Page:Encyclopædia Britannica, Ninth Edition, v. 12.djvu/539

523 MACHINERY.] HYDROMECHANICS is from 3 to 25 cubic feet per second, it is possible to con struct a bucket wheel on which the water acts chiefly by its weight. If the variation of the head-water level does not exceed 2 feet, an overshot wheel niay be used (fig. 179). The water is then projected over the summit of the wheel, and falls in a parabolic path into the buckets. With greater variation of head-water level, a pitch-back or high breast wheel is better. The water falls over the top of a sliding sluice into the wheel, on the same side as the head race channel. By adjusting the height of the sluice, the requisite supply is given to the wheel in all positions of the head-water level. The wheel consists of a cast-iron or wrought-iron axle C supporting the weight of the wheel. To this are attached two sets of arms A of wood or iron, which support circular segmental plates termed shrouds B. A cylindrical sole plate &amp;lt;ld extends between the shrouds on the inner side. The buckets are formed by wood planks or curved wrought-iron plates extending from shroud to shroud, the back of the buckets being formed by the sole plate. The efficiency may be taken at 075. Hence, if h.p. is the effec tive horse power, II the available fall, and Q the available water supply per second, h.p. = 075 ^5-0-085 QH. oou rf the peripheral velocity of the water wheel is too great, water is thrown out of the buckets before reaching the bottom of the fall. In practice, the circumferential velocity of water wheels of the kind now described is from 4^ to 10 feet per second, about 6 feet being the usual velocity of good iron wheels not of very small size. In order that the water may enter the buckets easily, it must have a greater velocity than the wheel. Usually the velocity of the water at the point where it enters the wheel is from 9 to 12 feet per second, and to produce this it must enter the wheel at a point 16 to 27 inches below the head-water level. Hence the diameter of an overshot wheel may be D = H-lto H- 21 feet. Overshot and high breast wheels work badly in back-water, and hence if the tail-water level varies, it is better to reduce the diameter of the wheel so that its greatest immersion in flood is not more than 1 foot. The depth d of the shrouds is about 10 to 16 inches. The number of buckets may be about . -n-D N--T-. d Let v be the peripheral velocity of the wheel. Then the capacity of that portion of the wheel which passes the sluice in one second is f. vb /-r,j ,&amp;lt;, Q!- (Dd-d 8 ) = v b d nearly, b being the breadth of the wheel between the shrouds. If, however, this quantity of water were allowed to pass on to the wheel the buckets would begin to spill their contents almost at the top of the fall. To diminish the loss from spilling, it is not only necessary to give the buckets a suitable form, but to restrict the water supply to one-fourth or one-third of the gross bucket capacity. Let m be the value of this ratio ; then, Q being the supply of water per second, This gives the breadth of the wheel if the water supply is known. The form of the buckets should be determined thus. The outer element of the bucket should be in the direction of mo tion of the water entering relatively to the wheel, so that the water may enter without splashing or shock. The buckets should retain the water as long as pos sible, and the width of opening of the buckets should be 2 or 3 inches greater than the thickness of the sheet of water entering. For a wooden Fig. ISO. bucket (fig. 180, A), take aJ = distance between two buckets on peri phery of wheel. Make cd = $ cb, and ic = f to ab. Join cd. For an iron bucket (fig. 180, B), take ed= cb ; ic=2 ab. Draw cO making an an^le of 10 to 15 with the radius at c. On Oc take a centre giving a circular arc passing near d, and round tho curve into the radial part of the bucket dc. There are two ways in which the power of a water wheel is given off to the machinery driven. In wooden wheels and wheels with rigid arms, a spur or bevil wheel keyed on the axle of the turbine will transmit the power to the shafting. It is obvious that the whole turning moment due to the weight of the water is then transmitted through the arms and axle of the water wheel. When the water wheel is an iron one, it usually has light iron suspension arms incapable of resisting the bending action due to the transmission of the turning effort to the axle. In that ,case spur segments are bolted to one of the shrouds, and the pinion to which the power is transmitted is placed so that the teeth in gear are, as nearly as may be, on the line of action of the resultant of the weight of the water in the loaded arc of the wheel. 167. The Foncelet Water Wheel, When the fall does not exceed 6 feet, the best water motor to adopt in many cases is the Poncelet undershot water wheel. In this the water acts very nearly in the same way as in a turbine, and the Poncelet wheel, although slightly less efficient than the best turbines, in normal conditions of working, is superior to most of them when working with a reduced supply of water. A general notion of the action of the water on a Poncelet wheel has already been given in 145. Fig. 181 shows its construction. The water penned back Fig. 181. between the side walls of the wheel pit is allowed to flow to the wheel under a movable sluice, at a velocity nearly equal to the velocity due to the whole fall. The water is guided down a slope of 1 in 10, or a curved race, and enters the wheel without shock. Gliding up the curved floats it comes to rest, falls back, and acquires at the point of discharge a backward velocity relative to the wheel nearly equal to the forward velocity of the wheel. Consequently it leaves the wheel deprived of nearly the whole of its original kinetic energy. Taking the efficiency at 60, and putting H for the available fall, h.p. for the horse-power, and Q for the water supply per second, h.p. =0-068 QH. The diameter D of the wheel does not depend on the fall. With, a straight channel of approach the smallest convenient diameter is about 14 feet, with a curved channel 10 feet. The diameter is often taken at four times the fall. Let H be the fall measured from the free surface of the head-water to the point F where the mean layer enters the wheel ; then the velocity at which the water enters is r= J1g, and the best circumferential velocity of the wheel is V = 55i&amp;gt; to 0&quot;6i&amp;gt;. The number of rotations of the wheel per second is N = TrD The thickness of the sheet of water entering the wheel is very im portant. The. best thickness according to experiment is 8 to 10 inches. The maximum thickness should not exceed 12 to 15 inches, when there is a surplus water supply. Let c, be the thickness of the sheet of water entering the wheel, and b its width ; then bcv = Q ; or b.