$
where u is the velocity of fluid in the boundary layer at a vertical distance y from tile plate surface and U is the free stream velocity. Prove that the boundary layer thickness may be given by the expression
$\delta =\frac{4.795x}{\left ( Re_{x} \right )^{\frac{1}{2}}}$
where Rex is the Reynolds number of the fluid at a distance x from the leading edge of the plate.