Hagen - Poiseuille Flow — Lesson 1

This lesson covers the exploration of Navier-Stokes equations in cylindrical coordinate, focusing on finding exact solutions in pipe flow. Two different problems are solved: Hagen Poiseuille flow (fully developed pipe flow) and flow through an annulus. The lesson explains the continuity equation, momentum equation, and components of viscous stress tensor for incompressible Newton fluid. It also discusses the concept of axisymmetric flow and how to apply it to the Z component of the momentum equation. The lesson concludes with the integration of the ordinary differential equation with proper boundary conditions to find the velocity distribution inside a fully developed pipe flow.

Video Highlights

01:37 - Introduction to Hagen Poiseuille flow and its assumptions.
09:34 - Discussion on the radius and volume flow rate inside the pipe.
15:04 - Explanation of the velocity distribution and shear stress distribution across the pipe.
25:08 - Discussion on fully developed flow in an annulus.
33:38 - Discussion on the radius and volume flow rate for a fully developed flow in an annulus.

Key Takeaways

- Navier-Stokes equations in cylindrical coordinate can be used to find exact solutions in pipe flow.
- Hagen Poiseuille flow and flow through an annulus are two examples of problems that can be solved using these equations.
- The continuity equation, momentum equation, and components of viscous stress tensor are crucial in these calculations.
- Axisymmetric flow is a key concept in these problems, affecting the Z component of the momentum equation.
- The ordinary differential equation can be integrated with proper boundary conditions to find the velocity distribution inside a fully developed pipe flow.