A Physical Introduction to Fluid Mechanics

Citation

Smits, A. J. (2000). A Physical Introduction to Fluid Mechanics. Wiley.

Chapter Summary

The book runs to roughly 530 pages. The contents list fourteen titled units, from Fluid Statics to Historical Notes, followed by appendices, answers to selected problems and an index. The publisher describes it as an introduction that connects theory and analysis to practical examples from engineering practice, with simple examples illustrating basic principles and more complex ones representative of engineering applications. The order of the chapters moves from fluids at rest, through the kinematics and laws of motion, to specific flow regimes and applications.

Fluid Statics

The contents begin with the treatment of fluids at rest. The book's opening pages also carry a part headed "The Nature of Fluids", starting on page 3.

Introduction to Fluid Motion I; Introduction to Fluid Motion II

Two successive chapters introduce fluid motion before the governing equations are written down in the chapters that follow.

Equations of Motion in Integral Form; Differential Equations of Motion

The equations of motion are developed twice, first in integral form and then as differential equations: the integral form relates to a finite region of fluid, the differential form to every point of the flow.

Incompressible, Irrotational Flows

A chapter on flows in which the density is constant and the fluid is irrotational, following directly after the differential equations of motion.

Dimensional Analysis

A chapter devoted to dimensional analysis. The publisher singles out dimensional reasoning, and the interpretation of results, as one of the book's key features.

Viscous Internal Flows; Viscous External Flows

Two chapters take up flows in which viscosity matters: first flows inside ducts and pipes, then flows around bodies.

Open Channel Flow; Compressible Flow; Turbomachines

Three application-oriented chapters follow: free-surface flow in channels, flows in which density changes are important, and machines that add or extract energy from a fluid.

Environmental Fluid Mechanics

The publisher says the book includes an introduction to engineering in the environment, included to spark reader interest.

Historical Notes

The publisher notes that historical references appear throughout the chapters, and a closing chapter collects historical notes on the subject.

Appendices and Answers

The back matter includes appendices, answers to selected problems and an index.

Key Concepts

The Basic Laws

• Fluid statics: the balance of forces in a fluid at rest.
• Integral and differential forms of the conservation laws: two complementary ways of writing the same physics, one for finite regions, the other for each point.

Special Flow Regimes

• Irrotational flow: flow without local rotation, which the book treats separately for incompressible fluids.
• Dimensional analysis and dimensionless numbers: the Reynolds, Froude and Mach numbers are among the dimensionless numbers that recur in the text.
• Viscous internal and external flows: friction in pipes and ducts, and drag on bodies.

Applications

• Open channel flow and compressible flow: free-surface flows and flows with significant density change.
• Turbomachines: pumps and similar devices.
• Environmental fluid mechanics: fluid mechanics applied to flows in nature and the built environment.

Critical Analysis

Strengths

• Physical concepts first. The publisher lists, as a key feature, that the underlying physical concepts are highlighted rather than the mathematical equations.
• Emphasis on reasoning. Dimensional reasoning and the interpretation of results are stressed, and the publisher says the examples teach when to use approximations and when those approximations break down.
• Range of examples. The text pairs simple examples that illustrate principles with more complex ones from engineering practice, so readers see how the ideas are used.
• Clear progression. The contents move from statics and kinematics to the integral and then the differential equations of motion, then to special flows and finally to applications.

Limitations

• Engineering orientation. The publisher presents the book as relevant to engineering and focused on real-world applications. A reader seeking a purely theoretical or mathematical treatment of continuum mechanics will find the emphasis elsewhere.
• No separate chapter on turbulence or numerical methods. The chapter list contains no chapter on turbulence or on computational fluid dynamics, so readers who need either will need another source.
• Only selected answers in the book. The contents list answers to selected problems only; a separate solutions volume exists for the book.
• Date. The book was published in 1999–2000.

Where It Fits in the Course

Smits is the one book in this mechanics course list that is about continuum mechanics rather than particle and rigid-body mechanics. Taylor's Classical Mechanics ends with a single chapter that introduces continuum mechanics, and Smits is the book to read to go further into fluids. Matter and Interactions, the first-year text built on the momentum principle, and Susskind and Hrabovsky's The Theoretical Minimum, a compact route to the Lagrangian and Hamiltonian formulations, come earlier or alongside; Morin's Introduction to Classical Mechanics is a problem-rich undergraduate text on the mechanics of particles and rigid bodies; and Goldstein, Poole and Safko's Classical Mechanics is the graduate treatment of the Lagrangian and Hamiltonian formulations. Smits does not continue that line, but it applies Newtonian conservation laws to a different kind of system.

How to Use This Book

Take it after a first course in mechanics and calculus; vector calculus will make the treatment of motion in integral and differential form easier. Physics and engineering students meeting fluids for the first time are its natural audience.

A practical plan:

• Core: the chapters from Fluid Statics through Viscous External Flows, in order. Stay with the pairing of integral and differential equations of motion and with Dimensional Analysis, which the publisher stresses.
• Selective: Open Channel Flow, Compressible Flow and Turbomachines can be chosen by interest or by the course's emphasis (civil, aerospace, mechanical).
• Browsing: Environmental Fluid Mechanics and Historical Notes can be read at any point to place the subject in context.

Work the problems at the end of each chapter and check against the selected answers, drawing the flow and estimating orders of magnitude before writing equations, as the publisher's emphasis on physical insight suggests.