Question

What parameter in boundary layer theory represents the thickness of the layer in which the velocity increases from zero at the surface to 99\% of the free stream velocity?.

• A. Displacement thickness
• B. Momentum thickness
• C. Energy thickness
• D. Boundary layer thickness

Hint:

Boundary Layer Thickness Definitions. Boundary Layer Thickness (\(\delta\)): Distance where \(u \approx 0.99 U_\infty\). Displacement Thickness (\(\delta^*\)): Measure of streamline displacement due to mass flow deficit. Momentum Thickness (\(\theta\)): Measure of momentum flux deficit.

Answer 1

The Correct Option is D

In fluid flow over a surface, the boundary layer is the region near the surface where viscous effects are significant and the fluid velocity changes from zero at the surface (due to the no-slip condition) to the free stream velocity (\(U_\infty\)) further away.
There are several ways to define the "thickness" of this layer: - Boundary Layer Thickness (\(\delta\)): Commonly defined as the distance from the surface where the fluid velocity \(u\) reaches a certain percentage (often 99%) of the free stream velocity \(U_\infty\).
This definition directly matches the description in the question.
- Displacement Thickness (\(\delta^*\)): Represents the distance by which the external streamlines are displaced outward due to the velocity deficit within the boundary layer.
- Momentum Thickness (\(\theta\)): Represents the loss of momentum flux within the boundary layer compared to potential flow.
- Energy Thickness (\(\delta_E\)): Represents the loss of kinetic energy flux within the boundary layer.
Therefore, the parameter representing the thickness where velocity reaches 99% of the free stream value is the boundary layer thickness (\(\delta\)).