Laminar Boundary Layer Thickness Calculator
Here’s a comprehensive table summarizing all you need to know about laminar boundary layer thickness:
| Aspect | Details |
|---|---|
| Definition | The distance from the wall to the point where the velocity is 99% of the free-stream velocity12 |
| Symbol | δ (delta) |
| Blasius Solution | δ ≈ 5.0√(νx/u₀) = 5.0x/√Re_x1 |
| Formula for Flat Plate | δ = 5x/√Re_x, where Re_x is the local Reynolds number based on distance from leading edge |
| Proportionality | δ ∝ x^(1/2), thickness increases with the square root of distance along the plate3 |
| Factors Affecting Growth | Increases as: fluid particle velocity decreases, surface roughness increases, fluid viscosity increases5 |
| Flow Characteristics | Smooth and steady flow, characterized by layers sliding past each other |
| Reynolds Number Range | Laminar boundary layers are found only at small Reynolds numbers6 |
| Velocity Profile | Gradual increase in velocity from wall to free stream6 |
| Growth Rate | Smaller compared to turbulent boundary layers6 |
| Wall Shear Stress | Lower compared to turbulent boundary layers6 |
| Heat Transfer | Lower rates compared to turbulent boundary layers6 |
Key Points
- Calculation: The Blasius solution is commonly used for calculating laminar boundary layer thickness over a flat plate.
- Reynolds Number: The local Reynolds number (Re_x) is crucial in determining the boundary layer thickness.
- Growth: The thickness increases with distance from the leading edge, but at a decreasing rate (square root relationship).
- Transition: At higher Reynolds numbers, the laminar boundary layer may transition to turbulent, changing its characteristics significantly.
- Importance: Understanding laminar boundary layer thickness is crucial in fluid dynamics, affecting drag, heat transfer, and other flow properties in various engineering applications.
This table provides a concise overview of the key aspects of laminar boundary layer thickness, including its definition, calculation methods, influencing factors, and characteristics compared to turbulent boundary layers.