Railways Technical Ability Fluid Mechanics and Machinery Question Bank Fluid Mechanics

  • 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) \[\delta /6\]

    Correct Answer: D

    Solution :

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

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