INTRODUCTION, HISTORY AND DEFINITION OF FLUIDS - FLUID MECHANICS (StudyCivilEngg.com)

INTRODUCTION, HISTORY AND DEFINITION OF FLUID

SUBJECT : FLUID MECHANICS

INTRODUCTION

A matter exists in either the solid state or the fluid state. The fluid state is further divided into the liquid and the gaseous states. In fact the same matter may exist in any one of the three states viz., solid, liquid and gaseous. For example water, which ordinarily occurs in a liquid state, may also occur under natural conditions in a solid state as ice and in a gaseous state as vapour. The solids, liquids and gases exhibit different characteristics on account of their different molecular structure. All substances consist of vast numbers of molecules separated by empty space. The molecules are continuously moving within the substance and they have an attraction for each other, but when the distance between them becomes very small (of the order of the diameter of the molecule) there is a force of repulsion between the molecules which pushes them apart. 

In solids the molecules are very closely spaced, but in liquids the spacing between the molecules is relatively large and in gases the space between the molecules is still larger. As such in a given volume a solid contains a large number of molecules, a liquid contains relatively less number of molecules and a gas contains much less number of molecules. It thus follows that in solids the force of attraction between the molecules is large on account of which there is very little movement of molecules within the solid mass and hence solids possess compact and rigid form. 

In liquids the force of attraction between the molecules is relatively less due to which the molecules can move freely within the liquid mass, but the force of attraction between the molecules is sufficient to keep the liquid together in a definite volume. 

In gases the force of attraction between the molecules is much less due to which the molecules of gases have greater freedom of movement so that the gases fill completely the container in which they are placed. It may, however, be stated that inspite of the larger mobility and spacing of the molecules of fluids, for mechanical analysis a fluid is considered to be continuum i.e., a continuous distribution of matter with no voids or empty spaces. This assumption is justifiable because ordinarily the fluids involved in most of the engineering problems have large number of molecules and the distances between them are small.

Another difference that exists between the solids and the fluids is in their relative abilities to resist the external forces. A solid can resist tensile, compressive and shear forces upto a certain limit. A fluid has no tensile strength or very little of it, and it can resist the compressive forces only when it is kept in a container. When subjected to a shearing force, a fluid deforms continuously as long as this force is applied. The inability of the fluids to resist shearing stress gives them their characteristic property to change shape or to flow. This, however, does not mean that the fluids do not offer any resistance to shearing forces. In fact as the fluids flow there exists shearing (or tangential) stresses between the adjacent fluid layers which result in opposing the movement of one layer over the other.

The amount of shear stress in a fluid depends on the magnitude of the rate of deformation of the fluid element. However, if a fluid is at rest no shear force can exist in it. The two classes of fluids, viz., gases and liquids also exhibit quite different characteristics. Gases can be compressed much readily under the action of external pressure and when the external pressure is removed the gases tend to expand indefinitely. On the other hand under ordinary conditions liquids are quite difficult to compress and therefore they may for most purposes be regarded as incompressible. Moreover, even if the pressure acting on a liquid mass is removed, still the cohesion between particles holds them together so that the liquid does not expand indefinitely and it may have a free surface, that is a surface from which all pressure except atmospheric pressure is removed.

HISTORY OF FLUID MECHANICS

Fluid mechanics is that branch of science which deals with the behaviour of the fluids at rest as well as in motion. In general the scope of fluid mechanics is very wide which includes the study of all liquids and gases. But usually it is confined to the study of liquids and those gases for which the effects due to compressibility may be neglected. The gases with appreciable compressibility effects are governed by the laws of Thermodynamics which are however dealt with under the subject of Gas dynamics. 

The problems, man encountered in the fields of water supply, irrigation, navigation and water power, resulted in the development of the fluid mechanics. However, with the exception of Archimedes (250 B.C.) Principle which is considered to be as true today as some 2250 years ago, little of the scant knowledge of the ancients appears in modern fluid mechanics. After the fall of Roman Empire (476 A.D.) there is no record of progress made in fluid mechanics until the time of Leonardo da Vinci (1500 A.D.), who designed the first chambered canal lock. However, upto da Vinci’s time, concepts of fluid motion must be considered to be more art than science. Some two hundred years ago mankind’s centuries of experience with the flow of water began to crystallize in scientific form. Two distinct Schools of thought gradually evolved in the treatment of fluid mechanics. 

One, commonly known as Classical Hydrodynamics, deals with theoretical aspects of the fluid flow, which assumes that shearing stresses are non-existent in the fluids, that is, ideal fluid concept. The other known as Hydraulics, deals with the practical aspects of fluid flow which has been developed from experimental findings and is, therefore, more of empirical nature. Notable contributions to theoretical hydrodynamics have been made by Euler, D’Alembert, Navier, Lagrange, Stokes, Kirchoff, Rayleigh, Rankine, Kelvin, Lamb and many others. Many investigators have contributed to the development of experimental hydraulics, notable amongst them being Chezy, Venturi, Bazin, Hagen, Poiseuille, Darcy, Weisbach, Kutter, Manning, Francis and several others. 

Although the empirical formulae developed in hydraulics have found useful application in several problems, it is not possible to extend them to the flow of fluids other than water and in the advanced field of aerodynamics. As such there was a definite need for a new approach to the problems of fluid flow—an approach which relied on classical hydrodynamics for its analytical development and at the same time on experimental means for checking the validity of the theoretical analysis. The modern Fluid Mechanics provides this new approach, taking a balanced view of both the theorists and the experimentalists. The generally recognized founder of the modern fluid mechanics is the German Professor, Ludwig Prandtl. His most notable contribution being the boundary layer theory which has had a tremendous influence upon the understanding of the problems involving fluid motion. Other notable contributors to the modern fluid mechanics are Blasius, Bakhmeteff, Nikuradse, Von-Karman, Reynolds, Rouse and many others. In this book the fundamental principles of fluid mechanics applicable to the problems involving the motion of a particular class of fluids called Newtonian fluids (such as water, air, kerosene, glycerine etc.) have been discussed along with the relevant portions of the experimental hydraulics.

DEFINITION OF A FLUID

In view of the above discussion a fluid may be defined as a substance which is capable of flowing. It has no definite shape of its own, but conforms to the shape of the containing vessel. Further even a small amount of shear force exerted on a fluid will cause it to undergo a deformation which continues as long as the force continues to be applied.

A liquid is a fluid, which possesses a definite volume, which varies only slightly with temperature and pressure. Since under ordinary conditions liquids are difficult to compress, they may be for all practical purposes regarded as incompressible. It forms a free surface or an interface separating it from the atmosphere or any other gas present. A gas is a fluid, which is compressible and possesses no definite volume but it always expands until its volume is equal to that of the container. Even a slight change in the temperature of a gas has a significant effect on its volume and pressure.

However, if the conditions are such that a gas undergoes a negligible change in its volume, it may be regarded as incompressible. But if the change in volume is not negligible the compressibility of the gas will have to be taken into account in the analysis. A vapour is a gas whose temperature and pressure are such that it is very near the liquid state. Thus steam may be considered as a vapour because its state is normally not far from that of water.  The fluids are also classified as ideal fluids and practical or real fluids. Ideal fluids are those fluids which have no viscosity and surface tension and they are incompressible.

As such for ideal fluids no resistance is encountered as the fluid moves. However, in nature the ideal fluids do not exist and therefore, these are only imaginary fluids. The existence of these imaginary fluids was conceived by the mathematicians in order to simplify the mathematical analysis of the fluids in motion. The fluids which have low viscosity such as air, water etc., may however be treated as ideal fluids without much error. Practical or real fluids are those fluids which are actually available in nature. These fluids possess the properties such as viscosity, surface tension and compressibility and therefore a certain amount of resistance is always offered by these fluids when they are set in motion.

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