Derivation of the Continuity Equation for Fluid Flow
MEC516/BME516 Chapter 4 Differential Relations for Fluid Flow, Part 2: Derivation of the general continuity equation for three dimensional unsteady compressible flow in Cartesian coordinates. The result is a partial differential equation. Vector notation is discussed. A numerical example is also presented.
Note: I've removed the discussion of cylindrical coordinates from this video -- it was done hastily when I first made this course, and had some issues. Cylindrical coordinates are now discussed in a separate video. Thanks to everyone who gave helpful comments!
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
Chapters
00:00 Introduction
00:08 Overview of the Presentation
01:07 Derivation of the Continuity Equation
04:29 Rate of Mass Storage in the Control Volume
07:31 Partial Differential equation for Continuity: Unsteady compressible flow
08:25 Continuity Equation for Compressible Flow in Vector Notation
09:53 Simplification: Continuity Equation for Incompressible Flow
11:28 Continuity Equation for Incompressible Flow in Vector Notation
12:14 Solved Example: Using the Continuity Equation
15:32 End Slide
Course Textbook: F.M. White and H. Xue, Fluid Mechanics, 9th Edition, McGraw-Hill, New York, 2021.
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