Fluids are not strictly continuous media in the way that all the successors of Euler and Bernoulli have assumed, for they are composed of discrete molecules.
The molecules, however, are so small and, except in gases at very low pressures, the number of molecules per millilitre is so enormous that they need not be viewed as individual entities. There are a few liquids, known as liquid crystals, in which the molecules are packed together in such a way as to make the properties of the medium locally anisotropic , but the vast majority of fluids including air and water are isotropic. A word perhaps is needed about the difference between gases and liquids , though the difference is easier to perceive than to describe. In gases the molecules are sufficiently far apart to move almost independently of one another, and gases tend to expand to fill any volume available to them.
In liquids the molecules are more or less in contact, and the short-range attractive forces between them make them cohere; the molecules are moving too fast to settle down into the ordered arrays that are characteristic of solids, but not so fast that they can fly apart. Thus, samples of liquid can exist as drops or as jets with free surfaces, or they can sit in beakers constrained only by gravity, in a way that samples of gas cannot.
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Such samples may evaporate in time, as molecules one by one pick up enough speed to escape across the free surface and are not replaced. The lifetime of liquid drops and jets, however, is normally long enough for evaporation to be ignored. There are two sorts of stress that may exist in any solid or fluid medium, and the difference between them may be illustrated by reference to a brick held between two hands. If the holder moves his hands toward each other, he exerts pressure on the brick; if he moves one hand toward his body and the other away from it, then he exerts what is called a shear stress.
A solid substance such as a brick can withstand stresses of both types, but fluids, by definition, yield to shear stresses no matter how small these stresses may be. This property, about which more will be said later, is a measure of the friction that arises when adjacent layers of fluid slip over one another. These three quantities are linked together by what is called the equation of state for the fluid.
For other fluids knowledge of the equation of state is often incomplete. When an element of fluid is compressed, the work done on it tends to heat it up. In reversible adiabatic processes for such gases, however, the temperature rises on compression at a rate such that. For liquids the ratio between the isothermal and adiabatic compressibilities is much closer to unity. The molar specific heat is the amount of heat required to raise the temperature of one mole through one degree. This is greater if the substance is allowed to expand as it is heated, and therefore to do work, than if its volume is fixed.
The principal molar specific heats, C P and C V , refer to heating at constant pressure and constant volume, respectively, and. Solids can be stretched without breaking, and liquids, though not gases, can withstand stretching, too. Water owes its high ideal strength to the fact that rupture involves breaking links of attraction between molecules on either side of the plane on which rupture occurs; work must be done to break these links.
However, its strength is drastically reduced by anything that provides a nucleus at which the process known as cavitation formation of vapour- or gas-filled cavities can begin, and a liquid containing suspended dust particles or dissolved gases is liable to cavitate quite easily. Work also must be done if a free liquid drop of spherical shape is to be drawn out into a long thin cylinder or deformed in any other way that increases its surface area.
Here again work is needed to break intermolecular links. The surface of a liquid behaves, in fact, as if it were an elastic membrane under tension, except that the tension exerted by an elastic membrane increases when the membrane is stretched in a way that the tension exerted by a liquid surface does not. Surface tension is what causes liquids to rise up capillary tubes, what supports hanging liquid drops, what limits the formation of ripples on the surface of liquids, and so on.
An introduction to the mechanics of fluids
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Institutional Subscription. Instructor Ancillary Support Materials. Free Shipping Free global shipping No minimum order. Provides illustrations and animations to demonstrate fluid behavior Includes examples and exercises drawn from a range of engineering fields Explains a range of computerized and traditional methods for flow visualization, and how to choose the correct one Features a fully reworked section on computational fluid dynamics based on discretization methods.
History of Fluid Mechanics 2.
Characteristics of a Fluid 3. Fluid Statics 4. Fundamentals of Flow 5. Flow of Viscous Fluid 7.
Flow in Pipes 8. Flow in an Open Water Channel 9.
Drag and Lift Dimensional Analysis and Law of Similarity Measurement of Flow Velocity and Flow Rate Flow of Ideal Fluid Flow of a Compressible Fluid Unsteady Flow Computational Fluid Dynamics Powered by. You are connected as.
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