Discussion
The dimensionless velocity profile is
Answer: A
The profile is \(u/U = 2(y/\delta) - (y/\delta)^{2}\).
Apply the three boundary conditions: no slip at the wall, free-stream velocity at the edge, and a smooth join with the free stream (zero slope) at the edge.
\[ \begin{aligned} u(0) = 0 &\Rightarrow a = 0 \\ \left.\tfrac{du}{dy}\right|_{\delta} = 0 &\Rightarrow b + 2c\delta = 0 \\ u(\delta) = U &\Rightarrow b\delta + c\delta^{2} = U \end{aligned} \]
These give \(b = 2U/\delta\) and \(c = -U/\delta^{2}\). The '+' option gives u = 3U at the edge. The 1.5 and 0.5 coefficients belong to a cubic profile and do not satisfy the zero-slope condition for a quadratic.
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