Mecanica de fluidos

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A Course in Fluid Mechanics with Vector Field Theory
by Dennis C. Prieve Department of Chemical Engineering Carnegie Mellon University Pittsburgh, PA 15213

An electronic version of this book in Adobe PDF® format was made available to students of 06-703, Department of Chemical Engineering, Carnegie Mellon University, Fall, 2000.

Copyright © 2000 by Dennis C. Prieve

06-703

1

Fall,2000

Table of Contents
ALGEBRA OF VECTORS AND TENSORS ..............................................................................................................................1 VECTOR M ULTIPLICATION ...................................................................................................................................................... 1 Definition of DyadicProduct..............................................................................................................................................2 DECOMPOSITION INTO SCALAR COMPONENTS.................................................................................................................... 3 SCALARFIELDS........................................................................................................................................................................... 3 GRADIENT OF A SCALAR ........................................................................................................................................................... 4 Geometric Meaning of theGradient..................................................................................................................................6 Applications of Gradient.....................................................................................................................................................7 CURVILINEAR COORDINATES ................................................................................................................................................... 7 Cylindrical Coordinates.....................................................................................................................................................7 Spherical Coordinates.........................................................................................................................................................8 DIFFERENTIATION OF VECTORS W.R.T .SCALARS................................................................................................................ 9 VECTOR FIELDS......................................................................................................................................................................... 11 Fluid Velocity as a VectorField......................................................................................................................................11 PARTIAL & M ATERIAL DERIVATIVES.................................................................................................................................. 12 CALCULUS OF VECTOR FIELDS ............................................................................................................................................14 GRADIENT OF A SCALAR (EXPLICIT).................................................................................................................................... 14 DIVERGENCE , CURL , AND GRADIENT .................................................................................................................................... 16 Physical Interpretation ofDivergence............................................................................................................................16 Calculation of ∇.v in R.C.C.S.........................................................................................................................................16 Evaluation of ∇×v and ∇v in R.C.C.S............................................................................................................................18...
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