530 in which case about ^th of the energy of the fall is carried away by the water discharged. The areas of the outlet and inlet surface of the wheel are then 1 0-125V20E If we take r , so that the axial velocity of discharge from the central orifices of the wheel is equal to tt , we get = 0-3984 /_Q_ V /H Q If, to obtain considerable steadying action of the centrifugal head, r, = 2r , then di = -^do- Speed of the Wheel. Let V, = 66/2^H, or the speed due to half the fall nearly. Then the number of rotations of the turbine per second is also Angle of Vanes with Outlet Surface. = 21 nearly. If this value is revised for the vane thickness it will ordinarily become about 25. Velocity vrith ichich the Water enters the Wheel. The head pro ducing the velocity is Vi2/ 11 2 ,..2 H- M 4- JA n I i T -I = H {l- -4356(1 + 0-0358) + "0156} = 0-5646H. Then the velocity is = -96V2#(-5646H) = 0-721 V27B. Anyle of Guide-Blades. fc -V-TO- 0178 7=10 nearly. Tangential Velocity of Water entering Wheel. Wi = v f cos 7=0 7101 /2<7H. Angle of Vanes at Inlet Surface. Cot fl-gL^-* 101 - 66 - -4008; -125 6 = 68 nearly. Hydraulic Efficiency of Wheel.
- = ~tr = -7l
9*1 = 0-9373. -66x2 This, however, neglects the friction of wheel covers and leak age. The efficiency from experiment has been found to be 075 to 0-80. Impulse and Partial Admission Turbines. 182. The principal defect of most turbines with complete admission is the imperfection of the arrangements for working with less than the normal supply. With most forms of turbine the efficiency is considerably reduced when the regulating sluices are partially closed, but it is exactly when the supply of water is deficient that it i most important to get out of it the greatest possible amount of work. The imperfection of the regulating arrangement is, therefore, from the practical point of view, a serious defect. All turbine makers have sought by various methods to improve the regulating mechanism. Fourneyron, by divid- [HYDRAULICS_ ng his wheel by horizontal diaphragms, virtually obtained three or more separate radial flow turbines, which could be successively set in action at their full power, but the arrangement is not altogether successful, because of the spreading of the water in the space between the wheel and guide-blades. M. Fontaine similarly employed two concentric axial flow turbines formed in the same casing. One was worked at full power, the other regulated. By
- his arrangement the loss of efficiency due to the action
of the regulating sluice affected only half the water power. Many makers have adopted the expedient of erecting two or three separate turbines on the same waterfall. Then one or more could be put out of action and the others worked at full power. This is an excellent plan, but the separate turbines cost more than a single one. All these methods are rather palliatives than remedies. The movable guide-blades of Professor James Thomson meet the difficulty directly, but of course they are not applicable to every form of turbine. A subsidiary defect of turbines with complete admission is their very great speed of rotation on high falls. The turbine wheel cannot be increased in diameter without great increase of the fluid friction in the passages and on the surface of the wheel, and it also becomes impossible in radial flow turbines to adjust properly the vane angles, if the diameter is made very large. M. Callon, in 1840, patented an arrangement of sluices for axial or outward flow turbines, which were to be closed successively as the water supply diminished. By preference the sluices were closed by pairs, two diametrically opposite sluices forming a pair. The wate* was thus admitted to opposite but equal arcs of the wheel, and the forces driving the turbine were symmetrically placed. As soon as this arrangement was adopted, a modification of the mode of action of the water in the turbine became necessary. If the turbine wheel passages remain full of water during the whole rotation, the water contained in each passage must be put into motion each time it passes an open portion of the sluice, and stopped each time it passes a closed portion of the sluice. It is thus put into motion and stopped twice in each rotation. This gives rise to violent eddying motions and great loss of energy in shock. To prevent this, the turbine wheel with partial admission must be placed above the tail water, and the wheel passages be allowed to clear themselves of water, while passing from one open portion of the sluices to the next. But if the wheel passages are free of water when they arrive at the open sluices, then there can be no pressure other than atmospheric pressure in the space between the sluices and wheel. The water must issue from the sluices with the whole velocity due to the head ; received on the curved vanes of the wheel, the jets must be gradually deviated and discharged with a radial velocity only, pre cisely in the same way as when a single jet strikes a curved vane in the free air. Turbines of this kind are therefore termed turbines of free deviation. There is no variation of pressure in the jet during the whole time of its action on the wheel, and the whole energy of the jet is imparted to the wheel,"simply by the impulse due to its gradual change of momentum. It is clear that the water may be admitted in exactly the same way to any fraction of the circumference at pleasure, without altering the efficiency of the wheel. The diameter of the wheel may be made as large as con venient, and thus the speed of rotation on high falls may be kept down to a manageable amount. The Poncelet water wheel is a turbine of free deviation, in which, how ever, the action of gravity causes the water to flow back along .the vanes, so that it is discharged at the same point of the wheel at which it enters.
So long as the tail-water level is invariable, no difficulty
