Question

Consider the flow of water over a smooth curved wall surface. It is given that the flow separates at some location R on the surface, known as the separation point.

Pick the CORRECT option(s).

• A. At R, the wall shear stress is zero.
• B. At R, \(\dfrac{\partial u}{\partial y} = 0\), where \(y\) is normal to the surface and \(u\) is the velocity of the flow tangential to the surface.
• C. At R, viscosity of the fluid becomes zero.
• D. Immediately downstream of R, the direction of flow is reversed locally.

Hint:

Think about what happens to the velocity gradient at the wall right at the point where the boundary layer lifts off.

Answer 1

The Correct Option is A, B, D

Flow separation happens when the fluid near a wall loses momentum against an adverse pressure gradient and the boundary layer lifts off the surface. The separation point R is defined by the state of the velocity gradient at the wall, not by any change in fluid property.

1. At R, the wall shear stress is zero: True. Wall shear stress is \(\tau_w = \mu \left(\dfrac{\partial u}{\partial y}\right)_{y=0}\), and at the separation point this stress vanishes because the flow direction right at the wall is about to reverse.
2. At R, \(\partial u/\partial y = 0\): True. This is just the mathematical form of the wall shear stress condition above, so it is another correct way to state the same separation criterion.
3. At R, viscosity of the fluid becomes zero: False. Viscosity is a fluid property that stays fixed for a given fluid and temperature. Separation is a flow event, not a change in the fluid itself.
4. Immediately downstream of R, the flow direction reverses locally: True. Past the separation point the adverse pressure gradient pushes fluid back near the wall, creating a local reverse flow and the recirculating wake region.

So the correct options are A, B and D.