Module 8: Differential Analysis of Fluid Flow: Conservation of Mass

As we discussed in module 5, conservation of mass requires that the mass, M, of a system remain constant as the system moves through the flow field. That analysis was conducted for a finite control volume. In this module, we apply the conservation of mass principles to a differential element.

Student Learning Outcomes: After completing this module, you should be able to:

* Apply the continuity equation to physical flows to find the velocity gradients

* Determine whether a flow is physically possible by using the continuity equation

* Find velocities given a stream function or find a stream function, streamlines, and volumetric flow rate, given the velocity profiles

* Check whether the flow is irrotational or rotational

* If irrotational, find the corresponding velocity potential

Lecture Videos:

Link to Module 8 Playlist Link to Module 8 Lecture Notes

Links to Individual Module 8 Videos:

Lecture 1 - Derivation and Discussion of Conservation of Mass: In this segment, we cover the derivation of the conservation of mass equation in the differential form. We also discuss the various aspects of the conservation of mass

Lecture 2 - Special Cases of Conservation of Mass Equation: This segment covers common special cases of the conservation of mass or continuity equation. We also go over a simple example to illustrate how to satisfy the conservation of mass. The example will also highlight the differences between integration constants for partial derivative and regular derivative

Lecture 3 - Streamfunction Concept: This segment covers the streamfunction concept, how streamfunction relates to streamlines, and obtaining the volumetric flow rate between two streamlines

Lecture 4 - Streamfunction - An Example: In this segment, we go over an example of obtaining streamfunction when the velocity components are known. The particular example of flow at a corner. Important points to note are the integration constants or functions for partial derivative

Lecture 5 - Velocity Potential Function and Vorticity: This segment covers a brief discussion of the vorticity concept that you need to understand the irrotational flow. It also includes the introduction of velocity potential function, its differences from streamfunction equation

Lecture 6 - Velocity Potential Function - An Example: In this segment, we cover an example of the velocity potential function. We discuss the preliminary step we have to take before delving into the mathematical approach. We also illustrate what issue you will face when trying to find a velocity potential that does not exist.

Lecture 7 - Comprehensive Example of Conservation of Mass, Streamfunction and Velocity Potential: In this segment, we go over a question we prepared that tests the students on conservation of mass, streamfunction, streamline, volumetric flow rate between streamlines, as well as velocity potential concept. This type of question is a good exam question to assess the learning of major topics in fluid mechanics

Lecture 8 - Module 8 Recap

Congratulations, you just finished module 8! Please proceed to module 9

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