Module 5: Finite Control Volume Analysis: Conservation of Mass:

Conservation of mass states that time rate of change of the mass of the coincident system = time rate of change of the mass of the contents of the coincident control volume + net rate of flow of mass through the control surface.

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

* Select an appropriate finite control volume to solve a fluid mechanics problem

* Analyze whether the case is steady vs. unsteady, constant density vs. variable density, incompressible vs. compressible, uniform flow vs. non-uniform flow

* Apply conservation of mass principle to the contents of a finite control volume to get important answers

Lecture Videos:

Link to Module 5 Playlist Link to Module 5 Lecture Notes

Links to Individual Module 5 Videos:

Lecture 1 - Conservation of Mass for a Control Volume: This segment derives the conservation of mass (or continuity) equation applied to a control volume from the Reynold's Transport Theorem. We also introduce the mass flow rate terminology.

Lecture 2 - Special Cases of Conservation of Mass: This segment discusses the special cases of conservation of mass (the continuity equation) applied to control volume. The specific special cases we discuss are steady vs unsteady, constant density vs variable density, incompressible vs compressible, and uniform flow vs non-uniform flow.

Lecture 3 - Example for Conservation of Mass: In this segment, we go over an example where there is a non-uniform velocity distribution. We emphasize the approach to convert the non-uniform velocity profile to the uniform (if possible) by separating the non-uniform inlet or exit into multiple sub-sections.

Lecture 4 - Example for Variable Density - Conservation of Mass: In this segment, we apply the conservation of mass (or continuity) equation to a control volume, where the air is flowing into a nozzle, where the temperature and pressure are variable (as expected in real life). We analyze the problem with the ideal gas law. We also discuss the error incorporated into the analysis, if the constant density is assumed.

Lecture 5 - Conservation of Mass for Parabolic Velocity Distribution in a Pipe: In this segment, we highlight how to apply the conservation of mass to realistic viscous pipe flow. The non-uniform velocity profile is parabolic in nature. Please pay close attention to how we obtain the differential area (dA) for a circular pipe, which is 2(Pi)rdr, as well as double integration of velocity times the differential area

Lecture 6 - Unsteady Water Tank with Both Inlet and Outlet: This segment analyzes a real-life application of an unsteady water tank with an inlet and outlet with different flow rates. As a result, the water level in the tank is changing. We do find the velocity of the water level increase with two separate control volume selections.

Lecture 7 - Module 5 Recap

Additional Videos (Short FE Exam type questions)

Lecture 8 - In this segment, we solve a practice problem from the continuity equation (conservation of mass) topic

Congratulations, you just finished module 5! Please proceed to module 6

College Fluid Mechanics

An Open Courseware

FE Exam Review and Practice