Advanced Fluid Mechanics

Control Volume Theorems and Applications

This section covers lectures 6-8.

Readings

Textbooks

Reading in: Panton, Ronald L. Incompressible Flow. 4th ed. Wiley, 2013. ISBN: 9781118013434. [Preview with Google Books]

• Chapter 5: Basic Laws

Reading in: Kundu, Pijush K., and Ira M. Cohen. Fluid Mechanics. 6th ed. Academic Press, 2015. ISBN: 9780124059351.

• Chapter 4: Conservation Laws
  • 4.1: Introduction
  • 4.2: Conservation of Mass
  • 4.3: Stream Functions
  • 4.4: Conservation of Momentum
  • 4.5: Constitutive Equation for a Newtonian Fluid
  • 4.6: Navier-Strokes Momentum Equation
  • 4.7: Noninertial Frame of Reference
  • 4.8: Conservation of Energy
  • 4.9: Special Forms of the Equations; Angular Momentum Principle for a Stationary Control Volume; Bernoulli Equations; Neglect of Gravity in Constant Density Flows; The Boussinesq Approximation; Summary

Reading in: Fay, James A. Introduction to Fluid Mechanics. MIT Press, 1994. ISBN: 9780262061650. [Preview with Google Books]

• Chapter 3: Conservation of Mass
• Chapter 5: Conservation of Momentum

Additional Reading

• Vincenti, Walter G. “Control-volume Analysis: A Difference in Thinking Between Engineering and Physics.” Technology and Culture 23, no. 2 (1982): 145–74.

Class Notes

• Fundamental Laws of Motion for Particles, Material Volumes, and Control Volumes (PDF)
• On Choosing and Using Control Volumes: Six Ways of Applying the Integral Mass Conservation Theorem to a Simple Problem (PDF)

Assignments

Problem Set 4

PROBLEMS	SOLUTIONS
Problem 3.05 (PDF)	Solution to Problem 3.05 (PDF)
Problem 4.25 (PDF)	Solution to Problem 4.25 (PDF)
Problem 4.27 (PDF)	Solution to Problem 4.27 (PDF)
Problem 5.02 (PDF)	Solution to Problem 5.02 (PDF)
Problem 5.09 (PDF)	Solution to Problem 5.09 (PDF)
Problem 5.10 (PDF)	Solution to Problem 5.10 (PDF)

Problem Set 5

PROBLEMS	SOLUTIONS
Problem 5.13 (PDF)	Solution to Problem 5.13 (PDF)
Problem 5.18 (PDF)	Solution to Problem 5.18 (PDF)
Problem 5.20 (PDF)	Solution to Problem 5.20 (PDF)
Problem 5.29 (PDF)	Solution to Problem 5.29 (PDF)
Problem 5.32 (PDF)	Solution to Problem 5.32 (PDF)
Problem 5.33 (PDF)	Solution to Problem 5.33 (PDF)