Fluid and the continuum
Definition of Fluids
A fluid can be defined as a substance that is capable of flowing.A liquid has no definite shape of its own but conforms to the shape of the container containing it.Furthermore, even a small amount of shear force applied to a fluid will cause it to undergo a deformation that continues as long as the force continues to be applied.A fluid is a fluid that has a definite volume, which changes only slightly with temperature and pressure.Since liquids are difficult to compress under normal conditions, they may be considered incompressible for all practical purposes.It forms a free surface or an interface separating it from the atmosphere or from any other gas present.
A gas is a liquid, which is compressible and has no definite volume, but always expands until its volume becomes 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 the gas undergoes a negligible change in its volume, it can be considered incompressible.But if the change in volume is not negligible then the compressibility of the gas has to be taken into account in the analysis.Vapor is a gas whose temperature and pressure are such that it is very close to the liquid state.Thus steam can be considered a vapor because its state is generally not far away from the state of water.
Fluids are also classified as ideal fluids and practical or real fluids.Ideal fluids are fluids that do not have viscosity and surface tension and are incompressible.As such for ideal fluids there is no resistance to the movement of the fluid.However, ideal fluids do not exist in nature and hence, these are only hypothetical fluids.The existence of these imaginary fluids was imagined by mathematicians in order to simplify the mathematical analysis of fluids in motion.
Liquids that have low viscosity like air, water, etc. can be considered ideal liquids without any error.Practical or real fluids are those fluids that are actually available in nature.These fluids have properties such as viscosity, surface tension, and compressibility and hence have a definite volume Resistance is always offered by these fluids when set in motion.
A gas is a liquid, which is compressible and has no definite volume, but always expands until its volume becomes 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 the gas undergoes a negligible change in its volume, it can be considered incompressible.But if the change in volume is not negligible then the compressibility of the gas has to be taken into account in the analysis.Vapor is a gas whose temperature and pressure are such that it is very close to the liquid state.Thus steam can be considered a vapor because its state is generally not far away from the state of water.
Fluids are also classified as ideal fluids and practical or real fluids.Ideal fluids are fluids that do not have viscosity and surface tension and are incompressible.As such for ideal fluids there is no resistance to the movement of the fluid.However, ideal fluids do not exist in nature and hence, these are only hypothetical fluids.The existence of these imaginary fluids was imagined by mathematicians in order to simplify the mathematical analysis of fluids in motion.
Liquids that have low viscosity like air, water, etc. can be considered ideal liquids without any error.Practical or real fluids are those fluids that are actually available in nature.These fluids have properties such as viscosity, surface tension, and compressibility and hence have a definite volume Resistance is always offered by these fluids when set in motion.
Definition of fluid mechanics
Fluid mechanics is a branch of science that deals with the behavior of 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 dynamicsThe problems faced by man in the fields of water supply, irrigation, navigation, and hydropower resulted in the development of fluid mechanics. However, with the exception of Archimedes (250 BC), the principle is considered to be as true today as it was about 2250 years ago, showing little knowledge of the ancients in modern fluid mechanics. There is no record of progress in fluid mechanics after the fall of the Roman Empire (476 AD). Leonardo da Vinci (1500 A.D.) designed the first chambered canal lock.However, by da Vinci's time, the concepts of fluid motion came to be considered 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 developed in the treatment of fluid mechanics. One, commonly known as classical hydrodynamics, deals with the theoretical aspects of fluid flow, which assumes that shear stresses do not exist in fluids, i.e. the ideal fluid concept.
The other, known as hydraulics, deals with practical aspects of fluid flow that have been developed from experimental findings and are, therefore, more of an empirical nature.
Notable contributions to theoretical hydrodynamics have been made by Euler, D'Alembert, Navier, and Lagrange.Stokes, Kirchhoff, Rayleigh, Rankin, Kelvin, Lamb, and many others.A number of inventors have contributed to the development of applied hydraulics, notable among them are Chazy,
Venturi, Bazin, Hagen, Poiseuille, Darcy, Weisbach, Kutter, Manning, Francis, and many others.
Although the empirical formulas developed in hydraulics have found useful applications in many problems, it has not been possible to extend them to the advanced field of flow and aerodynamics of fluids other than water.Thus there was a definite need for a new approach to fluid flow problems—an approach that relied on classical hydrodynamics for its analytical development as well as on experimental means of checking the validity of the theoretical analysis. Modern fluid mechanics offers a new perspective, balancing the views of both theorists.and experimentalists.The generally recognized founder of modern fluid mechanics is German professor Ludwig Prandtl.His most notable contribution is the boundary layer theory. which has had a tremendous impact on the understanding of problems involving fluid motion. Other notable contributors to modern fluid mechanics include Blasius, Bakhmeteff, Nikuradze, von-Karman, Reynolds, Rouse, and many others.In this book, the fundamental principles of fluid mechanics are applied to problems related to the motion of a special class of fluids called Newtonian fluids (such as water, air, kerosene, glycerin, etc.).
The other, known as hydraulics, deals with practical aspects of fluid flow that have been developed from experimental findings and are, therefore, more of an empirical nature.
Notable contributions to theoretical hydrodynamics have been made by Euler, D'Alembert, Navier, and Lagrange.Stokes, Kirchhoff, Rayleigh, Rankin, Kelvin, Lamb, and many others.A number of inventors have contributed to the development of applied hydraulics, notable among them are Chazy,
Venturi, Bazin, Hagen, Poiseuille, Darcy, Weisbach, Kutter, Manning, Francis, and many others.
Although the empirical formulas developed in hydraulics have found useful applications in many problems, it has not been possible to extend them to the advanced field of flow and aerodynamics of fluids other than water.Thus there was a definite need for a new approach to fluid flow problems—an approach that relied on classical hydrodynamics for its analytical development as well as on experimental means of checking the validity of the theoretical analysis. Modern fluid mechanics offers a new perspective, balancing the views of both theorists.and experimentalists.The generally recognized founder of modern fluid mechanics is German professor Ludwig Prandtl.His most notable contribution is the boundary layer theory. which has had a tremendous impact on the understanding of problems involving fluid motion. Other notable contributors to modern fluid mechanics include Blasius, Bakhmeteff, Nikuradze, von-Karman, Reynolds, Rouse, and many others.In this book, the fundamental principles of fluid mechanics are applied to problems related to the motion of a special class of fluids called Newtonian fluids (such as water, air, kerosene, glycerin, etc.).
The term continuum is applied to the mechanism of fluid flow.
Continuum refers to a continuous and homogeneous fluid medium.From the perspective of the continuum, the overall properties and behavior of liquids can be studied without considering their atomic and molecular structure. Although a fluid consists of discrete molecules, it is considered a continuous medium for the analysis of fluid flow problems.All voids or cavities, whether microscopic or macroscopic, that may occur in liquids are ignored.
The physical properties of fluids can be considered continuous from point to point and can be expressed by continuous algebraic functions of coordinates in space and time. Fluid properties thus remain constant at a point and are the same in all directions from a specified point. Since the molecular size and motion of fluid elements about their mean path are usually negligible compared to the dimensions of the device, this assumption of symmetry and isotropy is quite justified except in the fields of aerodynamics and rarefied gas dynamics.