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104
[TURBINES
HYDRAULICS


sluice successively, any number of sluices can be opened or closed as desired. The turbine is of 48 horse power on 5~12 ft. fall, and the supply of water varies from 35 to 112 cub. ft. per second. The Hence the vane angle at inlet surface is given by the equation cot0 = (wi -V.)/ug = (0-82-0-5)/o~45 = ~71; 0=55°. The relative velocity of the water striking the vane at the inlet

FIG. 200. efficiency in normal working is given as 73 %. The mean diameter of the wheel is 6 ft., and the speed 27-4 revolutions per minute. As an example of a partial admission radial How impulse turbine, a 100 h.p. turbine at Immenstadt may be taken. The fall varies from 538 to 570 ft. The external diameter of the wheel is 4% ft., and

F1o. 201. its internal diameter 3 ft. IO in. Normal speed 400 revs. per minute. Water is discharged into the wheel by a single nozzle, shown in fig. 202 with its regulating apparatus and some of the vanes. The water enters the wheel Y l e enf=;i§ 'ea€:.ii W % A tion of motion, & '® ' Zggle oilithe viiiireiil N § vanesis2o°. The

 § efficiency on trial
' &~ 199. Theory

of ythe Impulse I, ""' Turbine.-The / / theory of the im/ / g ' pulse turbine Q Z i g does not essen-Q Q tially differ from 2 Q, % that of 'the re° —' action turbine, except that there is no ressure in FIG- 202- the wlgeel opposing the discharge from the guide-blades. Hence the velocity with enters the wheel is simply U4 =0°96/ 2.§ (H ~ 5), which the water where l) is the height of the top of the wheel above the tail water. If the hydro pneumatic system is used, then b=0. Let Q". be the maximum supply of water, rl, rg the internal and external radii of the wheel at the inlet surface; then ui = Q, "/i1|'(f22-712)l. The value of u; may be about 0'45V 2g(Fl -5), whence rl, rg can be determined. The guide-blade angle is then given by the equation . Sin v =u</ve =0-45/0°94= -48; v = 29°- The value of ut should, however, be corrected for the space occupied by the guide-blades. The tangential velocity of the entering water is ru; =v; cos -y =o-82»/ zgl H -li i. The circumferential velocity of the wheel may be (at mean radius) Ve =o-5~/ 2gZH-5). edge is 14, =u¢ cosec0== 1-22u;. This relative velocity remains unchanged during the passage of the water over the vane; consequently the relative velocity at the point of discharge is vm = 1-22u;. Also in an axial flow turbine V., =V¢. If the final velocity of the water is axial, then cos¢ =V0/v, -, ,=V, /vfi =0°5/(I'22 X0-45) =cos 24° 23'. This should be corrected for the vane thickness. Neglectmg this, ua =v, ., sin 4: =v, ; sin 4> =u; cosec 0 sin ¢ =o-5u;. The discharging area of the wheel must therefore be greater than the inlet area in the ratio of at least 2 to 1. In some actual turbines the ratio is 7 to 3. This greater outlet area is obtained by splaying the wheel, as shown in the section (fig. 199). § 200. Pelton Wheel.-In the mining district of California about 186O simple impulse wheels were used, termed hurdy-gurdy wheels. The wheels rotated in a vertical plane, being supported on a horizontal axis. Round the circumference were fixed flat vanes which were struck normall by a jet from a nozzle of size varying with the head and quantity of, water. Such wheels have in fact long been used. They are not efficient, but they are very simply constructed. Then attempts were made to improve the efficiency, first by using hemispherical cup vanes, and] then by using a double cup vane with a central dividing ridge, an arrangement invented by Pelton. In this last form the water from the nozzle passes half to each side of the wheel, just escaping clear of the backs of the advancing buckets. F ig. 203 shows a Pelton vane. Some small modifications have been made by other makers, but they are not of any great importance. Fig. 204 shows a complete Pelton wheel with frame and casing, supply pipe and nozzle. Pelton wheels have been very largely used in America and to some extent in Europe. They are extremely simple and easy to construct or repair and on falls of 100 ft. or more are very efficient. The jet strikes taiientially to the mean radius of the buckets, and the face of the buckets is not quite radial but at right angles to the direction of the jet at the point of first impact. For greatest efficiency the peripheral velocity of the wheel at the mean radius of the buckets should be a little less than half the velocity of the jet. As the radius of the wheel can be taken arbitrarily, the number of revolutions per minute can be accommodated to that of the machinery to be driven. Pelton wheels have been made as small

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/f -, E?,2' .- - ' . . 1 if ~x § o FIG. 203. i;'-ip W ie ae » /2 ' W /./O - 12 7 ~ gt qs. ng e ¢' <1/M - » ==V' ': -in f f. s§ 14!» v g|; -~§ ii: r “ » FIG.'f2o4. V as 4 in. diameter, for driving sewing machines, and as large as 24 ft. The efficiency on high falls is about 80 %.- When large power is required two or three nozzles are used delivering on one wheel. The width of the buckets should be not less than seven times the diameter of the jet. At the Comstock mines, Nevada, there is a 36-in. Pelton wheel made of a solid steel disk with phosphor bronze buckets riveted to the rim. The head is 2100 ft. and the wheel makes 1150 revolutions per minute, the peripheral velocity being 180 ft. per sec. With a é-in. nozzle the wheel uses 32 cub. ft. of water per minute and develops loo h.p. At the Chollarshaft, Nevada, there are six Pelton wheels on a fall of 1680 ft. driving electrical generators. With § -in. nozzles each develops 125 h.p. § 201. Theory of the Pelton Wheel.-Suppose a jet with a velocity v strikes tangentially a curved vane AB (fig. 205) moving in the same direction with the velocity u. The water will flow over the

vane with the relative velocity v-u and at B will have the tangential