It is found theoretically that an undershot water-wheel, in which the water thus acts by its shock upon floats working in a straight mill race, only yields on efficient power equal to half the dynamical effort exerted upon it, oven under the most favourable circumstances. But in practice, Smeaton's experiments appear to show that the useful results rarely attain even that value; end that calling the weight of water r, and the height of the fall tr, the real effect does not exceed u. The useful effect of these wheels is, therefore, very small ; but the facility they present for variations in the diameters of the wheels, and in their velocities, renders them at times advantageous, when an unlimited supply of water is at hand.
In the previous remarks it was observed, that the useful effect of the undershot-wheel was improved by making the race concentric to the outer circumference of the wheeL The gain thus secured is propor tionate to the arc enclosed ; and the practice at the present day is, therefore, to make that arc as large as the fall will allow (fig. 2), and 1 and of the vertical fall in the inverse proportion to the height of the latter. But with ali these improvements, it seems to he very difficult to secure from the best undershot-wheels a greater useful effect than is represented by r n.
A species of undershot-wheel is sometimes used upon rivers, which consists of a vertical float-wheel worked by the current of the river, or even occasionally by the tide. The diameters of these wheels are rarely of considerable dimensions, and the proportion of the useful effect to the power actually exerted is but small ; nevertheless, these wheels are extremely useful in new countries, and they present one great advan tage from the fact of their not interfering in any way with the natural drainage conditions of a locality, as the other classes of mills with beads and dams almost inevitably do, from their upholding the water. [TIDAL The vertical orershot.rhecls with buckets, fig. 5, are those in which usually it is mule equal to 1 or of the available fall. A space of about half an inch is left between the circumference of the wheel and the surface of the enclosing arc of the race; the width of the stream is made such as to allow it to fall on the wheel with a thickness of about 8 inches, and the diameter and number of the floats arc calculated as before. The useful effect of theso wheels is said to range between and 31. Poneelet has, however, increased still more the useful effect of the undershot-wheels by making the floats curved, as shown in figs. 3 and 4, and by doubling their number, lie confines the the water is carried over the top of the wheel, and then made to strike the buckets upon the side of the mill-tail, so that the descent of the wheel is caused by the weight of the water on the unbalanced side ; the shock of the falling water adding slightly to the motive power. Aa in
ordinary undershot-wheels, the overshot ones consist of the axle, arms, rim, shrouds, sole, and buckets; which may be of wood or of iron, according to the resources of the locality where the mill is to be erected ; the advantage in the use of iron consisting in the facility witt which the buckets can be worked to the best theoretical outline, and in its durability ; the advantage of wood consisting in its primary economy, and its facility of repair.
The number of buckets on an overshot water-wheel is determined upon the following scale, which is found practically to be the most successful, namely, the diameters being given, the number becomes— water within a close race, and takes more than ordinary precautions to remove the tail-water; he makes the depth of the floats vary between That is to say, assuming the depth of the shrouds to be, as it usually is, 12 inches, and drawing a circle at one-third of that depth, measuring from the inside, the buckets are spaced upon that circle at distances apart of 13 inches, as nearly as may be. The length between the shrouds will be determined by the quantity of water they have to deliver ; and it is desirable not only to make the capacity of the buckets suffi cient to receive all the water which may pass into them from the hatch, but also to make their capacity equal to three times that volume, or the water would have a tendency to splash over, and to escape. Generally speaking, the water is carried over the top of the wheel, at a slight distance from it, and is made to strike the second or third bucket beyond the summit, at about 2 feet from the vertical lino passing through the centre ; because it is considered that the shock thus obtained increases the dynamical force of the water. A mere important precaution still than either of those named above, conslata in the provision of means of escape for the air contained originally in the bucket, or carried down by the falling water; and The wheats are usually 3 feet 4 inches in diameter, and 10 inches deep placed at the bottom of a cylinder about 7 feet 6 inches deep, and 3 feet 41 inches in diameter. A channel gradually diminishing in width, as shown, admits water at the side of the cylinder above the wheel and the water escaping from the sluice with violence acquires, iu its course round the cylinder, a centrifugal force which acts against the curved blades not only by its impulse, but by its weight. There are many localities where wheels of this description would be of value ; but even when the wheels are made of the best form, the useful effect they produce does not exceed 0.25 en, and it is very rarely that they attain more than en.