Module 12:  Navier-Stokes Equation

In module 9, we covered the differential form of the conservation of momentum. In that module, we made an assumption that fluid is inviscid and ended up with the Euler's equations. In this module, we relax the inviscid restriction and obtain the Navier - Stokes equations, which are a very important equation for establishing the foundation for further studies in fluid dynamics.

Student Learning Outcomes: After completing this module, you should be able to:

* Apply the Navier - Stokes equations to determine viscous flow characteristics between parallel plates and circular pipes.

Lecture Videos:

Link to Module 12 Playlist   Link to Module 12 Lecture Notes

Links to Individual Module 12 Videos:

Lecture 1 - Derivation and Discussion of the Navier-Stokes Equations: In this segment, we derive and discuss the Navier Stokes equations, including its boundary conditions.

Lecture 2 - Poiseuille Flow: Pressure driven flow between fixed parallel plates: In this segment, we derive and discuss the Poiseuille flow, which is a pressure-driven, steady, laminar, and fully-developed flow between fixed parallel plates. We also derive the volumetric flow rate and mean and maximum velocity values for Poiseuille flow.

Lecture 3 - Couette Flow and Combined Couette-Poiseuille Flow: In this segment, we discuss the Couette Flow and Combined Couette-Poiseuille Flow. Both these flows are for parallel plates with a fixed bottom plate and moving top plate. Couette flow has no pressure gradient in the direction of the flow and Couette-Poiseuille Flow has both pressure gradient and top plate moving.

Lecture 4 - Gravity Driven Liquid Film on an Inclined Surface: In this segment, we apply the conservation of mass and Navier Stokes equations to obtain the velocity distribution in a liquid film sliding down an inclined surface.

Lecture 5 - Hagen - Poiseuille Flow, Viscous flow in Circular Pipes: In this video, we apply the Navier-Stokes equations in cylindrical-polar coordinates to obtain the velocity profile and maximum (or centerline) velocity for a fully-developed, laminar and steady flow in circular pipes.

Lecture 6 - Hagen-Poiseuille Flow: Mean Velocity, Wall Shear Stress and Fanning Friction Factor: In this segment, we pick up where we left of in the last segment (12.5), and derive the mean velocity, wall shear stress as well as relate those two parameters to obtain the Fanning friction factor, which was also covered in module 11.

Lecture 7 - Module 12 Recap

                                Congratulations, you just finished all of the modules!