Interactive Self-Study Module: Using Boundary Conditions to Develop Velocity Profiles from the Navier-Stokes Equation
Overview:

This module uses screencasts and an interactive simulation to explain how to develop velocity profiles. The screencasts are used to show how to simplify the Navier-Stokes equation and use boundary conditions for different flow situations. Example problems allow the user to test themselves. We suggest using the learning resources in the following order:

  1. Attempt to answer the multiple choice ConcepTest and the example problem before watching the screencasts or working with the simulations.
  2. Watch the screencasts that describe boundary conditions and their application to the Navier-Stokes equation.
  3. Use the interactive simulation to further understand how velocity profiles change with changing fluid conditions and situations. 
  4. Try to solve the example problems before watching the solutions in the screencasts.
  5. Answer the ConcepTests.
Motivation:
The Navier-Stokes equation is considered to be the governing differential equation of motion for incompressible, Newtonian fluids. Understanding it, knowing how to simplify it, and applying boundary conditions allow us to develop velocity profiles for a variety of engineering situations.
This module is intended for a Fluid Mechanics course. 

Before studying this module, you should be able to:

  • Explain partial differential equations, pressure gradients, and velocity profiles.
  • Describe the no-slip boundary condition.
  • Apply Newton's second law.
  • Derive the Navier-Stokes equation. 

After studying this module, you should be able to:
  • Simplify the Navier-Stokes equation based on the system of interest.
  • Integrate a simplified Navier-Stokes equation.
  • Determine the appropriate boundary conditions to apply.
  • Apply boundary conditions to obtain a velocity profile.