Karman Pohlhausen Method for Non-zero Pressure Gradient Flows — Lesson 1

This lesson covers the derivation of the momentum integral equation considering a general boundary layer momentum equation with a non-zero pressure gradient. It further explains the solution of this momentum integral equation using the Karmann Pohlhausen method for flows with non-zero pressure gradients. The lesson also discusses the continuity equation, the momentum equation, and the Bernoulli's equation. It provides a detailed explanation of the boundary layer equation, the momentum integral equation, and the pressure gradient term. The lesson also explains how to calculate the displacement thickness, the momentum thickness, and the wall shear stress using the Karmann Pohlhausen method. It concludes with a comparison of the results obtained from the Karmann Pohlhausen method with the Blasius solution.

Video Highlights

00:34 - Derivation of the momentum integral equation considering the general boundary layer momentum equation with non-zero pressure gradient.
07:36 - Explanation of the concept of displacement thickness and momentum thickness.
11:17 - Explanation of the Karmann Pohlhausen method to solve the momentum integral equation.
16:11 - Explanation of the concept of Pohlhausen parameter.
33:52 - Explanation of the concept of wall shear stress.

Key Takeaways

- The momentum integral equation is derived considering a general boundary layer momentum equation with a non-zero pressure gradient.
- The Karmann Pohlhausen method is used to solve the momentum integral equation for flows with non-zero pressure gradients.
- The continuity equation, the momentum equation, and the Bernoulli's equation are discussed in detail.
- The boundary layer equation, the momentum integral equation, and the pressure gradient term are explained thoroughly.
- The displacement thickness, the momentum thickness, and the wall shear stress are calculated using the Karmann Pohlhausen method.
- The results obtained from the Karmann Pohlhausen method are compared with the Blasius solution.