Find the y-location where u = 0.5U∞ for the boundary layer of Problem 8.132.What is the value of v at that y-location? What is the shear stress there?

Question

Find the y-location where [latex]u=0.5 U_{\infty}[/latex] for the boundary layer of Problem 8.132.What is the value of v at that y-location? What is the shear stress there?

Accepted Answer

From Table 8.5 we interpolate for F'= 0.5 to be

[latex]\eta=\frac{0.5-0.3298}{0.6298-0.3298}(2-1)+1=1.57[/latex]

[latex]1.57=\sqrt{\frac{U_{\infty}}{v x}}=y \sqrt{\frac{5}{1.5 imes 10^{-5} imes 2}} . \quad herefore y=0.00385 m ext { or } \underline{3.85 mm }[/latex]

[latex]v=\sqrt{\frac{v U_{\infty}}{x}}\left(\frac{1}{2} ight)\left(\eta F^{\prime}-F ight)=\sqrt{\frac{1.5 imes 10^{-5} imes 5}{2}}(0.207)=\underline{0.00127 m / s }[/latex]

[latex] au=\mu\left(\frac{\partial u}{\partial y}+\frac{\partial v}{\partial x}^{ earrow0} ight)=F^{\prime \prime} ho U_{\infty}^{2} \sqrt{\frac{v}{x U_{\infty}}}=0.291(1.2) 5^{2} \sqrt{\frac{1.5 imes 10^{-5}}{2 imes 5}}=\underline{0.011 Pa }[/latex]

Question 8.136: Find the y-location where u = 0.5U∞ for the boundary layer o...

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