Internal Turbulent Flows — Lesson 2

This lesson covers the concept of internal turbulent flows, focusing on the universal velocity profile and its application in turbulent flows. It discusses the mean velocity profile and the skin friction coefficient for pipe flow cases. The lesson also explains the calculation of hydraulic diameter and Reynolds number. It further delves into the governing equations for pipe flow, including the continuity equation and the momentum equation. The lesson concludes with a detailed explanation of the fully developed flow condition and how it simplifies the governing equations.

Video Highlights

00:59 - Explanation of the entry length for turbulent flows, hydraulic diameter and Reynolds number.
03:18 - Governing equations for pipe flow.
08:34 - Explanation of the two-layer model for pipe flow.
12:57 - Simplification of the governing equation for fully developed flow and apparent shear stress.
19:22 - Discussion on the friction factor for pipe flow and 1/7th power law velocity profile.
26:32 - Calculation of mean velocity based on the 1/7th power law.

Key Takeaways

- The universal velocity profile derived for external turbulent flow can be applied to internal turbulent flows.
- The hydraulic diameter is calculated as four times the flow area divided by the perimeter.
- The Reynolds number is defined based on mean velocity and diameter divided by the fluid viscosity.
- The continuity equation and the momentum equation are the governing equations for pipe flow.
- For fully developed flow, the radial component of the velocity and the axial velocity gradient with respect to the axial direction are zero.