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
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