Turbulent Boundary Layer Flows — Lesson 1

This lesson covers the integral solution for turbulent boundary layer flows using the momentum integral equation. It explains how the exact solution for turbulent boundary layer flow is not possible, but the momentum integral method can be used to solve these flows by assuming the velocity profile and the wall shear stress from existing correlations based on experimental values. The lesson also discusses the Prandtl von Karman model, which was the first to solve this solution. The model uses the momentum integral equation derived for laminar boundary layer flows. The lesson further explains how to approximate the velocity profile for turbulent flows and how to calculate the shear stress in the momentum integral equation.

Video Highlights

01:15 - Introduction to the Prandtl von Karman model.
04:18 - Explanation of the shear stress for a pipe flow and the velocity profile in the pipe.
09:48 - Explanation of the momentum integral equation and the shear stress expression.
18:38 - Explanation of the limitation of the Prandtl von Karmann solution.
21:59 - Explanation of the boundary layer thickness and the skin friction coefficient.

Key Takeaways

- The momentum integral equation can be used to solve turbulent boundary layer flows.
- The Prandtl von Karman model was the first to solve this solution.
- The velocity profile for turbulent flows can be approximated using the Prandtl and Vankarmann model.
- The shear stress in the momentum integral equation is calculated based on the wall shear stress of the pipe flow.
- The boundary layer thickness and the wall shear stress can be calculated using the one seventh law of velocity profile and the Blasius correlation for the pipe flow.