Railways Technical Ability Fluid Mechanics and Machinery Question Bank Fluid Mechanics

  • question_answer If the velocity distribution in a turbulent boundary layer is given by \[\frac{u}{{{u}_{\infty }}}={{\left( \frac{y}{\delta } \right)}^{1/9}}\] then the ratio of displacement thickness to nominal boundary layer thickness will be:

    A) 1.0                               

    B) 0.6

    C) 0.3                               

    D) 0.1

    Correct Answer: D

    Solution :

    Displacement thickness, \[\delta '=\int\limits_{0}^{\delta }{\left( 1-\frac{u}{{{U}_{x}}} \right)}\,\,dy\] \[=\int\limits_{0}^{\delta }{\left[ 1-{{\left( \frac{y}{\delta } \right)}^{1/9}} \right]}\,\,dy\] \[=\left| y-\frac{1}{{{\delta }^{1/9}}}.{{y}^{10/9}}\times \frac{9}{10} \right|_{0}^{\delta }=\delta =\frac{9}{10}\,\delta =\frac{\delta }{10}\] \[\frac{\delta '}{\delta }=\frac{1}{10}=0.1\]


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