Flow Through Elliptical Duct — Lesson 3

This lesson covers the concept of Poiseuille flow inside an elliptical duct with a uniform cross-section. It delves into the process of finding the velocity profile for this flow, considering an infinitely long elliptical duct with a constant pressure gradient and negligible gravitational acceleration. The lesson also explains the governing equation and how to derive the velocity profile that satisfies the no-slip condition at the wall. It further discusses the calculation of the volumetric flow rate and average velocity. The lesson concludes with special cases of circular duct and flow between two infinite parallel plates.

Video Highlights

00:30 - Introduction to the lecture topic: Velocity profile for Poiseuille flow inside elliptical duct with uniform cross section.
03:14 - Assumption of the velocity profile inside the duct.
04:10 - Explanation of how the assumed velocity profile satisfies the no-slip condition at the tube walls.
08:58 - Calculation of the maximum velocity at the centerline of the duct.
10:15 - Calculation of the volumetric flow rate inside the elliptical duct.
28:01 - Special case considerations: Circular duct (Hagen-Poiseuille flow) and Flow between two infinite parallel plates (Plane Poiseuille flow).

Key Takeaways

- The velocity profile for Poiseuille flow inside an elliptical duct is derived considering an infinitely long duct with a constant pressure gradient.
- The governing equation plays a crucial role in deriving the velocity profile.
- The velocity profile is assumed in a way that it satisfies the no-slip condition at the wall.
- The volumetric flow rate and average velocity are calculated using the derived velocity profile.
- Special cases include the circular duct and flow between two infinite parallel plates, which follow the same principles but with different parameters.