Fluid Mechanics 5.5 - Solved Example Problem for Conservation of Mass - Parabolic Velocity Profile

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.

Module 5-- Finite Control Volume Analysis - Conservation of Mass
Conservation of mass is obtained by substituting B=mass and b=1 into the Reynold's Transport Theorem. The 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:
1) Select an appropriate finite control volume to solve a fluid mechanics problem.
2) Analyze whether the case is steady vs. unsteady, constant density vs. variable density, incompressible vs. compressible, uniform flow vs. non-uniform flow
3) Apply conservation of mass principle to the contents of a finite control volume to get important answers This material is based upon work supported by the National Science Foundation under Grant No. 2019664. Any opinions, findings, and conclusions, or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.