Vectors, Tensors and the Basic Equations of Fluid MechanicsThis introductory text is geared toward engineers, physicists, and applied mathematicians at the advanced undergraduate and graduate levels. It applies the mathematics of Cartesian and general tensors to physical field theories and demonstrates them chiefly in terms of the theory of fluid mechanics. Numerous exercises appear throughout the text. 1962 edition. |
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Vectors, Tensors and the Basic Equations of Fluid Mechanics Rutherford Aris No preview available - 1990 |
Common terms and phrases
algebra angle antisymmetric arbitrary base vectors called Cartesian coordinates Cartesian tensors Christoffel symbols closed curve constant constitutive equations contravariant vector convected coordinates coordinate lines coordinate system covariant vector curl curvature defined deformation denote derivative differentiation direction cosines element elementary equations of motion Euclidean Euclidean space example Exercise flow flux function geodesic given gradient Green's theorem incompressible integral irrotational irrotational vector field isotropic tensor length linear mathematical matrix metric tensor momentum Navier-Stokes equations Newtonian fluid normal notation orthogonal parallel permutation physical components plane polar position quotient rule rate of change rate of strain relation rotation scalar second order tensor Show ſº solenoidal stress tensor suffix summation surface vector symmetric tangent theory thermodynamic transformation Truesdell unit vector vanish vector field velocity volume write zero