Falkner-Skan Equation: Boundary Layer Flow over a Wedge — Lesson 4

This lesson covers the concept of boundary layer flow over a wedge, where the free stream velocity outside the boundary layer is not constant but a function of the axial direction. The lesson explains the derivation of the Blasius equation, the assumptions considered for boundary layer flow over a wedge, and the concept of wedge parameters. It also discusses the special cases of flow over a flat plate and flow over a vertical flat plate. The lesson further delves into the similarity transformation, the von Mises transformation, and the Faulkner-Skan equation. It concludes with a discussion on displacement thickness and moment of thickness in the context of boundary layer flow.

Video Highlights

01:04 - Explanation of boundary layer flow over a wedge, where velocity U Infinity is a function of the axial direction outside the boundary layer.
03:37 - Discussion on two special cases: when the wedge angle is 0 (flat plate) and when the wedge angle is 1 (vertical flat plate).
06:17 - Derivation of the ordinary differential equation from the boundary layer equations for flow over a wedge using the similarity transformation.
14:10 - Explanation of the boundary layer equation with the pressure gradient term and its transformation into the Faulkner scan equation.
26:24 - Discussion on the boundary conditions for the Faulkner scan equation.
31:30 - Explanation of the concept of displacement thickness and its calculation.

Key Takeaways

- The Blasius equation is derived considering flow over a flat plate where the velocity outside the boundary layer is constant.
- In the case of boundary layer flow over a wedge, the free stream velocity outside the boundary layer is not constant but a function of the axial direction.
- The wedge parameter 'M' is introduced, which is a function of the wedge angle 'beta'.
- The von Mises transformation is used to find the derivative of the stream function.
- The Faulkner-Skan equation, a third-order non-linear ordinary differential equation, is derived using similarity transformation.
- The concept of displacement thickness is introduced, which is the distance by which the external potential flow is displaced as a consequence of the decrease in velocity in the boundary layer.