Mecanica de fluidos
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...
Regístrate para leer el documento completo.