Fluid Mechanics 6.5 - Solved Example Problem 3 - Conservation of Momentum and Mass

In this segment, we highlight how to apply the conservation of momentum to obtain forces for 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 6 - Conservation of Momentum:
The conservation of momentum can be derived from Newton's second law. The time rate of change of the linear momentum of the system = Sum of external forces acting on the system. After establishing a control volume, we can apply Reynold's Transport Theorem by substituting in momentum for B.

Student Learning Outcomes:
After completing this module, you should be able to:
1) Select an appropriate finite control volume to solve the conservation of momentum equation.
2) Apply conservation of momentum to the contents of a finite control volume to get essential answers
3) Explain how velocity changes in fluid flows are related to forces 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.