Thus, for a chariot des Messageries Générales, on a pitched road, the experiments gave A = 0.0117 × 0.00361 (V2); while, with the springs wedged so as to prevent their action, the experiments gave, for the same carriage, on a similar road, A 0-02723 × 0.01312 (V2). At a speed of nine miles per hour, the springs diminish the resistance by one-half. = The experiments further showed that, while the pitched road was inferior to a solid gravel road when dry and in good repair, the latter lost its superiority when muddy or out of repair. INFLUENCE OF THE INCLINATION OF THE TRACES. The inclination of the traces, to produce the maximum effect, is given by the expression A × 0.96 fr in which h the height of the fore extremity of the trace above the point where it is attached to the carriage; b = the horizontal distance between these two points. is the radius of interior of the boxes, and r the radius of the wheel. The inclination given by this expression for ordinary carriages is very small; and for trucks with wheels of small diameter it is much less than the construction generally permits. It follows, from the preceding remarks, that it is advantageous to employ, for all carriages, wheels of as large a diameter as can be used, without interfering with the other essentials to the purposes to which they are to be adapted. Carts have, in this respect, the advantage over wagons; but, on the other hand, on rough roads, the thill horse, jerked about by the shafts, is soon fatigued. Now, by bringing the hind wheels as far forward as possible, and placing the load nearly over them, the wagon is, in effect, transformed into a cart; only care must be taken to place the centre of gravity of the load so far in front of the hind wheels that the wagon may not turn over in going up hill. ON THE DESTRUCTIVE EFFECTS PRODUCED BY CARRIAGES ON THE ROADS. If we take stones of mean diameter from 2 to 3 inches, and, on a road slightly moist and soft, place them first under the small wheels of a diligence, and then under the large wheels, we find that, in the former case, the stones, pushed forward by the small wheels, penetrate the surface, ploughing and tearing it up; while in the latter, being merely pressed and leant upon by the large wheels, they undergo no displacement.. From this simple experiment we are enabled to conclude that the wear of the roads by the wheels of carriages is greater the smaller the diameter of the wheels. Experiments having proved that on hard grounds the traction was but slightly increased when the breadths of the wheels was * En empierrement. diminished, we might also conclude that the wear of the road would be but slightly increased by diminishing the width of the felloes. Lastly, the resistance to rolling increasing with the velocity, it was natural to think that carriages going at a trot would do more injury to the roads than those going at a walk. But springs, by diminishing the intensity of the impacts, are able to compensate, in certain proportions, for the effects of the velocity. Experiments, made upon a grand scale, and having for their object to observe directly the destructive effects of carriages upon the roads, have confirmed these conclusions. These experiments showed that with equal loads, on a solid gravel road, wheels of two inches breadth produced considerably more wear than those of 41 inches, but that beyond the latter width there was scarcely any advantage, so far as the preservation of the road was concerned, in increasing the size of the tire of the wheel. Experiments made with wheels of the same breadth, and of diameters of 2.86 ft., 4.77 ft., and 6.69 ft., showed that after the carriage of 10018-2 tons, over tracks 218.72 yards long, the track passed over by the carriage with the smallest wheels was by far the most worn; while, on that passed over by the carriage with the wheels of 6.69 ft. diameter, the wear was scarcely perceptible. Experiments made upon two wagons exactly similar in all other respects, but one with and one without springs, showed that the wear of the roads, as well as the increase of traction, after the passage of 4577-36 tons over the same track, was sensibly the same for the carriage without springs, going at a walk of from 2-237 to 2-684 miles per hour, and for that, with springs, going at a trot of from 7.158 to 8.053 miles per hour. HYDRAULICS. THE DISCHARGE OF WATER BY SIMPLE ORIFICES AND TUBES. THE formulas for finding the quantities of water discharged in a given time are of an extensive and complicated nature. The more important and practical results are given in the following Deduc tions. When an aperture is made in the bottom or side of a vessel containing water or other homogeneous fluid, the whole of the particles of fluid in the vessel will descend in lines nearly vertical, until they arrive within three or four inches of the place of discharge, when they will acquire a direction more or less oblique, and flow directly towards the orifice. The particles, however, that are immediately over the orifice, descend vertically through the whole distance, while those nearer to the sides of the vessel, diverted into a direction more or less oblique as they approach the orifice, move with a less velocity than the former; and thus it is that there is produced a contraction in the size of the stream immediately beyond the opening, designated the vena contracta, and bearing a proportion to that of the orifice of about 5 to 8, if it pass through a thin plate, or of 6 to 8, if through a short cylindrical tube. But if the tube be conical to a length equal to half its larger diameter, having the issuing diameter less than the entering diameter in the proportion of 26 to 33, the stream does not become contracted. If the vessel be kept constantly full, there will flow from the aperture twice the quantity that the vessel is capable of containing, in the same time in which it would have emptied itself if not kept supplied. 1. How many horse-power (H. P.) is required to raise 6000 cubic feet of water the hour from a depth of 300 feet? A cubic foot of water weighs 62.5 lbs. avoirdupois. 6000 × 62.5 60 6250 × 300 Then = = 1875000 6250, the weight of water raised a minute. 1875000, the units of work each minute. = = 56-818 the horse-power required. 2. What quantity of water may be discharged through a cylindrical mouth-piece 2 inches in diameter, under a head of 25 feet? of a foot; .. the area of the cross section of the mouth-piece, in feet, is 1 1 X × 7854·021816. 6 6 Theory gives '021816 ✓2 g × 25 the cubic feet discharged each second; but experiments show that the effective discharge is 97 per cent. of this theoretical quantity: g = 32.2. Hence, 97 x 02181664.4 x 2584912, the cubic feet discharged each second. ·84912 × 62.5 = 53.0688 lbs. of water discharged each second. Effluent water produces, by its vis viva, about 6 per cent. less mechanical effect than does its weight by falling from the height of the head. 3. What quantity of water flows through a circular orifice in a thin horizontal plate, 3 inches in diameter, under a head of 49 feet? Taking the contraction of the fluid vein into account, the velocity of the discharge is about 97 per cent. of that given by theory. The theoretic velocity is 2g x 497 √6·44 = 56·21. .97 x 56-2154-523 the velocity of the discharge. The area of the transverse section of the contracted vein is '64 of the transverse section of the orifice. 25, and (25) x 78540490875 area of orifice. •. •64 × 0490875 = of the contracted vein. 031416, the area of the transverse section = Hence, 54-523 x 031416 1.7129, the cubic feet of water discharged each second. The later experiments of Poncelet, Bidone, and Lesbros give 563 for the coefficient of contraction. Water issuing through lesser orifices give greater coefficients of contraction, and become greater for elongated rectangles, than for those which approach the form of a square. Observations show that the result above obtained is too great; of this result are found to be very near the truth. 4. What quantity of water flows through a rectangular aperture 7.87 inches broad, and 3.94 inches deep, the surface of the water being 5 feet above the upper edge; the plate through which the water flows being 125 of an inch thick. 5 and 5.32833 are the heads of water above the uppermost and lowest horizontal surfaces. The theoretical discharge will be 2 g × ·65588 √2 g ((5·328) — (5)) = 3.9268 cubic feet. Table I. gives the coefficient of efflux in this case, 615, which is found opposite 5 feet and under 4 inches; for 3.94 is nearly equal 4. 3.9268 x 615 = 2.415 cubic feet, the effective discharge. 5. What water is discharged through a rectangular orifice in a thin plate 6 inches broad, 3 inches deep, under a head of 9 feet measured directly over the orifice? Table II. gives the coefficient of efflux between 604 and ·606; we shall take it at 605, then 3.033 × 605 1.833 cubic feet, the effective discharge. 6. A weir '82 feet broad, and 4.92 feet head of water, how many cubic feet are discharged each second? The quantity will be TABLE I.-The Coefficients for the Efflux through rectangular oriThe heads are measured where the fices in a thin vertical plate. water may be considered still. TABLE II.-The Coefficients for the Efflux through rectangular orifices in a thin vertical plate, the heads of water being measured directly over the orifice. |