Solutions to Navier-Stokes: Poiseuille and Couette Flow

MEC516/BME516 Fluid Mechanics, Chapter 4 Differential Relations for Fluid Flow, Part 5: Two exact solutions to the incompressible continuity and Navier-Stokes equations. One solution is for laminar steady flow between fixed parallel plates, where the flow is driven by a pressure gradient (Poiseuille Flow). The other solution is for laminar steady flow between parallel plates where the flow is driven only by the motion of the upper plate (Couette Flow). All of the videos in this Introductory Fluid Mechanics course, sample exams (with solutions), and a copy (pdf) of this presentation can be downloaded at: http://www.drdavidnaylor.net Course Textbook: F.M. White and H. Xue, Fluid Mechanics, 9th Edition, McGraw-Hill, New York, 2021. Chapters 00:00 Introduction 00:49 Flow between parallel plates (Poiseuille Flow) 01:50 Simplification of the Continuity equation 02:50 Discussion of developing flow 04:26 Simplification of the Navier-Stokes equation 07:31 Why is dp/dx a constant? 09:54 Integration and application of boundary conditions 12:12 Solution for the velocity profile 13:39 Integration to get the volume flow rate 16:00 Flow with upper plate moving (Couette Flow) 17:19 Simplification of the Continuity equation 17:37 Simplification of the Navier-Stokes equation 18:52 Integration and application of boundary conditions 19:57 Solution for the velocity profile 20:52 End notes #fluidmechanics #fluiddynamics