Derivation of the Navier-Stokes Equations

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In this video, we will derive the famous Navier-Stokes Equations by having a look at a simple Control Volume (CV). A small introduction to classical mechanics at given in the beginning. Comment, Like & Subscribe!

► Part 1 - Derivation of the Mass Conservation Equation:    • Derivation of the Mass Continuity Equ...  
► Part 3 - Derivation of the Energy Equation:    • Derivation of the Energy Equation  
► PDF of the presentation:   / derivation-of-34090956  

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🎵 Joachim Heinrich - Words

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Time Stamps
----------------------
0:00 - 1:38 : Intro to Classical Mechanics
1:39 - 3:13 : History of the Navier-Stokes Equations
3:14 - 4:24 : Recap - Fundamental Equations
4:25 - 6:26 : Fundamental Equations of Fluid Mechanics
6:27 - 7:10 : What is Missing? - Normal & Shear Stresses
7:11 - 7:30 : Body Forces
7:31 - 8:04 : Normal & Shear Stresses - Visualization
8:05 - 8:45 : Assembling of the Equations
8:46 - 8:58 : Simplify the Equations
8:59 - 9:27 : Questions that need to be answered
9:28 - 10:46 : The Stress Tensor
10:47 - 11:07 : Pressure
11:08 - 11:34 : Separate Stress Tensor
11:35 - 11:40: Preliminary Equations
11:41 - 12:10: Stokes Hypothesis
12:11 - 12:49 : Product Rule for RHS
12:50 - 14:20: Final Form of the NSE
14:21 - 15:12 : Substantial Derivative
15:13 - 15:49 : Lagrangian vs. Eulerian Frame of Reference
15:50 - 16:12 : The Navier-Stokes Equation (Newton's 2nd Law of Motion)
16:13 - End : Outro