• 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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