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 incompressible flow. The result is a partial differential equation. Vector notation and cylindrical coordinates are also discussed. A numerical example is also presented.

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
08:00 Overview of the Presentation
01:23 Derivation of the Continuity Equation
04:45 Conservation of Mass
05:36 Rate of Mass Storage in the Control Volume
07:47 Partial Differential equation for Continuity: Unsteady compressible flow
08:44 Continuity Equation for Compressible Flow in Vector Notation
10:10 Simplification: Continuity Equation for Incompressible Flow
11: 44 Continuity Equation for Incompressible Flow
12:03 Continuity Equation for Incompressible Flow in Vector Notation
12:32 Continuity Equation in Cylindrical Coordinates
15:07 Solved Example: Using the Continuity Equation
18:24 End Slide

Course Textbook: F.M. White and H. Xue, Fluid Mechanics, 9th Edition, McGraw-Hill, New York, 2021.

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