Popular Science Monthly/Volume 5/July 1874/The Hydraulics of Great Rivers
|THE HYDRAULICS OF GREAT RIVERS.|
AN important advance in our knowledge of hydraulics has been recently effected through the observations of M. Révy, a member of the Institute of Civil Engineers of Vienna, on the great rivers of Paraná and Uruguay in South America. The results of his observations have just been published in England, in a book entitled "The Paraná, the Uruguay, and the La Plata Estuaries," an excellent account of which appears in the April number of the Edinburgh Review from which the following statement is derived. Before giving the details and results of M. Révy's observations, it is advisable to furnish a brief description of the character and appearance of the streams observed.
The La Plata is simply an estuary or arm of the sea into which empty the Uruguay and the Paraná. It trends in a northwesterly direction, is 70 miles wide at its mouth, and 150 long to the mouth of the Uruguay. Higher up still it loses itself in the Paraná Guayaza and the Paraná de las Palmas, embouchures of the Paraná proper, which branches 72 miles above to form a delta. The Uruguay and the Paraná are the main arteries of the vast basin formed by the Andes on the west, the mountain-chain which runs parallel with the Atlantic Ocean on the east, and on the north by the great range of Cordilleras which stretch directly across the South American Continent at the fifteenth parallel of south latitude. Their water-shed is the southern slope of these Cordilleras, while that of the Amazon is the northern slope. Of the two rivers, the Paraná is much the larger, being second only to the mighty Amazon in size. It maintains an almost uniform width of three-fourths of a mile to a mile, and a depth of 50 to 70 feet for 852 miles, in a comparatively direct line from its mouth to the confluence of the Paraguay. Above this point it is not navigable except for small vessels, at certain seasons of the year; but the Paraguay, which is undoubtedly entitled to be considered the main stream, is navigable for 1,000 miles farther. The banks of the Paraná Guayaza rise only about two feet above the water, but are of firm soil. They are covered with dense forests of a glossy-leaved tree called sieba, somewhat resembling the laurel, and a thick undergrowth of rushes. The scenery retains this general character for 98 miles, where a bluff is sighted on the right or southwest bank of the river. About ten miles higher up, the river rushes with great force through the Straits of Obligado, a pass between two steep bluffs, about half the regular width of the river apart. At this point the stream is 150 feet deep. Excepting at this place, the left bank of the river is formed by an immense, low swamp, from 15 to 30 miles in width, for 253 miles from the mouth, while the right bank, for 100 miles above the straits, is formed by the high table-land of Buenos Ayres. The first cataract of the Paraná occurs about 150 miles above the confluence of the Paraguay, and it is this which renders the upper part of the river unnavigable, except for small vessels, during the floods which annually occur. About 550 miles above this cataract are the Falls of Guaira. These are not perpendicular, as Niagara, but inclined at an angle of about 50° from the horizon, with a fall of 50 feet. Above the falls, the Paraná is 4,500 yards wide, from which it suddenly contracts between granite walls 70 to 80 yards apart. Into this pass the water rushes with such tremendous fury, that clouds of spray arise and fall in perpetual rain over the neighborhood; the roar is such that no other sound can be heard, and the listener is made deaf by the thunder; even the very earth trembles, so that it has become desolate.
The Uruguay, a great river by itself, is almost insignificant in comparison. At the mouth, its channel is broad and deep, but at 200 miles above it dwindles into a torrent six feet deep, flowing through a rocky pass 145 feet wide. It is, however, subject to floods in September and October, during which it rises at the rate of three feet per day to 50 feet above the usual low-water line. At this time, the volume of the river is greatly increased by enlargement of the waterways, and a more than tenfold increase in the velocity of the current, which, at ordinary times, is about five miles per hour in the pass described.
The Paraná, on the other hand, although, as we have already seen, similarly subject to an annual overflow, displays nothing like the violent fluctuations of supply belonging to the Uruguay. M. Révy tells us that the ordinary annual rise at Rosario, 189 miles from the mouth of the Paraná Guayaza, where the river is about three-fourths of a mile wide, is 12 feet, and that the flood-level is always maintained for three months. The river occasionally rises to 24 feet above the low-water line, but this is rare, and its low-water supply never falls below half the volume of the ordinary flood. At a point near Rosario, where the river is 4,787 feet wide, a series of measurements has been made by M. Révy, which constitutes the largest measurement of a river section yet effected. "The depth increases by a gentle and regular slope, from that of a few inches, on the left shore, to 72 feet, at a distance of about 1,100 feet from the right bank. Thence it rapidly shallows to about 12 feet, and then rises gradually to the foot of a vertical cliff, forming the right-hand shore of the river." These measurements were made in January, when the river was at low water. The average depth was 471⁄2 feet, and the greatest 72 feet, while the sectional area measured 184,858 feet. The same section, during the ordinary flood, gives a measurement of 243,000 feet, or a little less than one-third greater. This, however, does not give an adequate idea of the increase in volume, as, at the height of the flood, the left bank of the river is submerged for many miles. The flow, independent of the escape over the marshes, is estimated, according to M. Révy's data, as 40,000,000 metric tons per hour at low water, 83,000,000 at the ordinary flood, and 169,000,000 at the occasional extraordinary floods.
The velocity of a river depends upon the inclination or fall of its course, and its surface velocity can be ascertained by determining the rate of that fall per mile, and vice versa we can ascertain the inclination by measurement of the surface velocity. But, as every one who has stirred up the bottom of a brook has observed, the surface-current flows faster than the under-current. The particles of sand at the top of the water are always carried some distance beyond those at the bottom. This retardation of the under-current is caused by the friction of the water against the bottom and sides of the brook. While therefore, it is easy to measure the velocity of the surface-current, it is difficult, because of this retardation beneath, to determine the mean velocity or actual flow of the river. This has never been satisfactorily done before. Many experiments, with a view to the accomplishment of this end, have indeed been made by eminent men, but they have failed to establish the relationship between the depth of the stream and the velocity of the flow. M. Révy has established that the velocity of a river is directly proportionate to its depth, diminishing or increasing therewith. "Thus if a shoal occurs in the middle of a channel, the velocity of the current over the shoal is less than that of the deeper water on either side; and this diminution of speed is proportionate to the loss of depth. So direct is this relation, that a plan of the surface velocities, if projected on an appropriate scale, coincides very closely with the section of the bottom of the river. Any want of parallelism between the two curves is capable of explanation either by the curvature of the banks, or by some physical irregularity of the channel." It was determined by actual experiment that the greatest velocity of current is at the surface and the least at the bottom, and that the increase of velocity "is in the simple ratio of the distance from the bottom." This decides that the mean velocity of a stream is to be found at half its depth. A result perfectly consistent with the previously expressed law that surface velocity is proportionate to depth, it is in fact a corollary, and one that was verified by experiment.
For determining the velocity of a stream, M. Révy employed an instrument called the current-metre. This consisted of a propeller-like wheel attached to a long axle and made to turn with rapidity when immersed in a running stream. The wheel is fastened to a kind of rudder which keeps it always against the stream. The upper end of the axle moves a set of cogs which turn a couple of indices upon a dial-plate. M. Révy is not the inventor of the instrument, but he improved it so as to greatly increase its utility. He first ascertained the correct reading of the metre by moving it through still water, and next made an extensible addition to the axle, so that the instrument could be adjusted to any depth.
An interesting verification of M. Révy's discoveries with regard to the velocity of currents was unexpectedly made. "In two successive measurements of the current of the La Plata, he found that there was a decrease of surface velocity and an accompanying increase of lower velocity. This at first seemed to contradict his previously-obtained results, but on further examination it was discovered that the depth at those points was sixteen inches greater. The water was banked up by its own mass so that the surface fall was less than at the point of previous measurements. "In obedience to known hydraulic law, this decreased surface-inclination was indicated by decreased velocity of surface-current. But the power of the whole moving mass was greater in proportion to its depth. And thus, while to the superficial gaze the velocity was less, the mean velocity was greater; and the river swept with more resistless energy over its bed. This luminous observation is the opening of an entirely new chapter in hydraulic science. It is, in fact, a case of the law of relation of speed to depth; but it is one that could scarcely have been arrived at by theory; although, now that it is experimentally ascertained, its theoretic reason is ascertainable."
These results, of course, require further verification elsewhere, but they cannot fail to be of the highest value both to experimental and practical science, for they will at any rate furnish method, and give new impetus to hydraulic investigation. Should they be verified, and they probably will be, it will follow that wherever water-power is desired, as in mill-races, or abundance of water-supply, as in aqueducts, depth of way should be secured at the expense of breadth.
And again, they will render valuable aid to the science of meteorology. We have as yet no knowledge of the constants of evaporation from water-surfaces. On this point the Edinburgh Reviewer remarks: "An unusually favorable opportunity now presents itself for the actual determination of the most steady and remarkable case of evaporation that occurs on the surface of our planet. In its headlong course from the foot of Hermon, the Jordan (well named the descender) may almost be said to consist of three continuous cataracts, divided by two lakes and terminating in a third. From the surface of that bituminous sea, the whole supply brought down by the Jordan and its affluents is exhaled in invisible vapor. By an accurate measurement of the volume discharged by the Jordan, we shall be furnished with evaporative data of the highest value."