Fluid Mechanics

Jean-Laurent Puebe

• Publisher: Wiley-ISTE
• Year: 2013
• ISBN:
  9781118623121
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Mechanics

This book examines the phenomena of fluid flow and transfer as governed by mechanics and thermodynamics. Part 1 concentrates on equations coming from balance laws and also discusses transportation phenomena and propagation of shock waves. Part 2 explains the basic methods of metrology, signal processing, and system modeling, using a selection of examples of fluid and thermal mechanics.

Chapter 1

Thermodynamics of Discrete Systems

The general objective of thermodynamics is to describe the properties of matter. After recalling the representational bases of material systems, thermostatics is dealt with by postulating the existence of a general equation of state which relates the extensive quantities. In this way we can forgo the need to delve into principles related to differential forms, and thereby simplify the presentation of traditional results. Then the thermodynamics of out of equilibrium systems are considered in terms of entropy dynamics, and discussed using simple examples. Finally, the phenomenological laws of linear thermodynamics are then considered.

1.1. The representational bases of a material system

1.1.1. Introduction

1.1.1.1. Geometric Euclidean space and physical quantities

The object of the physical sciences is the study of matter, for which the formulation of physical laws is necessary. However prior to the formulation of any such laws it is clearly necessary to characterize matter in terms of the various physical quantities which we can directly or indirectly measure. Matter is present all around us, and in a first instance we will limit ourselves to considering it in a static way, at a given instant which we can identify (this supposes a minimal definition of time); we perform geometric measurements in a 3D Cartesian coordinates system in order to identify the position and/or dimension of material elements. Measuring length presents no particular difficulty, excepting the choice of units. We will observe material elements in a geometric Euclidean space.

The geometric description of space is independent of the presence of matter; in other words the metric tensor does not depend on any physical quantity. This is not true for certain astrophysical phenomena which require us to place ourselves in the context of general relativity where geometric properties of space are no longer independent of the presence of matter. Simplistically put, the length of a meter depends on the mass found in its vicinity, which considerably complicates matters. In the following we exclude such phenomena, as they only become important at scales which greatly exceed those of our terrestrial physics.

We thus postulate (Axiom 1) the existence of a geometric space whose structure is independent of the properties of matter and the associated physical phenomena (gravitation, force fields, etc.).

We also admit (Axiom 2) that this space is homogenous and isotropic, which leads us to a traditional geometric Euclidean description of space R³ with its associated notions of length, surface and volume, whose scalar values are independent of the particular geometric frame of reference we choose to consider. This property of homogenity and isotropy will have important consequences for the expression of physical laws, which must not favor any given point or physical spatial direction. In particular, physical laws should neither favor any particular point in the universe, nor change as a result of a change in reference frame.

Finally, we suppose (Axiom 3) that matter can be characterized by physical quantities which are measurable at each instant in time, and not by mathematical entities (wavefunctions etc.) which allow, via mathematical operations, access to information of a probabilistic kind with regard to a physical quantity. This hypothesis of the possibility of directly measuring physical quantities supposes that the measure does not change the physical quantities of the material element considered. We therefore exclude microscopic phenomena relevant to quantum mechanics from our field of study, and we suppose the smallest material elements studied to contain a number of atoms or molecules sufficient for the neglect of statistical microscopic fluctuations to be justified.

1.1.1.2. The existence of isolated systems and the definition of time

The study of physical phenomena presupposes their reproducibility; the same effects should be observed under identical conditions. The establishment of physical laws thus supposes the definition of a time with the property of homogenity: in particular, quantifiable and reproducible observations of the evolution of a given material system must be possible.

The definition of time should thus be appropriately chosen. Previously associated with the length of the day, the definition of time has varied considerably between different individuals and epochs. For example, during the Roman period the lengths of the day and the night were respectively divided into seven and four parts, the Babylonians 2,000 years beforehand divided the day and the night each into 12 hours, which were clearly of unequal duration and varied according to the seasons. The Chinese and the Japanese divided each of the two cycles, from dawn to dusk and from dusk to dawn, into six periods. Japan only adopted the occidental system in 1873, but this did not prevent Japanese clockmakers from making mechanical clocks as early as the 17^th century, th...

Table of contents

• Cover
• Title Page
• Copyright
• Preface
• Chapter 1: Thermodynamics of Discrete Systems
• Chapter 2: Thermodynamics of Continuous Media
• Chapter 3: Physics of Energetic Systems in Flow
• Chapter 4: Fluid Dynamics Equations
• Chapter 5: Transport and Propagation
• Chapter 6: General Properties of Flows
• Chapter 7: Measurement, Representation and Analysis of Temporal Signals
• Chapter 8: Thermal Systems and Models
• Appendix 1: Laplace Transform
• Appendix 2: Hilbert Transform
• Appendix 3: Cepstral Analysis
• Appendix 4: Eigenfunctions of an Operator
• Bibliography
• Index