Fluid Mechanics

Analytical Methods

Michel Ledoux, Abdelkhalak El Hami

• Publisher: Wiley-ISTE
• Year: 2017
• ISBN:
  9781119384625
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Mechanics

The book aims to provide an efficient methodology of solving a fluid mechanics problem. It aims to meet different objectives of the student, the future engineer or scientist. Using simple sizing calculations, and more advanced analytical calculations, the book covers all the essential numerical approaches for solving complex practical problems.

1
Mechanics and Fluid

1.1. Introduction

The mechanics of fluids is a type of mechanics: it looks at the movement of matter when under the influence of forces. Matter here is in the “fluid state”.

This chapter is approached from the perspective of the foundations of the mechanics of point power. It will also later define what fluid is and which of this matter’s main characteristics are useful to know. These characteristics shall then be brought to “life” in later chapters.

1.1.1. Mechanics: what to remember

1.1.1.1. Who is afraid of mechanics?

For some curious reason, this branch of physics appears frightening to many students, a curse that thermodynamics also shares. Somewhat recoiled from, the mechanical engineer occupies a special place in the academic world. Some people even wonder whether mechanical engineers are actually physicists who have a strong handle on mathematics, or are in fact mathematicians lost among physicists. These classifications have not been made any simpler by the addition of digital calculations.

It cannot be stressed enough that the appearance of mechanics gave birth to mathematical physics.

By pairing movement with mathematics, the Neoplanitician, Galileo, created kinematics. And then, with a stroke of genius, although perhaps slightly mythically, Isaac Newton created dynamics by incorporating the fall of an apple and the Moon’s trajectory into one vision.

Descartes must not be left out of this Pantheon of emerging physics, for he created momentum, was engaged in heated debates with Newton and Leibnitz on this subject as well as others, and discovered kinetic energy through “life force”. Leibnitz and Newton were also the precursors to the differential approach in mechanics.

1.1.1.2. Principles to remember

Like a game of chess, the starting rules of mechanics are the simplest. And, like a game of chess, not all paths lead to an easy victory.

a) Remember that a position vector

is defined as a vector that links the starting point to another point in space. The coordinates of

are evidently the point’s three coordinates:

[1.1]

By definition, the point’s speed is the derivative of the position vector in relation to the time:

[1.2]

which, when passing, accelerates the position vector’s second derivative:

[1.3]

Remember that a vector is derived with regard to a scalar by deriving its components:

[1.4]

b) In 1687, Isaac Newton’s Philosophiae Naturalis Principia Mathematica outlined three laws, which indeed can be reduced into two:

1. 1) The principle of inertia;
2. 2) Fundamental dynamics law;
3. 3) The principle of action and reaction.

Let us take these three principles further:

Law no. 2. Let us begin with the fundamental dynamics principle, when applied to a constant mass (m) material point:

The acceleration that a body undergoes in an inertial frame of reference is proportional to the resulting forces that it undergoes, and is inversely proportional to its mass.

In modern notation (the notion of the vector was acquired in the 20th Century), this is written as:

[1.5]

NOTE: Vectorial notation reminds us that a given speed contains three pieces of information: a dir...

Table of contents

• Cover
• Table of Contents
• Title
• Copyright
• Preface
• 1 Mechanics and Fluid
• 2 Immobile Fluid
• 3 A Description of Flows
• 4 Dynamics of Inviscid Fluids
• 5 Viscous Fluid Flows: Calculating Head Losses
• 6 Calculation of Thrust and Propulsion
• Bibliography
• Index
• End User License Agreement