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What Using the laminar boundary layer velocity distribution $\frac{u}{U}=2(\frac{Y}{\delta})-(\frac{Y}{\delta})^2$

i. Check if boundary layer separation occurs.

ii. Determine boundary layer thickness (in terms of Re)

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Consider the Laminar boundary layer velocity distribution,

$\frac{u}{U} =2(\frac{Y}{δ})-(\frac{Y}{δ})^2$

Now, it can be seen from the figure that the flow can be identified as,

enter image description here

Which is positive, hence the boundary layer does not separate.

For the Boundary layer thickness, we know the Von Karman’s Momentum Integral equation,

$\frac{\tau_0}{ρU^2}= \frac{∂θ}{∂x}$

where, …

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