Fluid dynamics

“ The true doctrine of Hydrostatics, however, assuming the Idea of Pressure, which it involves, in common with the Mechanics of solid bodies, requires also a distinct Idea of a Fluid, as a body of which the parts are perfectly movable among each other by the slightest partial pressure, and in which all pressure exerted on one part is transferred to all other parts. ”

“ The theorems of hydrostatics are thus true for all stationary fluids, however viscous they may be; it is only when we come to hydrodynamics, the science of the motion of a fluid, that viscosity will make itself felt and modify the theory; unless we begin by postulating the perfect fluid, devoid of viscosity, so that the principle of the normality of fluid pressure is taken to hold when the fluid is in movement.
5. The Measurement of Fluid Pressure.—The pressure at any point of a plane in the interior of a fluid is the intensity of the normal thrust estimated per unit area of the plane. ”

“ But, further, in fluids such as water, air, steam, &c., to which the present division of the article relates, the tangential stresses that are called into action between contiguous portions during distortion or change of figure are always small compared with the weight, inertia, pressure, &c., which produce the visible motions it is the object of hydraulics to estimate. On the other hand, while a fluid passes easily from one form to another, it opposes considerable resistance to change of volume. ”

“ Properties of Fluids.—The fluids to which the laws of practical hydraulics relate are substances the parts of which possess very great mobility, or which offer a very small resistance to distortion independently of inertia. Under the general heading Hydromechanics a fluid is defined to be a substance which yields continually to the slightest tangential stress, and hence in a fluid at rest there can be no tangential stress. ”

“ Let AB (fig. 25) be any one elementary stream, in a steadily moving fluid mass. Then, from the steadiness of the motion, AB is a fixed path in space through which a stream of fluid is constantly flowing. Let OO be the free surface and XX any horizontal datum line. Let ω be the area of a normal cross section, v the velocity, p the intensity of pressure, and z the elevation above XX, of the elementary stream AB at A, and ω1, p1, v1, z1 the same quantities at B. Suppose that in a short time t the mass of fluid initially occupying AB comes to A′B′. ”

“ For if the body is removed, and replaced by the fluid as at first, this fluid is in equilibrium under its own weight and the thrust of the surrounding fluid, which must be equal and opposite, and the surrounding fluid acts in the same manner when the body replaces the displaced fluid again; so that the resultant thrust of the fluid acts vertically upward through the centre of gravity of the fluid displaced, and is equal to the weight. ”

“ Whence neither will a motion of the parts of the fluid among themselves, be changed by a pressure communicated to the external superficies, except so far as either the figure of the superficies may be somewhere alter'd, or that all the parts of the fluid, by pressing one another more intensely or remissly, may slide with more or less difficulty among themselves. ”

“ The leading thermodynamic properties of a fluid are determined by the relations which exist between the volume, pressure, temperature, energy, and entropy of a given mass of the fluid in a state of thermodynamic equilibrium. The same is true of a solid in regard to those properties which it exhibits in processes in which the pressure is the same in every direction about any point of the solid. ”

“ The explanation, of course, is simple. The brine is of greater specific gravity than the pure water; the pressure of the heavier fluid forces the lighter up in the tube. This action continues until, as you will see by this experiment, in the gradual diffusion of brine and pure water the salt is disseminated equally throughout the vessels, and the specific gravity of the mixed liquid becomes the same throughout, when the flow will cease. However, in the earth, where supplies are inexhaustible, the fountain flows unceasingly. ”

“ There are three physical states or conditions of matter, which are the solid, liquid and gaseous, which in this connection apply to Ice, Water and Steam. A solid offers resistance both to change of shape and to change of bulk.
A Fluid offers no resistance to change of shape. Again fluids can be divided into liquids and vapors or gases. Water is the most familiar example of a liquid. A liquid can be poured out in drops while a gas or vapor flows in a stream or streams. ”

“ It is only when two gases are flowing with unequal velocity, that is, when they have a relative motion, that these changes of relative distribution, which are called diffusion, take place. The best way out of the difficulty is to investigate the separate motions of the two fluids, taking account of the mechanical actions exerted on them, and supposing that the mutual action of the fluids causes either fluid to resist the relative motion of the other. ”

“ We may also suppose that in the narrow space or spaces between the solid and the envelop, which are filled with fluid, there is no motion of matter or transmission of heat across any surfaces which can be generated by moving normals to the surface of the solid, since the terms in the condition of equilibrium relating to such processes may be cancelled on account of the internal equilibrium of the fluids. ”

“ In ordinary hydraulics, liquids are treated as absolutely incompressible. In dealing with gases the changes of volume which accompany changes of pressure must be taken into account.
§ 3. Viscous fluids are those in which change of form under a continued stress proceeds gradually and increases indefinitely. A very viscous fluid opposes great resistance to change of form in a short time, and yet may be deformed considerably by a small stress acting for a long period. ”

“ What used to be called the "vis viva" of a body is double what is now called the energy of motion, or kinetic energy, of the body. The term liquid is merely a brief expression for a fluid, the mass of which per unit volume is the same throughout, and suffers no variation. The fluid, moreover, is supposed devoid of friction, that is, the relative motions of its parts are unresisted by tangential force between them. The chief theorem proved and discussed may be described as follows. ”

“ In the fluid condition water still possesses a surplus of cohesion over the antagonistic force of heat; when, however, the latter is applied in excess, then the quasi-struggle terminates; the heat overpowers the cohesive attraction, and converts the water into the most willing slave which has ever lent itself to the caprices of man—viz., into steam—glorious, useful steam: and now the other end of the chain is reached, where heat triumphs; whilst in solids, such as ice, cohesion is the conqueror, and the intermediate link is displayed in the fluid state of water. ”

“ Emily. A body of water, in falling, does certainly less injury than a solid body of the same weight.
Mrs. B. The particles of fluids, acting thus independently, press against each other in every direction, not only downwards, but upwards, and laterally or sideways; and in consequence of this equality of pressure, every particle remains at rest, in the fluid. If you agitate the fluid, you disturb this [Pg 121] equality of pressure, and the fluid will not rest, till its equilibrium is restored.
Plate xiii.
Caroline. The pressure downwards is very natural; it is the effect of gravity ”

“ This may sometimes, or perhaps generally, make it a necessary condition of equilibrium in cases of contact between a fluid and an amorphous solid which can be formed out of it, that the solid at the surface where it meets the fluid shall be sensibly in a state of hydrostatic stress. ”

“ Dubuat considered that if water were a perfect fluid, and the channels in which it flowed infinitely smooth, its motion would be continually accelerated, like that of bodies descending in an inclined plane. But as the motion of rivers is not continually accelerated, and soon arrives at a state of uniformity, it is evident that the viscosity of the water, and the friction of the channel in which it descends, must equal the accelerating force. ”

“ Heat promotes Fluidity very much by diminishing the Tenacity of Bodies. It makes many Bodies fluid which are not fluid in cold, and increases the Fluidity of tenacious Liquids, as of Oil, Balsam, and Honey, and thereby decreases their Resistance. But it decreases not the Resistance of Water considerably, as it would do if any considerable part of the Resistance of Water arose from the Attrition or Tenacity of its Parts. And therefore the Resistance of Water arises [Pg 368] principally and almost entirely from the Vis inertiæ of its Matter ”

“ 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. ”

“ 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. ”

“ 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. ”

“ Bodies swimming upon fluids, when they move straight forwards, cause the fluid to ascend at their fore parts and subside at their hinder parts, especially if they are of an obtuse figure; and thence they meet with a little more resistance than if they were acute at the head and tail. And bodies moving in elastic fluids, if they are obtuse behind and before, condense the fluid a little more at their fore parts, and relax the same at their hinder parts; and therefore meet also with a little more resistance than if they were acute at the head and tail. ”

“ Convection.—If a vessel containing any fluid be heated at the bottom, the bottom layers become less dense than those above, producing a condition of instability. The lighter portions of the fluid rise, and the heavier portions from above, coming to the bottom, are in their turn heated. ”

“ The method of imparting energy to or deriving it from a fluid, based on adhesive and viscous action, which consists in admitting the fluid to the central or peripheral portion of a rotably arranged system and causing it to flow, under the combined action of radial and tangential forces, in a spiral path towards the periphery, or the axis, of the rotating system, as set forth. ”

“ Whenever a body is moving in a fluid, its influence becomes sensible considerably in advance of the position it happens to occupy at any instant. The particles of fluid commence to adjust themselves to the impending change with just as much certainty as if the body acted directly on the distant particles through some independent agency, and when the body itself arrives on the scene the motion of the fluid is already conformable to its surfaces. ”

“ When dealing with real liquids not entirely free from viscosity, such resistance as does exist is due, as already mentioned, to skin friction and eddy formation. In the next place, leaving the consideration of the movement of wholly submerged bodies through liquids whether perfect or imperfect, we shall proceed to discuss the important question of the resistance offered by water to the motion through it of a floating object, such as a ship or swan. We have in this case to take into consideration the wave-making properties of the floating solid. ”

“ These branches of mechanical science are of great practical importance, and a knowledge of them would save from many blunders and failures resulting from incompetence. The same laws govern in the movement of all bodies, whether solid or liquid. Hydrostatics, Hydrodynamics, Hydraulics, etc., are branches of the same science, and worthy of separate mention only because they apply the general principles of statics and dynamics to the phenomena of rest or motion in liquids. ”

“ If the vessel was so large that in different parts of it the temperature and pressure were different, the diffusion would, indeed, still be perfect, because at all ordinary temperatures and pressures hydrogen and carbonic acid gas remain gaseous. But if the vapour introduced is of such a nature that at moderate temperatures and pressures it condenses, wholly or in part, or liquefies, the diffusion will not take place with the same uniformity. We need not go further for illustration than to the case of our own atmosphere as it actually exists. ”