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Conservation of Linear Momentum for a Continuum
 

Summary

This chapter begins with the consideration of forces being applied to systems at the Macroscopic and Microscopic levels. This leads to the definition of the traction vector (or stress vector) acting on a differential area element as well as the concept of body force density at a point in a continuum. In terms of the traction and body force distributions a detailed development of the conservation of linear momentum (COLM) for a continuum is given in cartesian coordinates for one, two and three dimensional continuum systems. The concept of the stress tensor and Cauchy's formula are introduced and the governing vector equation of COLM is then cast in terms of the stress tensor. Example problems are given in which COLM is applied to some fundamental problems in fluid mechanics:

  • Laminar Flow between two flat parallel plates (Couette and Poiseuille flows)
  • Laminar Flow through a cylindrical tube
  • Couette Viscometer.

Example problems are also included which illustrate the concepts of traction vector, stress tensor and Cauchy's formula.

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Chapter3.pdf

Chapter3.html

 

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