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the outer lip is dispensed with, and only the central rib retained for parting the water sideways, with the result that the efficiency of the Doble wheel is materially higher than that obtained from wheels made in the usual form.

(3) The angle cannot practically be made so great as 180°, because the water on leaving the sides of the vanes would strike the back edges of the vanes which immediately follow; hence for clearance purposes this angle must be made somewhat less than 180°, with a corresponding loss in efficiency. (4) Some of the energy of the jet is wasted in overcoming the friction of the axle.

In an actual wheel the maximum efficiency does not occur

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when the velocity of the jet is twice that of the vanes, but when the ratio is about 2.2.

The curve shown in Fig. 567c shows how the efficiency varies with a variation in speed ratio. The results were obtained from a small Pelton or tangent wheel in the author's laboratory; the available water pressure is about 30 lbs. per square inch. Probably much better results would be obtained with a higher water pressure.

This form of wheel possesses so many great advantages over the ordinary type of impulse turbine that it is rapidly coming into very general use for driving electrical and other installations; hence the question of accurately governing it is one of great importance. In cases in which a waste of water is immaterial, excellent results with small wheels can be

obtained by the Cassel governor, in which the two halves of the vanes are mounted on separate wheels. When the wheel is working at its full power the two halves are kept together, and thus form an ordinary Pelton wheel; when, however, the speed increases, the governor causes the two wheels to partially separate, and thus allows some of the water to escape between the central rib of the vanes. For much larger wheels Doble obtains the same result by affixing the jet nozzle to the end of a pivoted pipe in such a manner that the jet plays centrally on the vanes for full power, and when the speed increases, the governor deflects the nozzle to such an extent that the jet partially or fully misses the tips of the vanes, and so allows some of the water to escape without performing any work on the wheel.

But by far the most elegant and satisfactory device for regulating motors of this type is the conical expanding nozzle, which effects the desired regulation without allowing any waste of water. The nozzle is fitted with an internal cone of special construction, which can be advanced or withdrawn, and thereby it reduces or enlarges the area of the annular stream of water. Many have attempted to use a similar device, but have failed to get the jet to perfectly coalesce after it leaves the point of the cone. The cone in the Doble1 arrangement is balanced as regards shifting along the axis of the nozzle; therefore the governor only has to overcome a very small resistance in altering the area of the jet. Many other devices have been tried for varying the area of the jet in order to produce the desired regulation of speed, but not always with marked success. Another method in common use for governing and for regulating the power supplied to large wheels of this type is to employ several jets, any number of which can be brought to play on the vanes at will, but the arrangement is not altogether satisfactory, as the efficiency of the wheel decreases materially as the number of jets increases. In some tests made in California the following results were obtained :—

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1 A similar device is used by Messrs. Gilbert Gilkes & Co., Kendal.

Velocity of flow

The problem of governing water-wheels of this type, even when a perfect expanding nozzle can be produced, is one of considerable difficulty, and those who have experimented upon such motors have often obtained curious results which have greatly puzzled them. The theoretical treatment which follows is believed to throw much light on many hitherto unexplained phenomena, such as (i.) It has frequently been noticed that the speed of a water motor decreases when the area of the jet s increased, the head of water, and the load on the motor,

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Full open

0.4 0-5 0-6 0-7 0-8 closed. Ratio of Valve opening to Area of Pipe-N.

FIG. 567d.

remaining the same, and vice versa, when the area of the jet is decreased the speed increases. If the area of the jet is regulated by means of a governor, the motor under such circumstances will hunt in a most extraordinary manner, and the governor itself is blamed; but, generally speaking, the fault is not in the governor at all, but in the proportions of the pipe and jet. (ii.) A governor which controls the speed admirably in the case of a given water motor when working under certain conditions, may entirely fail in the case of a similar water motor when the conditions are only slightly altered, such as an alteration in the length or diameter of the supply pipe.

On p. 584 we showed that the velocity (V) of flow at any instant in a pipe is given by the expression

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In Fig. 567d we give a series of curves to show the manner in which V varies with the ratio of the area of the jet to the area of the cross-section of the pipe, viz. n. From these curves it will be seen that the velocity of flow falls off very slowly at first, as the area of the jet is diminished, and afterwards, as the "shut" position of the nozzle is approached, the velocity falls very rapidly. The velocity of efflux V1 of the jet itself is

also shown by full lined curves.

V

=

n

The quantity of water passing any cross-section of the main per second, or through the nozzle, is AV cubic feet per second, or 62.4AV lbs. per second.

The kinetic energy of the stream issuing from the nozzle is

62'4AV3
2gn2

Inserting the value of V, and reducing, we get

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Curves showing how the kinetic energy of the stream varies with n are given in Fig. 567e. Starting from a fully opened nozzle, the kinetic energy increases as the area of the jet is decreased up to a certain point, where it reaches its maximum value, and then it decreases as the area of the jet is further decreased. The increase in the kinetic energy, as the area of the jet decreases, will account for the curious action mentioned above, in which the speed of the motor was found to increase when the area of the jet was decreased, and vice versâ. The speed necessarily increases when the kinetic energy increases, if the load on the motor remains constant. If, however, the area of the jet be small compared with the area of the pipe, the kinetic energy varies directly as the area of the jet, or

Kinetic Energy of jet.

nearly so. Such a state is, of course, the only one consistent with good governing. From a large number of curves

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closed. Ratio of Valve opening to Area of Pipe-N. Full open.

FIG. 567e.

the values of n for maximum kinetic energy has been determined.

The kinetic energy is a maximum when n = 4'4^

L

hence for good governing the area of the jet must be less than

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