mills. The quantity of meal ground in an hour may be Performance found by the rules already given for vertical mills, of horizontal or by multiplying the product of the expense of water, and the relative fall, by 456lbs. and the result will be the quantity required. The thickness of the millstone at the centre and circumference, the thickness of the arbor and pivots, may be determined by the rules already laid down for vertical mills. boards. In horizontal wheels, the mill-course is sometimes Horizontal differently constructed. Instead of the water as- mills with insuming a horizontal direction before it strikes the clined floatwheel, as in the case of undershot-mills, the floatboard is so inclined as to receive the impulse perpendicularly, and in the direction of the declivity of the waterfall. When this construction is adopted, the greatest effect will be produced 5.67 H when the velocity of the float-boards is not less than 2 Sin. A' in which H represents the height of the waterfall, and A the angle which the direction of the fall makes with a vertical liné. But since this quantity increases as the sine of 4 decreases, it follows, that without taking from the effect of these wheels, we may diminish the angle A, and thus augment considerably the velocity of the float-boards, according to the nature of the machinery employed; whereas, in vertical wheels, there is only one determinate velocity, which produces a maximum effect.6 boards. In the southern provinces of France, where hori- With curvizontal wheels are very generally employed, the float- lineal floatboards are made of a curvilineal form, so as to be concave towards the stream, as represented in Plate I, Fig. 11. The Chevalier de Borda observes, that in theory a double effect is produced when the float-boards are concave, but that this effect is diminished in practice, from the difficulty of making the fluid enter and leave the curve in a proper direction. Notwithstanding this difficulty, however, and other defects which might be pointed out, horizontal wheels with concave float-boards are always superior to those in which the float-boards are plain, and even to vertical wheels, when there is a sufficient head of water. When the float-boards are plain, the wheel is driven merely by the impulse of the stream; but when they are concave, a part of the water acts by its weight, and increases the velocity of 6 See Mem. Acad. Par. 1767, p. 285. the wheel. If the fall of water be five or six feet, a horizontal wheel with concave float-boards may be erected, whose maximum effect will be to that of ordinary vertical wheels as 3 to 2.7 Conical hori zontal wheel with spiral float-boards. In the provinces of Guyenne and Languedoc, another species of horizontal wheels is employed for turning machinery. They consist of an inverted Plate I. cone, A B, with spiral float-boards of a curvilineal Fig. 12. form winding round its surface. The wheel moves on a vertical axis in the building DD, and is driven chiefly by the impulse of the water conveyed by the canal C to the oblique float-boards. When the water has spent its impulsive force, it descends along the spirals, and continues to act by its weight till it reaches the bottom, where it is carried off by the canal M. Double cornmills. On Double Corn-Mills. It frequently happens that one water-wheel drives two millstones, in which case the mill is said to be double; and when there is a copious discharge of water from a high fall, the same water-wheel may give sufficient velocity to three, four, or five millstones. Mr. Ferguson has given a brief description of a double mill in Vol. I, p. 66, and a drawing of one in Plate III, Fig. 4, but has laid down no maxim of construction for the use of the practical mechanic. In supplying this defect, and following M. Fabre, let us first attend to double horizontal mills, in which the axis CD (Fig. 7) is furnished with a wheel which gives motion to two trundles, the arbors of which carry the millstones. In order to find the weight of the equipage for each millstone, multiply the product of the expense of water, and the relative fall, by 48116 lbs, and divide the product by 2000, if there are two millstones, 3000 if there are three, and so on; the quotient will be the weight of the equipage of each millstone. To determine the radius of the wheel that drives Size of the wheel that the trundles, find first the radius of the millstones drives the trundles. by the rules already given, and having added it to 7 A new horizontal water-wheel has been recently described by Mr. Adamson. It consists of a horizontal wheel, with a number of vertical float-boards, descending below the general level of the wheel. The water is introduced into a cylindrical reservoir, which surrounds the wheel, and issues from a number of cuts at the bottom of the reservoir, in the direction of tangents to the wheel's circumference. Hence the water acts against all the float-boards at the same time. The power of this wheel is said to be double that of an undershot wheel. A full account of it will be found in the Journal of the Royal Institution, vol. iv, p. 46. half the distance between the two neighbouring mill-stones," subtract from this sum the radius of the lantern, which may be taken at pleasure, and the remainder will be the radius required when there are two millstones. But if there are three millstones, or four, or five, or six, before subtracting the radius of the lantern, divide the sum by 0.864, 0.705, 0.587, 0.5, respectively. The mean radius of the water-wheel may be found Size of the by multiplying the square root of the relative fall water-wheel. by the radius of the millstone, by the radius of the wheel that drives the trundles, and by 231, and then dividing the product by the radius of the lantern multiplied by 1000, the quotient will be the wheel's radius. It may happen, however, that the diameter of the wheel found in this way is too great. When this is the case, we may be certain that the radius of the lantern has been taken too small. In order then to get a less value for the wheel's radius, increase a little the radius of the lantern, and find new numbers both for the water-wheel, and that which drives the trundles, by the preceding rule. It may happen also, that in giving an arbitrary value to the radius of the lantern, the diameter of the wheel found by the rule may be too small, that is, less than seven times the breadth of the mill-course at the bottom of the fall. When this takes place, make the diameter of the water-wheel seven times the width of the mill-course, and you may find the radius of the other wheel and lanterns by the following rules. Size of the drives the trundles. 1. To find the radius of the wheel that impels the trundles; add the radius of the millstone to half the wheel that distance between any two adjoining millstones for a first quantity. Multiply the square root of the relative fall by the radius of the millstone and by .231; and having divided the product by the radius of the water-wheel, add unity to the quotient, and multiply the sum by 1 if there are two millstones, by .864 if there are three, by .705 if there are four, by .587 if there are five, and by .5 if there are six, and the result will be a second quantity. Divide the first by the second quantity, and the quotient will be the radius of the wheel that drives the trundles. 2. To find the radius of the lantern, multiply the Size of the radius of the wheel as found by the preceding rule, lantern. by the square root of the relative fall, and by .231, and divide 8 This quantity may be taken at pleasure, and should never be less than 2 feet, however great be the number of the millstones. the product by the radius of the water-wheel; the quotient will be the lantern's radius. By the rules formerly given, find the quantity of meal ground by one millstone, and having multiplied this by the number of millstones, the result will be the quantity ground by the compound mill. If the equipage of the millstone of a vertical mill, as found in page 25, should be too great, that is, if it should require too large a millstone, then we must employ a double mill, like that which is represented in Plate III, Fig. 4, Vol. I, or one which has more than two millstones. In order to know the equipage of each millstone, find it by the rule for a single mill, and having multiplied the quantity by .947, divide the product by the number of millstones, and the quotient will be the equipage of each millstone. The radius of the wheel D (Plate III, Fig. 4, Vol. I) will be found by the same rule which was given for horizontal mills; but it must be attended to, that the lantern whose radius is there employed is not B B, but FG or E H. Size of the To determine the mean radius of the large spurspur-wheel. wheel A A, which is fixed upon the arbor of the water-wheel, multiply the square of the radius of the lanterns FG or EH, by the radius of the water-wheel, and also by 4302, and a first quantity will be had. Multiply the square root of the relative fall by the radius of one of the millstones, and by the radius of the wheel D, and by 1000, and a second quantity will be obtained. Divide the first quantity by the second, and the quotient will be the mean radius of the wheel AA. The quantity of meal ground by a compound mill of this kind, is found by the same rule that was employed for compound mills driven by a horizontal water-wheel. Besant's undershot wheel. Besant's Undershot Wheel. The water-wheel invented by Mr. Besant of Brompton is constructed in the form of a hollow drum, so as to resist the admission of water. The float-boards are fixed obliquely in pairs on the periphery of the wheel, cach pair forming an acute angle, open at its vertex. This is represented in Plate I, Fig. 13, where AB is the wheel, CD its axle, and mn, op, the position of the float-boards. In common undershot wheels, their motion is greatly retarded by the resistance opposed by the tail water to the ascending float-boards; and their velocity is still farther diminished by the resistance of the air. But when the preceding construction is adopted, the resistance of the air and the tail water is greatly diminished by the oblique position of the float-boards. Undershot Wheel moving at Right Angles to the Stream. Undershot wheels have sometimes been constructed like windmills, having large inclined float-boards, and being driven in a plane perpendicular to the direction of the current. Albert Euler, who has examined theoretically this species of waterwheel, concludes that the effect will be twice as great as in common undershot wheels, and that in order to produce this ef fect, the velocity of the wheel, computed from the centre of impression, should be to the velocity of the water as radius is to thrice the sine of the inclination of the float-boards to the plane of the wheel. When the inclination is 60°, the ratio will be as 5 to 13 nearly, and when it is 30°, it will be nearly as 2 to 3. In this kind of wheel, a considerable advantage may also be gained by inclining the float-boards to the radius. In this case, the area of the float-boards ought to be much greater than the section of the current, and before one float-board leaves the current, the other ought to have fairly entered it. This construction may be employed with advantage in deep rivers that have but a small velocity. On the Construction of Breast Wheels. Breast wheels. A breast water-wheel is a wheel in which the water is delivered at a point intermediate between the upper and under point of a wheel with float-boards. It is generally delivered at a point below the level of the axis, as in Plate I, Fig. 14, but sometimes at a point higher than the level of the axis, as in Fig. 15. On breast wheels, buckets are never employed, but the float-boards are fitted accurately, with as little play as possible, to the mill-course, so that the water, after acting upon the float-boards by its impulse, is retained between the float-boards and the mill-course, and acts by its weight till it reaches the lowest part of the wheel. A breast wheel, as constructed by Mr. Smeaton, is represented in Fig. 14, where A B is a portion of the wheel, N M the canal which conveys the water to the wheel, M O P the curvilineal mill-course accurately fitted to the extremity of the floatboards, and cd the shuttle moved by a pinion a, for the purpose of regulating the admission of water upon the wheel. |