Turbulent Boundary Layer Thickness Calculator
Here’s a comprehensive table summarizing key information about turbulent boundary layer thickness:
| Aspect | Description |
|---|---|
| Definition | The distance from the wall to the point where the flow velocity reaches 99% of the free stream velocity12 |
| Formula | δ(x) ≈ 0.37x / (Re_x)^(1/5), where x is distance from leading edge and Re_x is Reynolds number1 |
| Reynolds Number | Re_x = u_0 * x / ν, where u_0 is free stream velocity and ν is kinematic viscosity1 |
| Assumptions | 1. Flow is turbulent from the start of the boundary layer 2. Boundary layer behaves in a geometrically similar manner1 |
| Comparison to Laminar | Turbulent boundary layers are thicker and have fuller velocity profiles than laminar ones4 |
| Velocity Profile | Characterized by steep gradient near the wall and more uniform flow away from the wall4 |
| Factors Affecting Thickness | Increases with: – Decreasing fluid particle velocity – Increasing surface roughness – Increasing fluid viscosity3 |
| Transition | Occurs at Re_x ≈ 500,000 for flat plates2 |
| Wall Shear Stress | Higher in turbulent boundary layers due to steeper velocity gradient at the wall4 |
| Mixing | Significant macroscopic mixing across layers, unlike in laminar flow4 |
| Empirical Relationships | Log law, Spalding’s law of the wall, and one-seventh-power law are commonly used to describe velocity profiles5 |
| Roughness Effects | Increased roughness leads to higher skin friction coefficient and thicker boundary layer5 |
This table provides a concise overview of the key aspects of turbulent boundary layer thickness, including its definition, calculation, characteristics, and factors that influence it.