Waves and ripples in water, air, and æther

by Sir J. A. Fleming

Fig. 27.—The production of a vortex ring in air.

A vortex motion in water may be either a terminated vortex, in which case its ends are on the surface, and are seen as eddies, or whirls; or it may be an endless vortex, in which case it is called a vortex ring. Such a ring is very easily made in the air as follows: A cubical wooden box about 18 inches in the side has a hole 6 inches in diameter made in the bottom ([see Fig. 27]). The open top of the box is covered tightly with elastic cloth. The box is then filled with the white vapour of ammonium chloride, by leading into it at the same time dry hydrochloric acid gas and dry ammonia gas. When quite full of dense white fumes, we give the cloth cover of the box a sharp blow with the fist, and from the round hole a white smoke ring leaps out and slides through the air. The experiment may be made on a smaller scale by using a cardboard box and filling it with the smoke of brown paper or tobacco.[13] If we look closely at the smoke ring as it glides through the air, we shall see that the motion of the air or smoke particles composing the ring is like that of an indiarubber umbrella-ring fitted tightly on a round ruler and pushed along. The ring turns itself continually over and over, the rotation being round the circular ring axis line. This rotatory motion is set up by the friction of the smoky air against the edge of the hole in the box, as the puff of air emerges from it when the back of the box is thumped. A simple but striking experiment may be made without filling the box with smoke. Place a lighted candle at a few feet away from the opening of the above-described box, and strike the back. An invisible vortex ring of air is formed and blows out the candle as it passes over it. Although it is quite easy to make a rotational motion in an imperfect fluid, and in fact difficult not to do it, yet of late years a very interesting and valuable discovery has been made by Professor Hele-Shaw, of a method of creating and rendering visible a motion in an imperfect liquid like water, which is irrotational. This discovery was that, if water is made to flow in a thin sheet between two plates, say of flat glass, not more than a fiftieth of an inch or so apart, the motion of the water is exactly that of a perfect fluid, and is irrotational. No matter what objects may be placed in the path of the water, it then flows round them just as if all fluid friction or viscosity was absent.

This interesting fact can be shown by means of an apparatus designed by Professor Hele-Shaw.[14] Two glass plates are held in a frame, and separated by a very small distance. By means of an inlet-pipe water is caused to flow between the plates. A metal block pierced with small holes is attached to the end of one plate, and this serves to introduce several small jets of coloured water into the main sheet. In constructing the apparatus great care has to be exercised to make the holes in the above-mentioned block very small (not more than ¹⁄₁₀₀ inch in diameter) and placed exactly at the right slope.

The main water inlet-pipe is connected by a rubber tube with a cistern of water placed about 4 feet above the level of the apparatus. The frame and glass plates are held vertically in the field of an optical lantern so as to project an image of the plates upon the screen. The side inlet-pipe leading to the pierced metal block is connected to another reservoir of water, coloured purple with permanganate of potash (Condy’s fluid), and the flow of both streams of water controlled by taps. The clear water is first allowed to flow down between the plates, so as to exclude all air-bubbles, and create a thin film of flowing water between two glass plates. The jets of coloured water are then introduced, and, after a little adjustment, we shall see that the coloured water flows down in narrow, parallel streams, not mixing with the clear water, and not showing any trace of eddies. The regularity of these streams of coloured water, and their sharp definition, shows that the liquid flow between the plates is altogether irrotational.

The lines marked out by the coloured water are called stream-lines, and they cut up the whole space into uniform tubes of flow. The characteristic of this flow of liquid is that the clear water in the space between two coloured streams of water never passes over into an adjacent tube. Hence we can divide up the whole sheet of liquid into tubular spaces called tubes of flow, by lines called stream-lines.

If now we dismount the apparatus and place between the glass a thin piece of indiarubber sheet—cut, say, into the shape of a ship, and of such thickness that it fills up the space between the glass plates—we shall be able to observe how the water flows round such an obstacle.

If the air is first driven out by the flow of the clear water, and then if the jets of coloured water are introduced, we see that the lines of liquid flow are delineated by coloured streams or narrow bands, and that these stream-lines bend round and enclose the obstructing object.

The space all round the ship-shaped solid body is thus cut up into tubes of flow by stream-lines, but these tubes of flow are now no longer straight, and no longer of equal width at all points.

They are narrower opposite the middle part of the obstruction than near either end.