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For the following velocity profiles, determine whether the flow has separated or on the verge of separation or will be attached with the surface.

For the following velocity profiles, determine whether the flow has separated or on the verge of separation or will be attached with the surface.

  1. uU=32(yδ)12(yδ)2

  2. uU=2(yδ)2(yδ)3

  3. uU=2(yδ)+(yδ)2

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Solution :

Given :

1st Velocity Profile

uU=32(yδ)12(yδ)3u=3U2(yδ)U2(yδ)3

Differentiating w.r.t. y, uy=3U2×1δU2×3(yδ)2×1δ

At y=0,

$$\begin{aligned}\left(\frac{\partial u}{\partial y}\right)_{y=0} &=\frac{3 U}{2\delta }-\frac{3 U}{2}\left(\frac{0}{\delta }\right)^{2} \times \frac{1}{\delta }\\ &=\frac{3 U}{2\delta …

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