Rotating Fluids in Engineering and Science

by Vanyo, James P.

• ISBN13: 9780486417042
• ISBN10: 0486417042
• Format: Paperback
• Copyright: 2012-02-29
• Publisher: Dover Publications

Summary

Lucid, well-written presentation for upper-level undergraduates or beginning graduate students. Invaluable for engineers and scientists whose projects require a knowledge of the theory. Part I reviews basic fluid mechanics needed to understand rest of text. Part II introduces concepts, theories, and equations specific to rotating fluids, and Part III presents numerous practical applications of the theory, in fields ranging from centrifuges to aerodynamics. "Highly recommended."-Choice.

Table of Contents

Preface	ix
PART I Fluid Mechanics Review	1	(96)
Rotating Fluid Phenomena	3	(20)
Mass and Momentum Conservation	23	(20)
Eulerian Mechanics	23	(1)
Mass Conservation	23	(3)
Force and Momentum	26	(3)
Navier-Stokes Equations	29	(6)
Dimensionless Equations and Ratios	35	(8)
Potential (Inviscid) Flow	43	(14)
Bemoulli Equation	43	(2)
Stream Functions and Velocity Potentials	45	(3)
Flow Past a Circular Cylinder	48	(5)
Pressure Components	53	(4)
Boundary Layers and Turbulence	57	(20)
Introduction and Two Solutions by Stokes	57	(3)
Prandtl Boundary Layer Equations	60	(4)
Flat Plate and Cylinder Solutions	64	(3)
Momentum Integral Equation	67	(3)
Turbulence and Stability	70	(7)
Wave Theory	77	(20)
Introduction and Definitions	77	(7)
Longitudinal Waves	84	(3)
Transverse Waves	87	(6)
Mach Cones	93	(4)
PART II Rotating Fluid Theory	97	(136)
Rotating Coordinate Systems	99	(14)
Intermediate Reference Frames	99	(3)
Fluids in a Rotating Frame	102	(2)
Ekman and Rossby Numbers	104	(2)
Application Examples	106	(7)
Coriolis Phenomena	113	(14)
Coriolis Forces vs. Accelerations	113	(4)
Coriolis and Angular Momentum	117	(2)
Coriolis Force-Acceleration Criteria	119	(2)
Application Examples	121	(6)
Rotation, Vorticity, and Circulation	127	(18)
Rotation	127	(1)
Vorticity	128	(6)
Circulation and Stokes Theorem	134	(3)
Application Examples	137	(8)
Vorticity as the Variable	145	(14)
Vorticity in Navier-Stokes Equations	145	(1)
Viscous Production of Vorticity	146	(4)
Relative Vorticity	150	(1)
Application Examples	150	(9)
Vortex Dynamics	159	(24)
Vortex Interactions in Two Dimensions	159	(4)
Conservation of Vorticity and Circulation	163	(6)
The Formula of Biot and Savart	169	(1)
Rankine's Combined Vortex	170	(3)
Vortex Intensification by Stretching	173	(3)
Application Examples	176	(7)
Secondary Flows	183	(18)
Boundary Layer Review	183	(1)
A Rotating Disk in a Stationary Fluid	183	(5)
A Rotating Fluid above a Stationary Surface	188	(3)
Enclosed Secondary Flows	191	(3)
Application Examples	194	(7)
Circular Pathline Flows	201	(14)
Theoretical Criteria	201	(1)
Some Important Flows	202	(7)
Application Examples	209	(6)
Rotation and Intertial Waves	215	(18)
Rayleigh Instability	215	(2)
Stability of Circular Pathline Flows	217	(2)
Rossby Waves and Inertial Waves	219	(3)
Atmospheric Rossby Waves I	222	(3)
Instability and Turbulence	225	(1)
Application Examples	226	(7)
PART III Rotating Fluid Applications	233	(168)
Pipes, Channels, and Rivers	235	(16)
Swirl in Straight Sections	235	(4)
Secondary Flow in Curved Sections	239	(5)
River Meandering	244	(1)
Abutment Undercutting	245	(1)
Study and Research Projects	246	(5)
Rotors and Centrifuges	251	(14)
Thin Disk in a Housing	251	(3)
Flow in a Cylindrical Annulus	254	(1)
Centrifuges	255	(5)
Cyclone Separators	260	(1)
Study and Research Projects	261	(4)
Wings, Lift, and Drag	265	(14)
Circulation and Lift (Inviscid)	265	(2)
Circulation and Lift (Viscous)	267	(2)
Kutta-Zhukowskii Theory	269	(1)
Finite Wings and Vortices	270	(3)
Vertical Momentum and Induced Drag	273	(2)
Study and Research Projects	275	(4)
Turbomachinery	279	(26)
Definitions and Classifications	279	(8)
Internal Flow Characteristics	287	(2)
Torque and Power Output	289	(2)
Flow Calculations	291	(7)
Performance Criteria	298	(2)
Study and Research Projects	300	(5)
Liquids in Precessing Spacecraft	305	(14)
Rigid-Body Dynamics	305	(4)
Energy Dissipation and Stability	309	(2)
Solution: Analysis and Computation	311	(2)
Solution: Scaled Experiments	313	(3)
Study and Research Projects	316	(3)
The Earth, Sun, and Moon	319	(14)
Introduction	319	(1)
Earth and Earth-Sun-Moon Dynamics	320	(2)
Motions in the Liquid Core	322	(3)
Chandler Wobble	325	(2)
Tides and Earth-Sun-Moon Dynamics	327	(2)
Study and Research Projects	329	(4)
Atmospheric Circulation	333	(16)
Introduction	333	(3)
Convective Flow Patterns	336	(2)
Coriolis Phenomena	338	(3)
Planetary Flow Dynamics	341	(2)
Atmospheric Rossby Waves II	343	(1)
Study and Research Projects	344	(5)
Oceanic Circulation	349	(16)
Flow Patterns and Energy Sources	349	(3)
Coriolis and Oceanic Gyres	352	(1)
Western Intensification and Elevated Centers	353	(2)
Localized Flow Phenomena	355	(2)
Some Quantitative Analyses	357	(4)
Study and Research Projects	361	(4)
Intense Atmospheric Vortices	365	(36)
Whirlwinds and Dust Devils	365	(1)
Large-Scale Vortex Storms	366	(2)
Hurricanes (Typhoons)	368	(5)
Tomadoes	373	(2)
Study and Research Projects	375	(4)
Appendices
A Mathematical Relationships	379	(6)
A.1 Vectors	379	(1)
A.2 Matrices	379	(1)
A.3 Direction Cosine Matrices	380	(2)
A. 4 Dyadics and Tensors	382	(1)
A.5 The Del Operator ∇	382	(1)
A.6 Operations Using ∇	383	(2)
B Stream Functions and Velocity Potentials	385	(4)
B.1 Summary	385	(1)
B.2 Basic Flows	385	(1)
B.3 Sums of Two Flows	386	(1)
B.4 Cylinders and Vortex Pairs	387	(2)
C Equations of Motion	389	(4)
C.1 Cartesian	389	(1)
C.2 Cylindrical	389	(1)
C.3 Spherical	390	(3)
D Fluid Properties	393	(4)
D.1 Units	393	(1)
D.2 Properties of Air	393	(1)
D.3 Properties of Water	394	(1)
D.4 Common Gases and Liquids	394	(1)
D.5 Compressible Fluids	395	(2)
E Geophysical Data	397	(4)
E.1 The Earth	397	(1)
E.2 The Sun	397	(1)
E.3 The Moon	397	(1)
E.4 The Planets	398	(1)
E.5 The Oceans	398	(1)
E.6 The Standard Atmosphere	399	(2)
References	401	(14)
Index	415