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For the number of buckets for wheels of from 10 to 20 feet in diameter, we may take
n = %d + 16
Thus for a wheel 15 feet in diameter,
n = 8 * 15 + 16 = 40
The wheel shown in the figure is 16 feet 8 inches in diameter, and 30 feet wide, and is driven by a fall 6 feet 6 inches high, yielding 20,000 cubic feet per minute. With a circumferential velocity of 11 or 12 feet per second, it afforded 140 horsespower.
This wheel gives a useful effect of 50 to 60 per cent. of the water power employed when well constructed, and may be used with advantage for falls not greater than about 6 feet. Above this the low breast wheel is certainly more advantageous and costs less.
Poncelet made some experiments on wheels of this class, with the friction break. The wheel was 11 feet diameter, 28 inches wide, and with 30 floats. He found the efficiency equal to 52 per cent. when the ratio of the velocity of the wheel to the water was 0*52. Morin has also experimented on these wheels, and for falls of from 3 to 4^ feet, with sluice openings of 6, 8, 10, and 11 inches, he found the efficiency 52, 57, 60, and 62 per cent. respectively.*
* In a conversation with General Poncelet on this subject I found that tl.e wheel which bears his name gives a duty of nearly 60 per cent, of the water employed. This is about the same as my own wheel with ventilated buckets for low falls, where the sole is entirely dispensed with. There is, however, this difference, namely, that in the Poncelet wheel the water is discharged upon the floats from under the sluice, whereas, in that of the ventilated wheel, it is discharged into buckets over the sluice from the upper surface of the fall.
It will be impossible in the present work to enter into details on the theory and construction of the immense variety of primemovers known under the name of turbines, the development of the principles of which we owe chiefly to continental mathematicians. Two varieties of horizontal wheels or turbines have long been employed on the Continent, which, although ill-devised and ineffective, yet presented evident advantages in their small size, cheapness, and simplicity of construction. These are known in France as roues a cuves and rouets volants, the former being a small wheel revolving on a vertical axis, and having inclined curved vanes or buckets arranged radially. It is placed in a pit so that the water passing vertically through it should act by pressure and reaction on the buckets. The rouet volant differs from this in having the water applied to the wheel at a small part only of the periphery, so as to drive the wheel by impulse. These wheels of from 3 to 5 feet in diameter with nine to twelve buckets are usually made of cast iron, and fixed upon a lever foot bridge, so that they can be slightly raised or depressed. The running millstone is fixed on the upper extremity of the vertical axis, so as to obviate the use of any gearing or belting. In regard to efficiency, the roues a cuves yield about 27 per cent. and the rouets volants about 30 to 40 per cent. of the water used.
General Poncelet was the first to demonstrate the principle and superior advantages of the turbine, and in 1827 M. Fourneyron recalled public attention in France very forcibly to the construction of the horizontal wheels by a turbine very happily conceived and executed. For this invention he received in 1833 a prize of 6,000 francs; and the principles of his machine have been investigated, and its superiority proved, by the ablest continental experimenters on hydraulics. In its present form it is equal in efficiency to the best hydraulic machines, and in many circumstances is very advantageously employed. Since then the manufacture of these turbines in countries where water power is much depended upon has assumed considerable importance, and very numerous modifications of its form and construction have been adopted.
1. Turbines in which the water passes vertically through the wheel.
Wheels of this class are composed of two annular cylinders, the upper fixed and the lower revolving on a vertical axis. The upper is fitted with guides to direct the water most effectively against similar curved vanes or buckets, turned in the opposite direction, in the lower wheel. The water passes from the reFig- 127. servoir or cistern placed over the upper cylinder, vertically downwards, acting on the revolving wheel by pressure as it glides over the surface of the vanes.
Burdinaboutl826 invented a turbine of this description (turbine a, Evacuation alternative),the efficiency of which was as much as 67 per cent. of the water power expended.
Fig. 127 represents Feu Jonval's turbine (known also as the Koechlin turbine). The fixed wheel is shown at A A, the revolving wheel at B B. The wheels consist of cast-iron rims, having wrought-iron guides grooved and riveted to them. The running wheel is keyed on the shaft C C, which is supported on a step D, firmly fixed by screws on the cast-iron bridge attached to the cylinder forming the tail-race. The regulation of the water is effected partly by a valve E resembling the throttle-valve of a steam-engine and placed beneath the wheel, or in some cases by a sluice at the opening of the conduit into the tail-race. This method, when much variation of power is required, reduces the efficiency of the wheel, but it has the merit of great simplicity and facility of construction. In the construction represented the vane carries outside the cylinder in which it is placed a wheel, acted on by a worm from a hand-wheel placed at any convenient point above the upper cistern. There are also employed movable divisions by which part of the inner periphery of the revolving wheel is enclosed, and the water passes through a narrower annular aperture on the external periphery. This arrangement is said to have operated effectively in America, so that a wheel giving 60 H. P. in wet seasons can work at 40 H. P. in dry seasons, without losing more than 15 or 16 per cent. of its efficiency.
These wheels are placed in an air-tight cylinder, for low falls at a depth of 4 to 6 feet below the surface, and for high falls at a distance not exceeding 30 feet above the level of the water in the tail-race, when lowest; so that in the upper part of the fall the water acts by pressure, in the part below the wheel by suction; hence, there is no inconvenience from backwater beyond the inevitable reduction of fall, and the waste water may, if necessary, be conveyed in an air-tight pipe to any convenient point of discharge, only taking care that its mouth be under water. In case of breakdown the wheel is very easily rendered accessible. These wheels are said to yield 75 per cent. of the power expended on falls above 12 feet.
Fig. 128 represents part of a similar turbine by M. Fromont, which received the Council Medal at the Great Exhibition of 1851. It differs from the last in the method of regulating the water, and is known as M. Fontaine Baron's turbine. A number of sluices s s are suspended in the fixed wheel by wroughtiron rods, and are raised or lowered simultaneously by means of wheel-work, so as to open or contract the orifices for the passage of the water. In awarding a medal to this turbine, the jury made the following remarks on its merits:—' 1 st. It occupies a small space; 2nd. Turning very rapidly, it may, when used for grinding flour, be made to communicate the motion directly to the millstones; 3rd. It works equally well under great and
small falls of water; 4th. It yields, when properly constructed, and with the supply of water for which it was constructed, a useful effect of 68 to 70 per cent., being an efficiency as high as any other hydraulic machine; 5th. The same wheel may be made to work at very different velocities, without materially altering its useful effect.'—Reports of Juries.
In designing a wheel of this description, we must take a distance a b equal to the distance between _6-29 x radius No. of vanes Take the angle a b c= 15° to 20°, and draw a c perpendicular to c b. Lay off
d c/equal to where 8 is the angle a b c, and /9 is taken
arbitrarily equal to 100° to 110°. Bisect c/in e, and through e draw g d perpendicular to c /, and cutting c din d. From d with radius d c, or d f, draw the arc to which c b will be a tangent. For the guides, take the angle / h k = a, so that
the floats, or
draw / m perpendicular to h k, cutting the top of the guide