The Equations of Hydrodynamics

This book provides derivations of the equations of hydrodynamics. The methodology employs various versions of Reynolds transport theorem. This approach provides an alternative to the more elementary first principles technique. The equations of hydrodynamics are presented in both integral and differential form. They are also written for the Lagrangian, Eulerian, and ALE descriptions of fluid motion. Differential equations are provided for the special cases of 2D and 1D geometries with...
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This book provides derivations of the equations of hydrodynamics. The methodology employs various versions of Reynolds transport theorem. This approach provides an alternative to the more elementary first principles technique. The equations of hydrodynamics are presented in both integral and differential form. They are also written for the Lagrangian, Eulerian, and ALE descriptions of fluid motion. Differential equations are provided for the special cases of 2D and 1D geometries with symmetry. The book also includes a brief summary of constitutive models and equations of state for solids, liquids, and gasses. The contents of this text provide the foundation of computational methods for hydrodynamics.