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Popular Science Monthly/Volume 39/September 1891/Views of Running Water

< Popular Science Monthly‎ | Volume 39‎ | September 1891

VIEWS OF RUNNING WATER.
By M. J. PICCARD.

IF we ask a person who has not thought about the matter to represent with a pencil, from memory, a stream or fall of water, in nine cases out of ten he will return the paper after having timidly ventured upon a few parallel scratches, looking as much as anything else like the ruts in a road or the hairs of a horse's tail. Yet we see liquids every day flowing along the gutter, and from bottles or pitchers; and we have all played near brooks and cascades. The persons who trace the parallel lines we have spoken of suppose they are representing the path traveled by the particles of water—that is, a movement, an immaterial thing which by its very nature defies all graphic representation. It is true that a luminous point in very rapid motion leaves on the retina the impression of a line. We are thus authorized to represent a flash of lightning, the course of a shell, and a gunshot; but we hesitate to resort to that artifice to represent the flight of an arrow through the air or the movement of a sword to strike. It will be well to make only a moderate use of it in representing water. In fact, these parallel lines do not exist, at least not under that form. Furthermore, lines do not show whether the stream is going to the right or to the left, or vice versa.

The effects accompanying the motion of water are, notwithstanding their extreme variety and apparent complication, subject to unchangeable hydraulic laws which it is possible to fix, with the aid of reason and experiment. Observation, even by itself, in the long run, develops an unconscious apperception in the inhabitant of the banks, whether he be fisherman, boatman, or raftsman. Special acquirements enable him to divine, according to the appearance of the surface, a thousand invisible things that are going on under the water. We do not, of course, intend to explore so vast a domain to the bottom, but to indicate how the subject may be approached, and how art and science are benefited by the investigation of it. What are the typical phenomena of running water, which, to simple sight, give rise to the impression of motion in a definite direction, and which are susceptible of being rendered graphically? Let us begin our experiments by fixing a low dam across an even-bottomed channel. Immediately above the dam the interrupted water will form a swell, on the back of which a system of fine parallel striæ may be observed. According to the depth and speed of the current, a second or several similar swells may be formed, but of lessening dimensions (Fig. 1). These are stationary swells, which we call eddy-waves or ripples.

To simplify the matter, we neglect what goes on below the dam. On the other hand, we inquire what happens when the dam is

PSM V39 D664 Eddy waves or ripples.jpg
Fig. 1.

high enough to force the formation of a small lake. We should be apt to suppose that the water would pass, gradually diminishing in speed and increasing in depth, following a regular curve, from the condition of motion to that of relative repose. This is not the case. The passage is made suddenly, with a shock. The whole system of ripples and striæ which was before immediately at the head of the dam is transferred to the place where the water of the stream strikes against the comparatively still water of the lake. Besides, the two points being possibly distant from one another, the effect, or the eddy, appears before the cause, the obstacle (Fig. 1, ii). It is in this way, by the appearance of the surface, that the raftsman going down a river can judge, from the variations of speed, of the depth of the stream, and the size and position of reefs hidden under the water, frequently a considerable distance below the point where he is. Is not this the supreme end of art—to cause to be foretold by outer forms what is going on in the domain of invisible things, and to divine the reality without laying it bare? Water lends itself eminently to this end. It obeys mechanical laws, not as a machine which exposes them bluntly and fatally, but with a variety of suggestions and a lightness that leave the field clear for the imagination.

Let us, in our experimental canal, reduce the dam to a single obstacle in the middle of the stream. The eddy-wave, instead of being straight, bends around on either side, and takes the form of a parabola with a Λ more or less open according to the velocity of the stream. Moreover, the branches of the parabola, turned back by the side-walls of the canal, if it is not too broad, take a figure below the obstacle in which the first traces of a lozenge appear (Fig. 2, iii). Lastly, let us place the obstacles on the sides

PSM V39 D665 Forms of eddy waves.jpg
Fig. 2.—Forms of Eddy-waves.

of the canal. We find that the waves are turned toward the middle of the stream, and that by intercrossing with those coming from the opposite bank, and by their own return, a system of lozenges is produced on the surface of the water (Fig. 2, iv, and Figs. 3 and 4).

In this we see the pre-eminently typical phenomenon of running water. Every inequality of the shore, whether promontory or bay, plant or pebble, stake or bridge pier, is the starting-point for centripetal lines which go on in graceful undulations to lose themselves in the stream, or, meeting with others, to form quadrilles of rhombs, often with the most charming effect. By the direction of these lines the observer divines the course of the current, and their inclination furnishes him with an exact measure of its velocity.

In the case of cascades, the greater variety of the phenomena forces us to go more into detail. We begin with an inclined vessel, glass, pot, or pail, in process of emptying. How does the surface

PSM V39 D666 System of lozenges produced by eddy waves 1.png
Fig. 3.—System of Lozenges produced by Eddy-waves.
 
PSM V39 D666 System of lozenges produced by eddy waves 2.png
Fig. 4.—System of Lozenges produced by Eddy-waves.

of the outrunning liquid look? It would be safe to wager ten to one that any person at the first instance would represent it as in Fig. 5, v, by parallel parabolic lines. We not rarely find artistic productions in this style dating from the time when they composed landscapes from fancy in their studios. Without being too severe on these errors, which are still not far away from us, we will try to do better, and to correct the faults of the figure, one at a time.

We lay aside, for the moment, the usual ribbon-like form, which is false, and examine first the question of the vertical lines. They are formed by the series, A, a, a, of points by which the same molecule of water passes (or is supposed to pass) successively. Is there any proof of their material existence? No. It must be admitted that in certain cases, like that of a thin sheet falling from a regular dam or gliding over a smooth, rock, the irregularities of the latter may produce lines in the direction of the current; but true painters make only the most moderate use of the straight line.

Are there not more grounds of resemblance between the points A and B or α and β which appertain, however, to different generators than between the points A and α of the same generator? Suppose the liquid sheet decomposed into its elementary veins; each of them is differently constituted in its several parts. At its

PSM V39 D667 Wave streams.jpg
Fig. 5.

origin it is full, uniform, and transparent; lower down it shows real or apparent swellings and contractions; and still farther down it resolves itself into distinct drops. The water-sheet should consequently have an entirely different constitution at A from that at α, but the same at A and at B. It is proper, therefore, to represent as similar, not the points of the same parabola, but those of the same horizontal range; so, in the reflection of surrounding objects, the surface at the upper part of the parabola, making a smaller angle with the horizon, would produce a different effect from that at the lower part. At A and B it would reflect chiefly the sky; at a and b, perhaps, the rocks; while at α and β it would be white and reflect nothing.

Independently of phenomena which we are still to study, and paradoxical as it may appear, we can say that, if there are bands or zones in a cascade, they are rather horizontal than vertical. Our design vi, Fig. 5, still false and incomplete in many respects, looks more like a real fall of water than the design v, Fig. 5, with which we started. By this horizontal rather than vertical disposition of the effects of light, color, and reflections, the image gains much in life and truth.

When the eye has become accustomed, by repeated observations, to the peculiarities of the liquid elements, it can at last distinguish, in each jet of any velocity, a jerking or vibratory movement, a kind of trepidation or pulsation, directed horizontally, up and down, or down and up. It was believed formerly to be an optical illusion; but instantaneous photography and other observations establish beyond a doubt that the motion of a jet of water is never continuous, but is intermittent, periodic. Design vii, Fig. 5, which represents a jet from a hydrant or fire-engine at the moment of elevating, and design viii, representing a vertical jet from a narrow hole, are schematic but faithful reproductions of numerous observations. The photographs of Figs. 6 and 7, taken from nature at the overflow of a factory flume on Sunday, when no wheel or turbine was moving, are convincing.

PSM V39 D668 Vibratory motion of falling water 1.png
Fig. 6. Vibratory Motion of Falling Water.
 
PSM V39 D668 Vibratory motion of falling water 2.png
Fig. 7. Vibratory Motion of Falling Water.

This intermittent character of the stream is due to the same cause as the sound produced by the air in blowing through a keyhole; it is produced in the same way as the wavy tufts in smoke escaping from a chimney. Water, as well as air, is elastic, but in a less degree, and differences in its pressure are propagated in waves. Ample explanations on the subject may be found in the chapters on undulations in treatises on physics; but the theory of the liquid wave is complicated, and far from being exhausted. We limit ourselves to saying that water, like air, is greatly disposed, every time the velocity of the stream is changed, by shock against a foreign body or by an abrupt contraction or enlargement of the channel, to go into vibrations and to communicate them to the walls of the orifice whence it escapes or to any object against which it strikes. Persons of delicate ear believe that they can distinguish the fundamental note of a cascade. Savart has determined the tone of a liquid vein. Another cause of discontinuity in a cascade is derived from waves in the river or the supply-basin, which, continuing into the fall, produce puffs and ripples. The phenomenon is accentuated by the resistance of the air. When, by any means, one of these jets deviates a little from the route which the one before it followed, the masses projected ahead, having to open the way, are retarded, and are then joined by those which follow them. The phenomenon is one of accumulation, like that which produces the billows on the sea-coast and the bars at the mouths of rivers, under the action of the tide. But shortly these bold spurts, rended and scattered by the same cause that produced them, the friction of the air, meet their end by being reduced to dust. When too near, the observer, engaged with a thousand details, is not struck so much as he is at a distance, by the phenomena as a whole and their periodicity. We can distinguish, then, the periodical ranges of jets which are partly transformed into spurts, and in the tumultuous rush between two rocks the bubbles or vibrations produced by the shock. The line is nowhere vertical.

When the waves coming down from the feeding-basin reach the upper edge of the cascade parallel to that edge, the bubbles are dispersed in horizontal bands. But if the wave comes down at an angle, it forms rows of inclined fringes; while, if the cascade is fed by a brook with the characteristic waves of Fig. 2 (iv), starting from both shores toward the middle, those waves will continue the same in the cascade in the shape of more or less stationary lozenges. In this case, again, we are far away from vertical parallel lines.

It is time to look more closely at the form and constitution of the liquid sheet. In Fig. 5 (v) it is represented by two parallel lines as a ribbon, such as any person not instructed would design from memory. It is in reality wholly different, as will appear from Fig. 8 (x). Let us begin at the top. Immediately at the opening of the flow, from the moment when it is wholly abandoned to itself, the sheet begins to narrow and take the form of a triangular tongue, pointed below. Let us, before we go further, look into the cause of this first change of form. When we make the experiment with an inclined cylindrical vessel, as in Fig. 5 (v), our inclination is at first to attribute the contraction to the oblique centripetal direction communicated to the lateral molecules by the elliptical form of the surface of the water in the interior of the vessel. This explanation is insufficient, for the sheet escaping from a tube, a canal, or a prismatic vase with parallel sides, assumes the same form Figs. 8 (x), 13, 14, 15, 16, and 17. The explanation that next suggests itself depends on the acceleration of velocity during the fall, which should have as a necessary result a progressive diminution of the section-surface. It may be proved PSM V39 D670 Form and constitution of a liquid sheet falling.jpgFig. 8.—Form and Constitution of a Liquid Sheet falling. experimentally that this has nothing to do with the triangular form by giving an upward direction to the jet from a flattened tube; the stream takes the form of a tongue all the same (Fig. 10).

Is it because the lateral parts of the liquid ribbon, having to overcome in the canal or the tube a more considerable friction than in the central part of the current, have at their issue a less mean velocity than the latter, and are therefore attracted by them? The effect incontestably exists; but we shall demonstrate, when we come to speak of the liquid vein, that it is negligible in comparison with another cause. After trying these various causes and eliminating them one after the other, we are brought to the conclusion that the essential cause that draws toward the middle the edges of a liquid sheet falling freely is the force of cohesion, or capillary tension. It is the same force that causes a freely suspended liquid mass to take the spherical form, as in Plateau's, well-known experiment, and in the world of the stars. It is only in this state of least surface that the attractions between the molecules

PSM V39 D670 Tongue like form of a water jet squirting from a flattened tube.jpg
Fig. 9. Fig. 10.—Tongue-like Form of a Jet of Water spurting from a Flattened Tube.

are in equilibrium. A falling liquid sheet will, therefore, tend toward a cylindrical or contracting form. Does it really become a cylinder and keep the form? What takes place lower down? These questions require knowledge of other peculiarities of the primary tongue.

When water is subjected to a shock or to pressure, the pressure does not distribute itself insensibly through all the mass with gradual diminution. We have already shown this in the formation of swells by changes of slope in streams. We have another experiment. Slowly close a faucet till the liquid vein flows in a mere thread (Fig. 11, xv). The orifice in this case being perfectly cylindrical, the contraction is due on one side to the adherence of the liquid to the sides of the hole, and on the other side to acceleration, and takes place equally in all directions. Intercalate a solid body or a liquid surface at a few centimetres from the hole. The pressure at the base of the column augmenting by resistance, we might expect the vein to take the continuous form of two reversed cones (Fig. 11, xvi). It does not, but takes the form of swellings, of knots regularly placed, which give the vein the appearance of a chaplet (Fig. 11, xvii). This phenomenon, interesting as a case of PSM V39 D671 Varying flow characteristics.jpgFig. 11. action at a distance, and also as a case of vibrating action, has been observed by Savart and is described by him in the second of his memoirs. What the pressure caused by shock produces here, the pressure caused by cohesive attraction (capillary pressure or superficial tension) produces on the edges of the liquid sheet: a series of knots is formed. The section of the jet loses the form of the hole as soon as it leaves it, but the increase of thickness at the expense of breadth does not take place continuously; the central sheet is still thin and even, while the edges are already transformed into thick cords followed by other smaller ones. It is the same system of swells and ripples that we met before. The striæ of one side cross those of the other side, and the tongue is covered with a system of lozenges producing a very pretty effect (Fig. 8, x, and, in section, xviii).

Now that we know the details of the form and constitution of the upper part of the liquid sheet, let us see what occurs lower down. On issuing from the canal, the lateral molecules of the sheet are subjected to the action of a component of horizontal centripetal velocity which turns them toward the middle. The particles in the middle, on the other hand, thrown toward the outside, acquire also a horizontal component, but centrifugal (Fig. 8, xiv). The point of stable equilibrium is where the jet has a cylindrical form. But there are various things to be observed.

As the rope-walker does not cease oscillating when he reaches the point of stable equilibrium, but by virtue of his inertia goes as far beyond it on the other side, so the horizontal oscillation of the molecules of water, repeating itself, produces a new sheet in a plane perpendicular to the first one, but this time in the form of a double tongue—that is, of a disk or lentil. The phenomenon repeating itself anew, a second contraction is followed by a new disk in the same plane as the first tongue, and so on; the disks alternating in the two vertical planes of breadth and depth, as in a paper fidibus. In the photographs reproduced in Figs. 16 and 17, a mirror fixed at an angle of 45° in the vertical plane gives, besides the front view of the vein, its image as seen in profile. A mechanical demonstration can be given of the movement of which the vein is the seat by a parallelogram of basket-work, which we press upon while holding it horizontally, and making it pass, by alternate compression of the extremities, from the oblong to the square shape, and then to the oblong the other way, return to the square, etc. The example of the fidibus is not quite exact. We comprehend at first that, in consequence of the acceleration, the disks will continue lengthening and deviating more and more—we can easily distinguish eight of them, sometimes twelve or more—till at last the molecules of water yielding to this dissociating action of weight group themselves in little cohesion-drops. There is another difference, in that the disks are not superposed as in the fidibus, but are boxed into one another—that is, one begins to form by deviation before the preceding one has done contracting. This is the necessary consequence of a third difference: that the disks are not plainly flat, but are thin in the middle, like the primitive tongue from which they are derived, and are flanked by thick cords on the edges (Fig. 8, xviii). We can, therefore, regard each disk as formed by the shock of the two cords of the disk above it. If this shock is exerted in a horizontal plane, the PSM V39 D672 Flow shapes of various constraints.jpgFig. 12. new disk will spread out equally in every direction, having its center at the point of the shock. Acceleration becoming a factor, the spreading is prolonged farther down than up; the disk is thrown out of center, but does not for that cease to encroach upon its predecessors. The case is like that of the links of a chain, which enter within one another. Nowhere, then, not even at the point of minimum surface, can the jet be cylindrical; at the minimum, it assumes the form of a rounded cross (Fig. 8, xix).

Thus we find that, in the phenomenon so simple in appearance of a fall of water, all the complications that arise one after another under the fullest examination are explained logically down to the most minute details. We can already draw one important conclusion: every mass of falling water, if it is not rigorously cylindrical and vertical in its origin, becomes necessarily the seat of horizontal oscillations—independently of the vertical vibrations which were first considered. Not a single molecule of which the

PSM V39 D673 Liquid sheet forms escaping from a parallel walled vessel.jpg
 
Fig. 13. Fig. 14. Fig. 15.
Instantaneous Photographs showing the Form of Liquid Sheets escaping from a Canal or from a Prismatic Vessel with Parallel Walls.

mass is composed follows a straight or parabolical line in its fall. All, without exception, describe a sinuous or zigzag course. Such is the general phenomenon. Let us follow out some of its details. PSM V39 D673 Reflection of escaping liquid veins at 45 degrees.jpgFig. 16.Fig. 17. Escaping Liquid Veins and their Profiles, as shown by Reflection at 45° in the Vertical Plane. For the jet to be rigorously cylindrical in its origin is not a sufficient condition of its preserving that form. When it issues horizontally in full gush from a fountain, the parabolic trajectories, upper and lower, lose their parallelism and cause by approaching one another a flattening of the jet. From this fact arise horizontal undulations, only slightly marked, it is true, but which suffice, if the light is favorable, for producing the illusion of swellings and contractions (Fig. 12, xxi). Even When a liquid Vein issues vertically from the bottom of a vessel by a circular hole, it assumes a helicoidal form in consequence of a motion of rotation which develops gradually within the vessel. This is independent of the vertical vibrations, of which the bottom of the vessel becomes the seat, and which it communicates to the whole jet.

The tongue-shaped sheet is bordered on its outer edge, as we have already shown, by swellings or cords, when everything is rigorously symmetrical; these two cords, meeting at the base of

PSM V39 D674 Cords formed on the edges of liquid tongues.jpg
Fig. 18.—Instantaneous Photograph showing the Cords formed on the Edges of Liquid Tongues, as is seen in Fig. 14.

the tongue and flattening against one another, form a second sheet in a plane perpendicular to the former one—and so on. But when, for any reason, on account of the slight inclination of the canal, for example, it happens that the two cords do not exactly meet, one passes before the other, and one of two things may result. They will either roll up upon one another like a corkscrew and

PSM V39 D674 Tremulousness of cascades of broad sheets.jpg
Fig. 19.—Photograph showing the Tremulousness peculiar to Cascades with Broad Sheets.

follow a helicoidal course (Fig. 12, xxii, and 13), or else, by some trifling cause they will miss, and, lanced in opposite directions, without regarding the thin median sheet that connects them, they will go each to its own side, never to find one another. The primary sheet is cut into two veins, which, losing trace of their common origin, remain definitely separated (Fig. 14).

When the sheet is very shallow and very wide, like that which spreads over a river dam, insignificant inequalities at the dam are enough to provoke a division into many distinct sheets. Consider two of these near one another (Fig. 12, xxiii). It may happen that cord a of the left arc and cord c of the right arc, coming very near to each other, join; thus are united molecules of water which an instant before had come out of the sluiceway at a considerable distance apart. Inversely, two molecules, neighbors till then arrived together at the same point b of the dam, are separated, one passing by b1, the other by b2 to reach the bottom widely separated. So also with the molecules a1 and a2. In the most regular fall, not a single molecule reaches the bottom by the most direct way. The same molecules which were traveling parallel in the bed of the canal, quietly keeping alongside of one another, seem, as soon as they reach the dam, to be suddenly taken with a frantic thirst for liberty, throwing themselves to the right and the left, joining, separating, and joining again; it is a go and come that never ceases till they find themselves newly imprisoned in the bed of a brook. Hence the serpentine course of the threads of water, the sparkling, the tremulousness which are common to cascades with broad sheets, and constitute their charm. The photographic reproductions (Figs. 18 and 19) represent, as well as can be done graphically, most of the characteristics which we have just described.

This is what occurs normally, under the influence of weight, cohesion, and inertia. When water runs out from a regular orifice, or over a horizontal dam, how complicated everything becomes when these conditions of regularity are not fulfilled, or when other forces come into play! One force that plays an important part in this matter is adherence between the molecules of the water and the walls of the vessel. This it is which often causes a liquid to follow a different way from that which is mechanically pointed out to it by inertia, weight, and cohesion. It then springs out into prohibited roads; instead of going to the cup held out to receive it, it chooses to follow the rim of a bottle and to spatter itself over the white cloth. Instead of precipitating itself into the pool with its companions, some capricious vein allows itself to be tempted by a nothing, to glide along a wall of rocks, and to trace those silvery threads which are often more graceful than the cascade itself. Yet adherence is a physical force, the effects of which may be foreseen and calculated up to a certain point. There are other factors, varying infinitely, but also calculable, which constitute, we might say, a part of the cascade, and contribute to impress a special, individual character on it—its height, the larger or smaller mass of water, the nature of the bed and the form of the opening through which the water escapes, the shape of the rocks over which it flows or against which it rebounds. Each stream of water has its own life. Pagans have personified rivers by surrounding their sources and their shores with divinities. To us, also, the torrent and its cascades are the soul of the valley.

And yet there is another and a foreign force that plays havoc with all our calculations—the wind. "Then, in the air, there are endless assaults between the coquettish sylph and the rogue who pursues her. Sometimes he seizes her of a sudden and carries her off with a puff to drop her as abruptly; sometimes he entices her and plays a thousand tricks upon her; then he grows bolder, embraces her, and makes her dance upon herself with a giddy velocity; and often he takes her so well on the wing that, like a flight of little floating clouds, she whitens in the distance in space. But soon the brook is formed again; it undulates and balances itself like a waving scarf, while all around a thousand limpid threads glide along the rock, and make a joyous court of falls in miniature to the green cascade."—Translated for The Popular Science Monthly from the Revue Scientifique.