Correct Answer - Option 4 : u = 0, v = 0
Concept:
The point of separation may be defined as the limit between forward and reverse flow in the layers very close to the wall i.e. at the point at separation
\({\left( {\frac{{\partial u}}{{\partial y}}} \right)_{y = 0}} = 0\)
At boundary conditions and the equation ( simplifies since ∂u/∂t = 0.) Assuming Steady-state condition.
- At the plate surface, there is no flow across it, which implies that v = 0 at y = 0.
- Due to the viscosity, we have the no-slip condition at the plate. In other words, u = 0 at y = 0.
- At infinity (outside the boundary layer), away from the plate, we have that u → U as y → infinity
For a given velocity profile, it can be determined whether the boundary has separated, or on the verge of separation, or will not separate from the following condition:
i) \({\left( {\frac{{\partial u}}{{\partial y}}} \right)_{y = 0}} < 0\) the flow has separated
ii) \({\left( {\frac{{\partial u}}{{\partial y}}} \right)_{y = 0}} = 0\) the flow is on the verge of separation.
ii) \({\left( {\frac{{\partial u}}{{\partial y}}} \right)_{y = 0}} > 0\) the flow will not separate or flow will remain attached with the surface.
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