Fluid Mechanics 121 Derivation and Discussion of the NavierStokes Equations

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In this segment, we derive and discuss the Navier Stokes equations, including its boundary conditions. • Table of Contents: • 6:30 - Navier Stokes Equations in Cartesian Coordinates • 10:20 - Navier Stokes Equations in Cylindrical Polar Coordinates • 12:30 - Commonly Observed Boundary Conditions • 15:20 - Laminar, Turbulent and Transitional Flow, Entrance Region and Fully-Developed Flow • Module 12: Navier Stokes Equations: • In module 9, we covered the differential form of the conservation of momentum. We also 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 use the Navier Stokes equations to determine viscous flow characteristics between parallel plates and circular tubes. This material is based upon work supported by the National Science Foundation under Grant No. 2019664. Any opinions, findings, and conclusions, or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.

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