Derivation of the Navier-Stokes Equations

📈 APEX Consulting: https://theapexconsulting.com 🌎 Website: http://jousefmurad.com 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 Equation   ► Part 3 - Derivation of the Energy Equation:    • Derivation of the Energy Equation   ► PDF of the presentation:   / derivation-of-34090956   ONLINE PRESENCE ================ 🌍 My website - http://jousefmurad.com/ 💌 My weekly science newsletter - https://jousef.substack.com/ 📸 Instagram -   / jousefmrd   🐦 Twitter -   / jousefm2   SUPPORT MY WORK ================= 👕 Science Merch: https://engineered-mind.creator-sprin... 👉 Become my Patreon:   / theengiineer   🧠 Subscribe for more free videos: https://bit.ly/2RLmMxq RECOMMENDATIONS ================== 🎥 1 Month Free of Skillshare Premium: https://bit.ly/3E3bXwC 📕 Books on AI, Data Science & Programming: https://bit.ly/2I1lUD1 - use "podengineered20" to get a 40% discount! 🎵 Joachim Heinrich - Words –––––––––––––––––––––––––––––– As a member of SimScale, some pictures in this video have been used from the SimScale platform. SimScale is the world’s first production-ready SaaS application for engineering simulation, completely cloud-based and easily accessible through a web browser. Try CFD and FEA now by creating a free Community account in minutes: https://bit.ly/316Aqgt Contact: If you need help or have any questions or want to collaborate feel free to reach out to me via email: [email protected] #NavierStokes #Physics #Engineering 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