Elastic fluid

“ If a fluid be composed of particles mutually flying each other, and the density be as the compression, the centrifugal forces of the particles will be reciprocally proportional to the distances of their centres. And vice versa, particles flying each other with forces that are reciprocally proportional to the distances of their centres, compose an elastic fluid, whose density is as the compression. ”

“ Of all bodies, the air is the most eminent for this property, and it has thence obtained the name of an elastic fluid. Hard bodies are in the next degree elastic; if two ivory, or hardened steel balls are struck together, the parts at which they touch, will be flattened; but their elasticity will make them instantaneously resume their former shape. ”

“ The resistance of a body moving very swift in an elastic fluid is almost the same as if the parts of the fluid were destitute of their centrifugal forces, and did not fly from each other: if so be that the elasticity of the fluid arise from the centrifugal forces of the particles, and the velocity be so great as not to allow the particles time enough to act. ”

“ Fluid. A form of matter, in which its particles readily flow, or slide, over each other. Airs, or gases, are called elastic fluids, because they are readily reduced to a smaller bulk by pressure. Liquids, are denominated non-elastic fluids, because they suffer but little diminution of bulk, by any mechanical force.
Focus. That point in which converging rays unite.
Force. That power which acts upon a body, either tending to create, or to stop motion.
Fountain. A jet, or stream of water, forced upwards by the weight of other water, by the elasticity of air, or some other mechanical pressure. ”

“ For when I have collected an elastic fluid, and observe concerning it that its expansive power is increased by heat and diminished by cold, while it still uniformly retains its elastic fluidity, but also discover in it properties and behaviour different from those of common air, then I consider myself justified in believing that this is a peculiar kind of air. ”

“ Examples.— The variable thermic condition of an elastic fluid is a complex accident, capable of being completely expressed by two independent accidents, which may be any two out of these three quantities—the temperature, the density, the pressure—or any two independent functions of these quantities. ”

“ The grains of powder are suddenly converted into a permanently elastic air, occupying about four hundred and seventy-two times more space than their own bulk. The elastic fluid expands with a velocity calculated at the rate of about ten thousand feet per second; and its pressure or force, when thus expanding, has been estimated as equal to one thousand atmospheres, that is, one thousand times greater than the atmospheric pressure upon a base of the same extent. ”

“ By the first of these conditions all the terms having ρ as a factor may be neglected, and the equations thus become the equations of equilibrium of the fluid; as such, they are applicable to fluid whether incompressible or elastic, and however the pressure may affect the viscosity. ”

“ A fluid must be compressed to become continued; it must be continued and non-elastic, that all the pressure arising from its compression may be propagated in an instant; and so acting equally upon all parts of the body moved, may produce no change of the resistance. The pressure arising from the motion of the body is spent in generating a motion in the parts of the fluid, and this creates the resistance. ”

“ In our egg, consisting of an extensible membrane filled with an incompressible fluid and under external pressure, the equation of the envelope is pn + T (1 ⁄ r + 1 ⁄ r′) = P, where pn is the normal component of external pressure at a point where r and r′ are the radii of curvature, T is the tension of the envelope, and P the internal fluid pressure. This is simply the equation of an elastic surface where T represents the coefficient of elasticity; in other words, a flexible elastic shell has the same math­e­mat­i­cal properties as our fluid, membrane-covered egg. ”

“ The second essay of the set, ‘On the Force of Steam,’ gave the first table of its varying elasticity at temperatures from 32° to 212°, and described the ‘dew-point hygrometer’ (p. 582) . The issue of some recent experiments was remarkably anticipated in the following sentence: ‘There can scarcely be a doubt entertained respecting the reducibility of all elastic fluids of whatever kind into liquids; and we ought not to despair of effecting it in low temperatures, and by strong pressure exerted upon the unmixed gases’ (p. 550) . ”

“ The heat absorbed and evolved by the rarefaction and condensation of air is exactly proportional to the force evolved and absorbed in these operations. In fact, the changes of temperature produced by these rarefactions and condensations of air show that the heat of elastic fluids is the mechanical force possessed by them; and since the temperature of a gas determines its elastic force, it follows that the elastic force or pressure must be the effect of the motion of the constituent particles in any gas. ”

“ Solidity, Liquidity, and elastic Fluidity; and that of the active powers on which they depend, and by which they are changed, such as Gravitation, Cohesion, Calorific repulsion, or Heat, and Attractions chemical and electrical;—the laws of which he has expounded in a lucid and masterly manner; although it will be only necessary to quote the following passage, to show that the greatest philosopher may occasionally slide into error. "In solids, the attractive force predominates over the repulsive; in fluids, and in elastic fluids, they may be regarded as in different states of equilibrium ”

“ A fluid, on the other hand, on account of its lack of rigidity, cannot support a transverse vibration. Hence it was natural that Green, in searching for a dynamical explanation of the ether, should have proposed in a paper read before the Cambridge Philosophical Society in 1837 that the ether has the elastic properties of a solid. ”

“ This theory requires us to suppose that a subtile imponderable fluid pervades all space, and even interpenetrates bodies—gaseous, liquid, and solid; that this fluid is enormously elastic, for that it resists compression with a force almost beyond calculation. The particles of luminous bodies, themselves in rapid vibratory motion, are supposed to communicate movement to the particles of the ether, which are displaced from a position 409of equilibrium, to which they return, executing backwards and forwards movements, like the stalks of corn in a field over which a gust of wind passes. ”

“ Liquid gases.—The rending and upheaving of continental masses are operations which are not difficult to explain, when we are once convinced that heat, of sufficient power, not only to melt but to reduce to a gaseous form a great variety of substances, is accumulated in certain parts of the interior. We see that elastic fluids are capable of projecting solid masses to immense heights in the air ”

“ Modern research, however, has greatly enlarged and modified our views on the constitution of these elastic fluids. Gases are now considered to be composed of an almost infinite number of small particles or molecules, which are constantly moving in every direction with velocities of all conceivable magnitudes. ”

“ When the fluid has only to surmount the atmospheric pressure, it has a force of dissolution which is proper to it, and which in a charge of 8 lbs. of powder (the specific gravity 944.72, for a 24 pounder,) acts upon the surface of the least resistance with an energy equivalent to 9747.8074 lbs.
2. The fluid retarded in its expansion by a surface of least resistance, whose tenacity (occasioned by the compactness and pressure of the wadding, &c.) is t = 31, acquires by its elasticity of force = 52839.1463 lbs. at the instant when that surface yields to its action. ”

“ It possesses so-called elasticity of bulk. In the case of water having a free surface there is, as we have seen, a resistance to any change of level in the surface. This may be called an elasticity of surface form. Whenever an elastic material is strained or deformed, energy has to be expended on it to create the deformation. Thus to wind up a watch-spring, stretch a piece of indiarubber, compress some air, or bend a bow, requires an energy expenditure. ”

“ There seems every reason therefore to expect that the increasing elasticity is directly as the volatility of the substance, and that by further and more correct observation of the forces, a general law may be deduced, by the aid of which, and only a single observation of the force of any vapour in contact with its fluid, its elasticity at any other temperature may be obtained. ”

“ If we take the two extreme cases in the relation of ρ and P, so that, firstly, the elasticity be supposed zero, we shall have any finite pressure, however small, produce an infinite density, and the fluid becomes identical with the medium of Newton. ”

“ The æther is a perfect fluid endowed with rotational elasticity; so in the first place we have — and this is the most difficult part of our undertaking — to construct a material model of a perfect fluid, which is a type of medium nowhere existing in the material world. ”

“ The author of this work observes, that if a fluid draws its force partly from a gaseous or aeriform matter, and partly from the action of caloric, which rarefies that aeriform matter; then its density in proportion to its dilatation, will follow the inverse ratios of the squares of the spaces described. He then investigates two classes of formulæ: the first appertains to fluids which possess simply the fluid or aeriform elasticity, which are free from all heat exceeding the temperature of the atmosphere. ”

“ In density there is a great difference; water, which is the type of liquids, is 770 times as heavy as air, the type of gaseous bodies, while under the pressure of one atmosphere. A spiral spring only shows elasticity when it is compressed; it loses its tension when it has returned to its primitive condition. A gas has no original volume; it is always elastic, or in other words, it is always striving to attain a greater volume; this tendency to indefinite expansion is the chief property by which gases are distinguished from liquids. ”

“ It will now be necessary for me to give you some account of the mechanical properties of fluids—a science which, when applied to liquids, is divided into two parts, hydrostatics and hydraulics. Hydrostatics, treats of the weight and pressure of fluids; and hydraulics, of the motion of fluids, and the effects produced by this motion. A fluid is a substance which yields to the slightest pressure. If you dip your hand into a basin of water, you are scarcely sensible of meeting with any resistance.
Emily. The attraction of cohesion is then, I suppose, less powerful in fluids, than in solids? ”

“ The term viscosity has been described in the Glossary at the beginning of this work; a perfect fluid is incapable of resisting—except by its weight or inertia—a change of shape. Such a substance does not actually exist for all fluids have viscosity or internal friction.
This is defined as a resistance to a change of shape depending on the rate at which the change is effected, but, as the fluids which engineers have to deal with are water and vapors and gases, it simplifies nearly all the calculations to assume that they have no internal viscosity or friction. ”

“ When the attractive and repulsive forces are at equilibrium within the liquid, there is supposed to be in the immediate vicinity of the free surface a tendency to the dispersion of the particles which is constantly opposed by the attractive forces. The condition of the superficial layer may be compared with that of a thin, elastic membrane under stretch, the cohesion of which constantly opposes itself to a more considerable elongation. The superficial layer of a liquid is thus subject to a contractile force or tension, by virtue of which it tends to become as small as possible. ”

“ It is probable, however, that there are many cases in which the integral belonging to the less dense fluid is negative. If the denser body be solid we can often demonstrate this; for the liquid tends to spread itself over the surface of the solid, so as to increase the area of the surface of contact, even although in so doing it is obliged to increase the free surface in opposition to the surface-tension. ”

“ A solid body—a metallic bar for example—alternately heated and cooled increases and diminishes in length, and can move bodies fastened to its ends. A liquid alternately heated and cooled increases and diminishes in volume, and can overcome obstacles of greater or less size, opposed to its dilatation. An aeriform fluid is susceptible of considerable change of volume by variations of temperature. If it is enclosed in an expansible space, such as a cylinder provided with a piston, it will produce movements of great extent. ”

“ For this it will be necessary to consider the variations of the energy of the fluids only so far as they are immediately connected with the changes in the solid. We may suppose the solid with so much of the fluid as is in close proximity to it to be enclosed in a fixed envelop, which is impermeable to matter and to heat, and to which the solid is firmly attached wherever they meet. ”