What Is the Falkner-Skan Wedge Flow Boundary Layer Calculator?
The Falkner-Skan solution describes laminar boundary layers in flows where the external velocity varies as U(x) = C·x^m.
The Hartree parameter β = 2m / (m + 1) directly quantifies the imposed pressure gradient.
How Does the Falkner-Skan Wedge Flow Boundary Layer Calculator Work?
Positive β corresponds to favorable pressure gradients (dp/dx < 0), thinning the boundary layer and stabilizing against separation.
Negative β corresponds to adverse pressure gradients; at β = -0.1988, the wall shear stress f"(0) vanishes, signifying separation onset.
Falkner-Skan Wedge Flow Boundary Layer Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
Relates wedge half-angle to external velocity exponent m = beta / (2 - beta) and evaluates boundary layer thickness parameters.
How to Use the Falkner-Skan Wedge Flow Boundary Layer Calculator
- Specify the Hartree pressure gradient parameter β.
- Input the edge freestream velocity, kinematic viscosity, and streamwise station x.
- Inspect displacement thickness, momentum thickness, and skin friction coefficient.
Step-by-Step Example Calculation
Zero-Gradient Flat Plate Airflow (Blasius)
Input Values:
Understanding Your Result
Displacement thickness δ* measures mass flow deflection away from the surface.
The shape factor H = δ*/θ indicates transition susceptibility and proximity to separation.
Factors That Affect the Result
- Accelerating flows (β > 0) reduce boundary layer thickness and increase skin friction.
- Decelerating flows (β < 0) thicken the boundary layer and drive wall shear toward zero.
When Should You Use This Calculator?
- Aerodynamic wing leading-edge wedge design and turbine airfoil boundary layer analysis.
- Estimating separation margins on diffusing aerodynamic surfaces.
Assumptions & Limitations
- Valid for 2D, laminar, incompressible boundary layer flow under similarity conditions.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Semi-analytical approximation matching Runge-Kutta numerical integration within 1%.