#jsDisabledContent { display:none; } My Account | Register | Help

# A Course in Fluid Mechanics with Vector Field Theory

## By Prieve, Dennis C.

Description
Physics Literature

Table of Contents ALGEBRA OF VECTORS AND TENSORS ..............................................................................................................................1 VECTOR MULTIPLICATION.....................................................................................................................................................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..................................................................................................................................................7 Cylindrical Coordinates ....................................................................................................................................................7 Spherical Coordinates........................................................................................................................................................8 DIFFERENTIATION OF VECTORS W.R.T. SCALARS................................................................................................................9 VECTOR FIELDS........................................................................................................................................................................ 11 Fluid Velocity as a Vector Field.....................................................................................................................................11 PARTIAL & MATERIAL DERIVATIVES................................................................................................................................. 12 CALCULUS OF VECTOR FIELDS...........................................................................................................................................14 GRADIENT OF A SCALAR (EXPLICIT)................................................................................................................................... 14 DIVERGENCE, CURL, AND GRADIENT................................................................................................................................... 16 Physical Interpretation of Divergence...........................................................................................................................16 Calculation of ¥.v in R.C.C.S........................................................................................................................................16 Evaluation of ¥?v and ¥v in R.C.C.S............................................................................................................................18 Evaluation of ¥.v, ¥?v and ¥v in Curvilinear Coordinates ...................................................................................19 Physical Interpretation of Curl.......................................................................................................................................20 VECTOR FIELD THEORY..........................................................................................................................................................22 DIVERGENCE THEOREM.......................................................................................................................................................... 23 Corollaries of the Divergence Theorem.........................................................................................................................24 The Continuity Equation..................................................................................................................................................24 Reynolds Transport Theorem...........................................................................................................................................26 STOKES THEOREM................................................................................................................................................................... 27 Velocity Circulation: Physical Meaning .......................................................................................................................28 DERIVABLE FROM A SCALAR POTENTIAL.......................................................................................................................... 29 THEOREM III............................................................................................................................................................................. 31 TRANSPOSE OF A TENSOR, IDENTITY TENSOR.................................................................................................................... 31 DIVERGENCE OF A TENSOR .................................................................................................................................................... 32

Book Id: WPLBN0000694974
Format Type: PDF eBook
File Size: 1.34 MB.
Reproduction Date: 2005

Title: A Course in Fluid Mechanics with Vector Field Theory
Author: Prieve, Dennis C.
Volume:
Language: English
Subject:
Collection: Physics Literature
Subcollection:
Historic
Publication Date:
Publisher:
 This book will be permanently flagged as inappropriate and made unaccessible to everyone. Are you certain this book is inappropriate?
 Other Books I Looked at: Click to view all Books in my History A Course in Fluid Mechanics with Vector ... (by Prieve, Dennis C.) (22) People also read these books: Click to view all Additional Books Argument Principle  (132) Applications to the Behavioral and Manag...  (200) Applications  (132) Appendix B : Lawton's Proof of Theorem 9...  (175) Appendix a : Weil's Proof of Theorem 8. ...  (200) An Introduction to Lie Groups  (118) All Games Bright and Beautiful  (132) A Little about Representations  (200) A Geometrical Vector in Three Dimensiona...  (155) Take-Away Games (by Zieve, Michael) (118) Scientific Computing with Maple Programm... (by Zeng, Zhonggang) (200) Littlewood Richardson Semigroups (by Zelevinsky, Andrei) (29) Other Books by Same Author: Click to view all books by Prieve, Dennis C. A Course in Fluid Mechanics with Vector ... (by Prieve, Dennis C.) (22) A Course in Fluid Mechanics with Vector ... (by Prieve, Dennis C.) (155) Other Books with Same Subject: Click to view all books in Science., Physics, Physics--Research Doing Physics with Quaternions (by Sweetser, Douglas B.) (155) Fundamentals of Computational Fluid Dyna... (by Lomax, Harvard) (1) Sample Teaching Course Outline  (175) Motionmountain  (132) Vibrations and Waves (by Crowell, Benjamin) (200) Workbook on Aspects of Dynamical Meteoro... (by Gertenbach, Jan D.) (132) Doing Physics with Quaternions (by Sweetser, Douglas B.) (118) Novel Gravity Probe B Gravitational Wave... (by Cahill, Reginald T.) (200) Diffuse Matter in the Universe Subtitle ... (by Dopita, Michael A.) (200) Prospect Quarks to Cosmos to Consciousne...  (118)
Copyright © 2010 World Public Library. All rights reserved. eBooks from World Public Library are sponsored by the World Public Library Association,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.