velocity or momentum, from the uniform pressure of 30 inches above it, that one cubic inch let fall from the top will acquire in falling down to the level of the aperture; one would therefore suppose that a cubic inch of water let fall through a space of 30 inches, and then impinging upon another body, would be capable of producing an equal effect by collision, as if the same cubic inch had descended through the same space with a slower motion, and produced its effects gradually for in both cases gravity acts upon an equal quantity of matter, through an equal space; and consequently, that whatever was the ratio, between power and effect in undershot-wheels, the same would obtain in overshot, and indeed in all others; yet, however conclusive this reasoning may seem, it appears, upon trial, that the effect of the gravity of descending bodies is very different from the effect of the stroke of such as are non-elastic, though generated by an equal mechanical power." : : Gravity, it is true, acts for a longer space of time upon the body that descends slowly, than upon one that falls quickly but this cannot occasion the difference in the effect; for an elastic body falling through the same space in the same time will, by collision upon another elastic body, rebound nearly to the height from which it fell: or, by communicating its motion, cause an equal one to ascend to the same height. The observations and deductions which Mr. Smeaton made from his experiments were as follows First.-As concerning the ratio between the power and effect of Overshot-wheels. "The effective power of water must be reckoned upon the whole descent; because it must be raised to that height, in order to be in a condition of producing the same effect a second time. The ratio between the powers so estimated, and the effect at the maximum as deduced from the several sets of experiments, is shown to range from 10 to 7-6 to that of 10 to 5.2; that is, nearly from 4 to 3 and from 4 to 2. In these experiments, where the heads of water and quantities expended are least, the proportion is nearly as 4 to 3; but where the heads and quantities are greatest, it approaches nearer to that of 4 to 2, and by a medium of the whole the ratio is that of 3 to 2 nearly. We have seen before, in our observations upon the effects of undershot-wheels, that the general ratio of the power to the effect when greatest was 3 to 1; the effect, therefore, of overshot wheels, under the same circumstances of quantity and fall, is, at a medium, double to that of the undershot. Second. As to the proper height of the wheel in proportion to the whole descent: : It has been observed, that the effect of the same quantity of water descending through the same space is double, when acting by its gravity upon an overshot-wheel, to what the same produces when acting by its impulse upon an undershot. Therefore the whole height at the fall should be made available, because, when the water is laid upon the top of the wheel, it is upon the gravity, and not the impulse, that the effect depends. A sufficient fall, however, must be given to lay on the water with a velocity somewhat greater than that of the circumference of the wheel, otherwise the wheel will not only be retarded by the buckets striking the water, but a part of it will be dashed over and lost, while the buckets will not be so well filled; but no greater velocity should be given than is sufficient to accomplish these objects, as it would be power wasted. Third. As to the best velocity of the wheel's circumference in order to produce the greatest effect: If a heavy body fall fairly from the surface of the head to the bottom of the descent, it will take a certain time in falling, but during the fall no mechanical effect is produced; for in this case the whole action of gravity is spent in giving the body a certain velocity; but if this body in falling be made to act upon something else, so as to produce a mechanical effect, the falling body will be retarded, because a part of the action of gravity is then spent in producing the effect, and the remainder only in giving motion to the falling body; and therefore the slower a body descends, the greater will be the action of gravity applicable to produce a mechanical effect. If an overshot-wheel had no friction, or other resistance, the greatest velocity it could attain would be half a revolution in the same time that a heavy body laid upon the top of it would take to fall through its diameter, but no mechanical effect could be derived from the wheel. It is an advantage in practice that the velocity of the wheel should not be diminished farther than what will procure some adequate benefit in point of power, because, as the motion becomes slower, the buckets must be made larger, and the wheel being loaded with water, the stress upon every part of the work will be increased in proportion. Mr. Smeaton's experiments showed that the best effect was obtained when the velocity of the wheel's circumference was a little more than three feet, or a second; and hence, it became a general rule to make the speed of the overshot water wheels at their circumference 3 feet per second, or 210 feet per minute. Experience showed this velocity to be applicable to the highest water-wheels as well as the lowest, and if all other parts of the work be properly adapted thereto, it will produce very nearly the greatest effect possible; but it has also been practically shown, that the velocity of high wheels may be increased beyond this rate without appreciable loss, as the height of the fall and the diameter of the wheel increase, and that a wheel of 24 feet high may move at the rate of 6 feet per second without any considerable loss of power. The author has constructed several overshot water-wheels of iron 30 feet diameter and upwards; and for these he has adopted a speed of 6 feet per second with great advantage. The circumference of a 30 feet wheel is 92.24 feet, and if it move at the rate of 34 feet per second, or 210 per minute, it makes only 2.275 revolutions, but if it go at the rate of 6 feet, it makes very nearly four revolutions per minute. The greater speed is advantageous, also, because it requires less gear-work to bring it up to the required rate for driving machinery; and because the load upon the water-wheel and its axle are reduced nearly in the inverse ratio of the speeds. After making the requisite allowances, it will be found that a fall of 7 inches will bring the water upon the wheel with a speed of 3 feet full, and that a fall of 18 inches will give a velocity to the stream of full 6 feet per second; and, consequently, that the increase of speed and the reduction of load upon the wheel, as before stated, are gained at the expense of one foot of fall, making a difference of effect between a wheel of 31 feet diameter, at the slower speed, and a wheel of 30 feet diameter at the greater, in the ratio of 44-6 to 43.0; but the steadiness and regularity of motion derived from the momentum of the quicker wheel render this difference practically inappreciable as compared with the gain. By the foregoing comparison it will be seen how far the rule laid down by M. Smeaton may in practice be departed from as the diameter of the wheel increases. The diameter, however, has its limits, and a water-wheel of great height is costly, cumbrous, and slow. A wheel was erected in South Wales by Messrs. Crawshay, at the Cyfarthfa Iron Works, near Merthyr Tydvil, 50 feet in diameter and 6 feet wide: it had 156 buckets, and made 2 revolutions per minute. This wheel, erected in the year 1800, was used to blow the furnaces. It was for some time the largest and most powerful water-wheel in use; but it has since been considerably surpassed. Mr. John Taylor applied a fall of water in the mining district, near Tavistock, 526 feet in height, to give motion, to seventeen water-wheels; eight of them employed in pumping water from a depth of nearly 200 fathoms. The diameter of the largest of these wheels being 51 feet, with a width of 10 feet in the clear across the face; the smallest of the eight wheels being 32 feet in diameter, and the others of intermediate. size. Four other wheels give motion to machinery for drawing up the ores to the surface; and the remaining five are employed to drive mills for crushing and stamping the ores. The performance of the largest wheel was as follows: diameter, 51 feet; breadth, within the shrouding, 10 feet; the water poured into its buckets was at the rate of 5632 gallons per minute, which, at 10lb. per gallon, would be 56,320lb. weight descending 51 feet 2,872,320lb. descending 1 foot. That is the power expended; which, being divided by 33,000 for a horse's power, according to Mr. Watt, gives 87.0 horse-power expended. The wheel, when so supplied, made 5 revolutions per minute, and worked 6 pumps of the diameters and depths annexed. The length of stroke on all the pumps was 6 feet, and the effective stroke or motion in the pumps to raise water was at the rate of 30 feet per minute. The weight of the columns of water in all the six pumps amounting to 66,415 lb., being raised 30 feet per minute, is equal to 1,992,450 lb. per minute raised 1 foot; that is the power actually exerted in raising the water, which, being divided by 33,000, gives 60-36 horse-power realised. The useful effect, or work done, being at the rate of 69.4 per cent. of the power expended, the remaining 30-6 per cent. being lost, partly by friction of the pump-work and resistance to the motion of the water through the pump, and by other retarding causes; this, however, is good duty for such a wheel so applied. A wheel larger in diameter, but not so powerful, has been made by Messrs. Donkin & Co., of London, namely 76 feet |