Navier-Stokes Equation Final Exam Question
MEC516/BME516 Fluid Mechanics I: A Fluid Mechanics Final Exam question on solving the Navier-Stokes equations (Chapter 4). Calculation of the fully-developed velocity field between two parallel plates, with a pressure gradient and one plate moving. (This is a classical exact solution that dates back 100+ years: Couette flow with a pressure gradient.)
All the videos for this course and a copy (pdf) of this fluid mechanics presentation can be downloaded at: http://www.drdavidnaylor.net
This website also includes an exam bank and solved problem sets.
Course Textbook: F.M. White and H. Xue, Fluid Mechanics, 9th Edition, McGraw-Hill, New York, 2021.
Chapters
00:00 Intro (Navier-Stokes Exam Question)
00:33 Problem Statement (Navier-Stokes Problem)
01:58 Continuity Equation (compressible and incompressible flow)
02:32 Navier-Stokes equations (conservation of momentum)
03:14 Discussion of the simplifications and boundary conditions
04:40 Simplification of the continuity equation (fully developed flow)
05:46 Simplification of the x-momentum equation
10:04 Integration of the simplified momentum equation
10:41 Application of the lower no-slip boundary condition
12:18 Application of the upper no-slip boundary condition
13:52 Expression for the velocity distribution
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