Railways Technical Ability Fluid Mechanics and Machinery Question Bank Fluid Mechanics

  • question_answer In a laminar boundary layer over a flat plate, what would be the ratio of wall shear stresses \[{{\tau }_{1}}\] and \[{{\tau }_{2}}\] at the two sections which lie at distances \[{{x}_{1}}=30\,\,cm\] and \[{{x}_{2}}=90\,\,cm\] from the leading edge of the plate?

    A) \[\frac{{{\tau }_{1}}}{{{\tau }_{2}}}=3.0\]                  

    B) \[\frac{{{\tau }_{1}}}{{{\tau }_{2}}}=\frac{1}{3}\]

    C) \[\frac{{{\tau }_{1}}}{{{\tau }_{2}}}=\,\,{{\left( 3.0 \right)}^{1/2}}\]               

    D) \[\frac{{{\tau }_{1}}}{{{\tau }_{2}}}=\,\,\left( 3.0 \right)\]

    Correct Answer: C

    Solution :

    Boundary shear stress \[\propto \frac{1}{\sqrt{{{\operatorname{Re}}_{x}}}}\propto \frac{1}{\sqrt{x}}\] \[\frac{{{\tau }_{1}}}{{{\tau }_{2}}}=\sqrt{\frac{{{x}_{2}}}{{{x}_{1}}}}=\sqrt{\frac{90}{30}}=\sqrt{3}\]

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