Current (fluid dynamics)

“ If the positions of these partitions are so adjusted that the volumes of flow in all the elementary streams are equal, they represent to the mind the velocity as well as the direction of motion of the particles in different parts of the current, for the velocities are inversely proportional to the cross sections of the elementary streams. No actual fluid is devoid of viscosity, and the effect of viscosity is to render the motion of a fluid sinuous, or rotational or eddying under most ordinary conditions. ”

“ The motion at any instant of every part of the fluid, single vortex tube is knotted on itself, it can never become untied. (6.) The motion at any instant of every part of the fluid, including the vortex rings themselves, may be accurately represented by conceiving an electric current to occupy the place of each vortex ring, the strength of the current being proportional to that of the ring. The magnetic force at any point of space will then represent in direction and magnitude the velocity of the fluid at the corresponding point of the fluid. ”

“ And since the weight of the vapors which ascend must continually equal that of the products of condensation which are falling, it is further evident that the upward currents, rushing through contracted channels, must move with enormous velocity, and therefore, of course, that the pressure and temperature must rapidly increase from the free surface downward. ”

“ This however, would be the amount of accumulation to produce an equilibrium of the forces at the surface, but as this accumulation would then produce greater pressure there upon the bottom than towards the poles and at the equator, it would produce, as in the case of the atmosphere, a flowing out from beneath this accumulation towards the poles and the equator, and settling down of the surface above, below the state of equilibrium, sufficient to cause a counter-current at the surface from the poles and the equator to supply the currents below. ”

“ The water at the head of a weir is passing every instant from slower into quicker motion; but (until broken in the air) the fast flowing water is just as dense as the slowly flowing water. But a fan alternately compresses and rarefies the air between it and the cheek, and the violence of a destructive gust in a gale of wind means a momentary increase in velocity and density of which I cannot myself in the least explain,—and find in no book on dynamics explained,—the mechanical causation. ”

“ 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. ”

“ The downward flow at the area of high pressure compresses the air near the surface of the earth and rarefies it in the higher regions of the atmosphere, while the opposite effect is going on over the center of low pressure, the air being rarefied nearer the surface of the earth, but condensed above normal in the higher regions by the upward current, which causes an overflow back toward the rarefied upper regions over the area of high pressure. ”

“ Also of a low barometer.—But, be that as it may, the air which these vapour-bearing winds—vapour-bearing because they blow over such an immense tract of ocean—pour into this stopping-place has to ascend and flow off as an upper current, to make room for that which is continually flowing in below. In ascending it expands and grows cool, and, as it grows cool, condensation of its vapour commences; with this, vast quantities of latent heat, which converted the water out at sea into vapour for these winds, are set free in the upper air. ”

“ Disturbed equilibrium is the great cause of oceanic currents. Heat and cold are the chief agents in creating this disturbance.
It is obvious that when a portion of water in any vessel sinks, another portion must of necessity flow into the space which it has left, and if the cause which induced the sinking continue, so the flow to fill up will continue, and thus a current will be established.
Heat at the equator warms the sea-water, and makes it light; cold at the poles chills it, and makes it heavy. Hot water, being light, rises; cold water, being heavy, sinks. ”

“ The forenoon maximum is conceived to be due to the rapidly increasing temperature, and the rapid evaporation owing to the great dryness of the air at this time of the day, and to the increased elasticity of the lowermost stratum of air which results therefrom, until a steady ascending current has set in. As the day advances, the vapour becomes more equally diffused upwards through the air, an ascending current, more or less strong and steady, is set in motion, a diminution of elasticity follows, and the pressure falls to the afternoon minimum. ”

“ In black smoker systems, this can result in pressure fluctuations that are a factor of ∼4×102 greater than those generated by turbulent shear in a uniform flow [7] . Thus pressure perturbations generated by this source mechanism may equal ∼2.4 Pa, which is similar in magnitude to the pressures measured near Sully and Puffer (Table 1) , and suggests that fluid heterogeneity may play a role in sound production in these vents.
Mass flux variations at the vent orifice caused by pulsating flow can produce monopole acoustic radiation [20] , [21] . ”

“ 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′. ”

“ Causes of Ocean Currents The primary generating forces are wind and differences in water density caused by variations in heat and salinity Currents generated by these forces are modified by such factors as depth of water, underwater topography including shape of the basin in which the current is running, extent and location of land, and deflection by the rotation of the Earth. ”

“ On examining the matter in greater detail, it is evident that the form of the dead water region is determined primarily by the dynamics of the live stream, and if the fluid be supposed frictionless the dead water will extend indefinitely rearward, and its pressure will throughout be uniform. If now we take into account the effects of viscosity there will be a frictional or viscous drag acting tangentially at the surface of discontinuity between the dead water and the live stream, and referring to Fig. ”

“ The results also indicate that when the current is at its maximum the surface flow is faster than at any depth below it, but when at its minimum the velocity at a depth of 15 fathoms or even down to 65 fathoms is greater than at the surface, and that there is at times a current running south along the bottom in all parts of the stream except on the extreme eastern side. ”

“ We may conceive that a current is induced from or to the surrounding space by the rarefaction or condensation attending the transmission of such a current along a wire, and that rotation should follow, just as a bent pipe full of small holes at the lower end, and immersed in water as a syphon, will generate a vorticose motion in the water ”

“ Precisely as when a spring has been bent one way, it flies not back only, but beyond the mean position, till it is almost equally bent the other way, so the current of air which rushes in towards a place of unduly diminished pressure does more than restore the mean pressure, so that presently a return current carries off the excess of air thus carried in. ”

“ It is not probable that the subject of heat transfer in boilers will ever be on any other than an experimental basis until the mathematical expression connecting the quantity of fluid which will flow through a channel of any section under a given head has been found and some explanation of its derivation obtained. Taking the simplest possible section, namely, a circle, it is found that at low velocities the loss of head is directly proportional to the velocity and the fluid flows in straight stream lines or the motion is direct. ”

“ The meeting of these upper currents produces an accumulation of atmosphere from under which the air flows out in both directions on account of the increased pressure; a strong and steady current, as we have seen, towards the equator, and another not so strong and somewhat variable over the middle latitudes, towardg the poles, having at the same time an eastern motion, and producing what are called the passage-winds. ”

“ Having found the relation between the velocities of the vortices and the electromotive forces when the centres of the vortices are at rest, we must extend our theory to the case of a fluid medium containing vortices, and subject to all the varieties of fluid motion. If we fix our attention on any one elementary portion of a fluid, we shall find that it not only travels from one place to another, but also changes its form and position, so as to be elongated in certain directions and compressed in others, and at the same time (in the most general case) turned round by a displacement of rotation. ”

“ According to this theory, all storms are produced by an ascending current of warmer atmosphere above by means of the caloric given out of the vapor which is condensed as it ascends to colder regions above. Therefore, as long as this ascending current can be supplied with air saturated with vapor this continual rarefaction must take place, and also the ascent of the air from all sides to supply its place. If, then, all the lower stratum of atmosphere over a large district were saturated with vapor, without some disturbing cause, it might remain undisturbed ”

“ But we have pointed out that if the rate of cooling as we ascend in the still air is less than the rate at which an ascending current will be dynamically cooled, such a rising current will come to rest. If, on the other hand, the rate of cooling in the ascending current be less than in the still air, the equilibrium will be unstable, and a violent uprush will result. ”

“ Burning the coal on a voyage has the reverse effect on a steamer.
Hydrodynamics
20. In considering the motion of a fluid we shall suppose it non-viscous, so that whatever the state of motion the stress across any section is normal, and the principle of the normality and thence of the equality of fluid pressure can be employed, as in hydrostatics. The practical problems of fluid motion, which are amenable to mathematical analysis when viscosity is taken into account, are excluded from treatment here, as constituting a separate branch called “hydraulics” (q.v.) ”

“ The equation of state for hydrothermal fluid at high temperatures and pressures predicts a significant volume decrease when this fluid mixes and exchanges heat with ambient seawater [18] . This process will produce monopole acoustic radiation with the source located in the jet mixing region some distance above the vent orifice. To the best of our knowledge, this sound source mechanism has not been investigated, thus there is no theory to quantify the magnitude of the pressure perturbations it may generate. ”

“ It is true that, in the present state of our information, we can not tell why this “rain dust” should not be gradually precipitated from this upper current, and descend into the stratum of trade winds, as it passes from the equator to higher northern latitudes; neither can we tell why the vapor which the same winds carry along should not, in like manner, be precipitated on the way ”

“ But his reasoning seems to be confined to the conduction of heat through solid bodies; and the conditions of the problem are wholly altered when we reason about a fluid nucleus, as we must do if it be assumed that the heat augments from the surface to the interior, according to the rate observed in mines. For when the heat of the lower portion of a fluid is increased, a circulation begins throughout the mass, by the ascent of hotter, and the descent of colder currents. ”

“ Thus the forces that are conspiring to increase the energy of the storm are powerfully assisted by the presence and condensation of aqueous vapor, and the increasing updraught and rarefaction are at once marked by the decreasing barometric pressure at the center. ”

“ A few words will indicate the magnitude of the forces which are called into silent and comparatively unobserved operation in the atmosphere by the sun's heat in the production and recondensation of aqueous vapor. It has, as I noticed, been estimated that on the average five feet of water falls annually as rain over the whole earth. Supposing that condensation takes place at an average height of 3,000 feet above the surface, the force of evaporation must be equivalent to a power capable of lifting five feet of water, over the whole surface of the globe, 3,000 feet during the year. ”