• # question_answer The velocity distributions in laminar boundary layer is given by the relation $u/{{u}_{\infty }}=\,y/\delta .$ what is the momentum thickness for the boundary layer? A) $\delta /2$                    B) $\delta /3$C) $\delta /4$                                D) $\delta /6$

$\frac{U}{{{U}_{\infty }}}=\frac{y}{\delta }$  Momentum thickness, $\theta =\int\limits_{0}^{\delta }{\frac{u}{{{U}_{\infty }}}}\,\left( 1-\frac{u}{{{U}_{\infty }}} \right)\,dy=\int\limits_{0}^{\delta }{\frac{y}{\delta }}\,\left( 1-\frac{y}{\delta } \right)\,dy$ $=\left| \frac{{{y}^{2}}}{2\delta }-\frac{{{y}^{3}}}{3{{\delta }^{2}}} \right|_{0}^{\delta }=\frac{\delta }{2}-\frac{\delta }{3}=\frac{\delta }{6}$