# A Primer in Fluid MechanicsDynamics of Flows in One Space Dimension

## Preview

## Book Description

This distinctive text presents the basic principles of fluid mechanics by means of one-dimensional flow examples - differing significantly in style and content from other books.

A Primer in Fluid Mechanics contains:

Novel provisos in the text include

Chapters also discuss physical properties, atmospheric stability, thermodynamics, energy and momentum equations, dimensional analysis, and historical perspectives of flows in pipes and conduits.

A Primer in Fluid Mechanics offers a rigorous text for the curious student and for the research engineer seeking a readily available guide to the more refined treatments in the literature - supporting classical and current discussions as well as theoretical and practical concepts.

## Table of Contents

Fluid Properties - Kinetic Theory of Gases

Introduction

The Macroscopic View of Matter

The Liquid State

On the Kinetic Theory of Gases

Mass Density

Pressure in a Gas

The Molecular Mean-Free-Path Length

Relation between Viscosity and Mean-Free-Path Length

On Heat Conduction

On the Units of Viscosity

On the Viscosity of Real Gases

Heat Conduction Coefficient for Dilute Gases

On the Viscosity of Liquids

Availability and Future Sources of Fluid Property Data

Fluid Statics

Introduction

Equilibrium and Pressure in a Fluid

Classification of Forces

The Fundamental Equation of Fluid Statics

Equation of Fluid Statics for a Uniform Gravitational Field

Pressure-Height Relation in a Liquid

Elementary Pressure-Measuring Instruments

An Application in Manometry

Forces and Moments on Submerged Surfaces

Applications Involving Forces and Moments on Curved Surfaces

Forces on Submerged Bodies

The Concept of Static Stability

Application: Stability of a Buoy

On the Stability of a Floating Parabolic Segment

Fluid Statics of the Atmosphere

US Standard Atmosphere

Concept of Geopotential Height

Stability of the Atmosphere

Buoyancy in the Atmosphere

Application of the Inverse Square Law of Gravitation: Pressure at the Center of the Earth

Surface Tension

The Equation of Fluid Mechanics

Introduction

Concepts from Kinematics

Relating Observed Motion for Two Different Observers

Kinematics in a Flow Field

Time Derivatives and the Substantial Derivative

Illustrative Examples

Example Involving Other Time Derivatives

Concept of a One-Dimensional Flow

The Postulates of Fluid Dynamics

The Continuity Equation

Invariance of Continuity Equation under Change of Observer

The Dynamical Equation of Motion

On Newton's Second Law

On Concepts from Thermodynamics

The First Law of Thermodynamics

The Second Law of Thermodynamics

The Energy Equation

Dissipation and the Role of Friction

Wok and the Integrated Form of the Energy Equation

The Linear Momentum Equation

Summary

Applications in Constant-Density Flow

Introduction

A Catalogue of Restrictions

The Equations of Incompressible (Constant-Density) Flow

Bernoulli's Equation

Total Pressure

Frictionless Flow out of a Pressurized Reservoir

On Quasi-Steady Flow

Flow Losses in Internal Inlets

Elementary Flow Metering Devices

Two Flow-Rate Examples

Pitot and Pitot-Static Tubes

Elementary Applications of the Momentum Equation

The Borda-Carnot Relation for a Sudden Enlargement

The Borda Mouthpiece

Forces on Vanes, Power Production

The Rocket-Sled Water Brake

The Water Sprinkler Problem

Dimensional Analysis, Dynamical Similitude and Inspectional Analysis

Dimensions versus Units

Standards in Science and Technology

Complete Physical Equations and Dimensional Homogeneity

A Primitive Example of Dimensional Homogeneity

The Role of Dimensionless Parameters

The Buckingham Pi Theorem

Application of the Pi Theorem

Alternative Method for Determining the Pi-Ratios

Example Where the Number of Pi-Ratios Is Greater than M-N

Kinematical and Dynamical Similarity

On the Physical Significance of the Reynolds Number

Inspectional Analysis

Dynamical Similarity and Modeling

A Dimensional Analysis and an Inspectional Analysis Compared to the Complete Solution

Effects of Viscosity in Pipes and Conduits

A Historical Note

The Experiments of Hagen and Poiseuille on Flow through Capillary Tubes

Stokes' Solution for Hagen-Poiseuille Flow

On the Correlation of Theory and Experiment

The Darcy-Weisbach Equation for Head Loss in a Pipe

Reynolds' Experiments on the Nature of Turbulence and the Discovery of a Criterion for the Transition from Laminar to Turbulent Flow

The Application of Dimensional Analysis to Pipe Flow

Zagarola and the Superpipe

Flow in Artificially Roughened Pipes

Flow Losses in Commercial Pipes

Pumping Power to Maintain a Pipe Flow

Computation of Power Required in a Non-Uniform Duct

Hydraulic Calculations for Simple Conduits and Flow Loops

Steady Flow through an Elastic Tube

Steady Compressible Flow

Introductory Remarks

Thermodynamics of Fluids

The Equations of Steady One-Dimensional Flow

On the Propagation of Disturbances

The Speed of Sound

On the Maximum Speed of a Fluid Expanding into a Vacuum

Discrepancies between Theory and Experiment

Total Conditions in a Compressible Flow - Introduction to Mach Number

Application - Temperature Rise at the Nose of a Re-Entry Vehicle

Necessary Conditions for Accelerating a Flow in an Ideal Nozzle

Isentropic Flow through a de Laval Nozzle

The Appearance of Shock Waves in a Convergent-Divergent Nozzle

Normal Shock Waves

On the Structure of Shock Waves

Analysis of Flow through a de Laval Nozzle with Shock Waves

Fanno Processes

Isothermal Flow

The Inflow Problem

Non-Steady Flow

Introduction

Analysis of Starting Flow in a Pipe Supplied by an Infinite Reservoir

Non-Steady Liquid Flow through an Orifice in a Reservoir

The Draining of a Conical Reservoir

On the Notion of Characteristics

Theory of Hyperbolic Equations for Functions of Two Independent Variables

The General Equations for One-Dimensional Non-Steady Gas Flow in a Constant-Area Duct

Impulsive Motion of a Piston in a Duct

Propagation of an Isentropic Finite-Amplitude Compression Pulse

An Approach to Acoustics

## Reviews

"Unique...Meticulously accurate...The author gives a refreshingly original discussion."

- Ronald L. Panton, Mechanical Engineering Department, University of Texas at Austin