E-Book Content
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 Dyadic Product..............................................................................................................................................2 DECOMPOSITION INTO SCALAR COMPONENTS.................................................................................................................... 3 SCALAR FIELDS........................................................................................................................................................................... 3 GRADIENT OF A SCALAR ........................................................................................................................................................... 4 Geometric Meaning of the Gradient..................................................................................................................................6 Applications of Gradient.....................................................................................................................................................7 CURVILINEAR COORDINATES ...............................................................................