Question

In laminar boundary layer flow over a flat plate, wall shear stress:

• A. Constant
• B. Decreases with distance
• C. Increases with distance
• D. Zero

Hint:

In laminar boundary layers, the shear stress decreases as the distance from the wall increases because the velocity gradient decreases. This is a characteristic feature of the flow in the boundary layer.

Answer 1

The Correct Option is B

In a laminar boundary layer flow, the fluid near the surface (boundary) moves slower than the fluid further away from the surface due to viscous forces. The wall shear stress is the frictional force per unit area exerted by the fluid on the surface. In a laminar boundary layer, the shear stress is highest at the wall and decreases as we move away from the surface into the boundary layer.
This decrease in shear stress occurs because the velocity profile in the boundary layer gradually becomes less steep as the flow develops. The fluid near the wall has a zero velocity (no-slip condition), and the velocity increases with distance from the wall. The shear stress is directly related to the velocity gradient at the wall, and as the distance from the wall increases, the velocity gradient decreases, leading to a reduction in shear stress.
Thus, in laminar boundary layer flow over a flat plate, the wall shear stress decreases with distance.
- Constant shear stress would imply no change in the velocity gradient, which is not the case in a developing boundary layer.
- Increases with distance would suggest that the shear stress grows as we move further from the wall, which is not true for laminar flow.
- Zero shear stress is incorrect because there is always some shear stress at the wall, even in laminar flow.
Therefore, the correct answer is that the wall shear stress decreases with distance.