Navier-Stokes Final Exam Question (Liquid Film)

MEC516/BME516 Fluid Mechanics I: A Fluid Mechanics Final Exam question on solving the Navier-Stokes equations (Chapter 4). The velocity and pressure fields are calculated for a gravity-driven liquid film on an inclined plate. This unique aspect of this problem is the no shear stress boundary condition at the top of the liquid film.

All the videos in this course 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
0:00 Introduction
0:18 Problem statement
1:23 Discussion of the assumptions & boundary conditions
3:34 Solution for the velocity field u(y)
7:18 Application of the boundary conditions
9:45 Final Answer for the velocity field u(y)
9:59 Solution for the dp/dy
10:51 Final answer for dp/dy
11:42 Animation and discussion of DNS turbulence modelling

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