[CFD | ENG] Simple shear flow for a Newtonian fluid. Analytical solution for the velocity profile скачать в хорошем качестве

[CFD | ENG] Simple shear flow for a Newtonian fluid. Analytical solution for the velocity profile

In this video, and using new audiovisual tools, we will solve analytically the Navier-Stokes equations for the simple shear flow, which is a standard flow for which we can derive an exact equation for the velocity profile. We will start by describing the geometry of this flow, where we will consider an incompressible, Newtonian fluid with constant physical properties. Then, we will give a brief introduction to what is laminar and turbulent flows, and we will analyse step by step each of the terms of both the continuity and momentum conservation equations in Cartesian coordinates to obtain a simple second-order ordinary differential for the component of the velocity in the x-direction. Lastly, we will solve this equation to obtain an analytical equation for the velocity profile of a Newtonian fluid, where we will conclude by explaining the physical meaning of this equation. Timestamps 00:00 Introduction to the flow and definition of the geometry 01:09 How momentum is being transferred in simple shear flow? 07:23 Points to consider to solve the simple shear flow problem 09:07 Brief description of laminar and turbulent flow 17:52 Boundary conditions 18:37 What does the continuity equation tell us about the system? 20:46 Simplification of the Navier-Stokes equation for the x-component 24:13 Simplification of the Navier-Stokes equation for the y-component 26:46 Simplification of the Navier-Stokes equation for the z-component 27:38 Simplified decoupled system of equations 29:45 Solution of the 2nd order ordinary differential equation for Ux 32:57 Physical interpretation of the equation for the velocity profile 34:44 Definition and calculation of the average velocity 40:27 Importante of the simple shear flow This video is part of the course called "Introduction to CFD" which I am offering for free in the channel. The presentation called "Introduction to the momentum conservation equation and the Navier-Stokes equations", which is the previous video, can be found here:    • [CFD | ENG] Introduction to the momentum c...   The next video called "Shear flow with pressure gradient for a Newtonian fluid. Solution" can be found here:    • [CFD | ENG] Shear flow with pressure gradi...   I encourage you to watch all the videos of the course. Enjoy the content. Links of interest Personal webpage where you can read more about my research related to fluid dynamics and other popular-science articles: https://hugocastillocom.wordpress.com