Balance Equations

  • Chung FangEmail author
Part of the Springer Textbooks in Earth Sciences, Geography and Environment book series (STEGE)


The motions of a fluid can be described by using the time rates of change of physical variables defined on the fluid. To reach this end, within the continuum hypothesis, fluid as a continuum should a priori be assumed and the fundamentals of continuum mechanics need to be introduced, including the concepts of material body, reference and present configurations, and motion of a fluid element. Based on these, the material derivative of physical variable and deformation of a material may be defined to obtain the expressions of velocity and acceleration of a fluid element.

Further Reading

  1. R. Aris, Vectors, Tensors, and the Basic Equations of Fluid Mechanics (Dover, New York, 1962)zbMATHGoogle Scholar
  2. G.K. Batchelor, An Introduction to Fluid Dynamics (Cambridge University Press, Cambridge, 1992)Google Scholar
  3. P. Chadwick, Continuum Mechanics (Dover, New York, 1976)Google Scholar
  4. A.J. Chorin, J.E. Marsden, A Mathematical Introduction to Fluid Mechanics, 2nd edn. (Springer, Berlin, 1990)CrossRefGoogle Scholar
  5. I.G. Currie, Fundamental Mechanics of Fluids, 2nd edn. (McGraw-Hill, Singapore, 1993)zbMATHGoogle Scholar
  6. K. Hutter, K. Jönk, Continuum Methods of Physical Modeling (Springer, Berlin, 2004)CrossRefGoogle Scholar
  7. I.S. Liu, Continuum Mechanics (Springer, Berlin, 2002)CrossRefGoogle Scholar
  8. J.E. Marsden, T.S. Ratiu, Introduction to Mechanics and Symmetry, 2nd edn. (Springer, Berlin, 1999)CrossRefGoogle Scholar
  9. I. Müller, W.H. Müller, Fundamentals of Thermodynamics and Applications (Springer, Berlin, 2009)zbMATHGoogle Scholar
  10. C. Truesdell, A First Course in Rational Continuum Mechanics, Volume 1 (Academic Press, New York, 1977)Google Scholar
  11. C. Truesdell, R.G. Muncaster, Fundamentals of Maxwell’s Kinetic Theory of a Simple Monatomic Gas (Academic Press, New York, 1980)Google Scholar
  12. C. Truesdell, W. Noll, The Non-Linear Field Theories of Mechanics (Springer, Berlin, 1992)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2019

Authors and Affiliations

  1. 1.Department of Civil EngineeringNational Cheng Kung UniversityTainanTaiwan

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