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 #fluidmechanics #fluiddynamics