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

Step 1: Recall what defines a separation point.
In boundary layer flow over a curved wall, the fluid near the surface loses kinetic energy to friction and to the adverse pressure gradient once the wall curves away from the flow.
Separation is the point R where the velocity profile close to the wall stops moving forward.

Step 2: Write the wall condition in math form.
The tangential velocity is $u$ and $y$ is measured normal to the wall, so the wall shear stress is $\tau_w = \mu \left(\dfrac{\partial u}{\partial y}\right)_{y=0}$.
At R the fluid right at the wall is on the verge of reversing, so $\partial u/\partial y = 0$ there, and since $\mu$ is not zero, $\tau_w = 0$ too. This makes both A and B correct restatements of the same fact.

Step 3: Check the remaining options.
Viscosity $\mu$ is a property of the fluid and does not drop to zero at separation, so option C is wrong.
Just past R, the adverse pressure gradient overpowers the forward momentum near the wall, so the flow there turns backward, giving a local reverse flow and confirming option D.

Final Answer:
Options A, B and D describe the separation point correctly.
\[ \boxed{\text{A, B, D}} \]