APPLIED MECHANICS. 



[WATIR-FOWKR BUEAST- WHEELS. 



to that it do not become heaped up, and retard the ' have to lift 270 cubic feet 13 feet high every minute. 

 scending floats. 



In estimating the power of a breast- wheel, we may 



suppose, for the sake of simplicity, that the water is 



, red on the horizontal lino of the centre, and keeps 



all the buckets, from that line to the bottom, full (Fig. 



t of the weight of any bucket, such 



IfeUfc 



as A, to turn the wheel, depends upon the leverage with 

 which it acts, which would be measured by the length 

 ( I ; of the horizontal line intercepted between the centre 

 of the wheel and the middle of that bucket. Were we to 

 divide the circumference from D to E into a great number 

 of equal parts, and calculate their combined effect as de- 

 pendent on the leverage with which they respectively act, 

 we should find it to be the same as if one weight bear- 

 ing the same proportion to the total weight in the circum- 

 ference I) E as the length of C D, the radius, bears to 

 the portion of the circumference D E acted on at D. In 

 ;ill the weight of water in D E 



:rn the wheel, is the same as that of a column D F 

 of the same width and thickness hanging at 1). The 

 same principle is true if the water do not deliver at the 

 f the centre of the wheel ; for if it be delivered at 

 G, the effect of at of water between G E would 



be the same as that of a column of equal area and of 

 the height G F acting at D. 



If, now, we take the particular case of a wheel 25 feet 

 in diameter, with bucket* 1 foot broad and 1 foot deep, 

 receiving the water at the level of the centre, and making 

 3 revolutions per minute, we may compute its power, 

 and the proportion which its useful effect bears to the 

 expended power of the water. The buckets being 1 foot 



>, the circle passing through their middle points 

 would have a diameter of 24 feet, and therefore a radius 

 of 12 feet and a circumference of 75J feet, making 3 re- 

 volutions per minute. The water in the buckets, there- 

 fore, moves at the rate of 75fc X 3 = 22f>J feet per 

 minute ; and the weight of the column, having an area 

 of 1 square foot, and being 12 feet high, is 12 X 02& = 



750 



Ibs. The power then is 7 - * 226J = ab(mt g 



horse-power. 



The quantity of water required to fill the buckets is 



cubic feet per minute, for it must three times fill 



the whole circumference every minute ; and as there must 



bo considerable waste from the inaccuracy with which 



the floats fit the bottom and sides of the sweep in which 



revolve, we may reckon 20 per cent, more, or alto- 



. ' cubic feet per minute, to cover this waste ; 



, -1 1, cubic foot per second. If we take the stream 



at the spout 1 foot wide, and inches or J t hs of a foot deep, 



ita area must be Jths of a square foot, through which 4i 



cubic feet have to flow per second. The velocity of the 



water must, therefore, be 6 feet per second, or that due 



to a fall of nearly 7 inches. The water in working the 



wheel has to descend 12 feet, and we must allow at least 



6 inches more of depth at the bottom of the wheel to 



clear the float* of back water, and the total descent is 



therefore 13 feet : in other words, in order to raise the 



water up to the proper level to work the wheel, we should 



The power required for this would be 27 " X '^ *!? 



about 6 hone-power We found the effective power 

 of the wheel about 5i horse-power ; that is, 77 per cent. 

 of the power expended. We believe t!i ally, 



this estimate would be found too high, and that we < 

 not depend on obtaining, in useful effect, more than GO to 

 70 per cent, of the water-power expended. 



The annexed plate represents an ingenious and, we 

 believe, a very effective construction of water-w 

 combining in one the principles of a breast and nnd.-i-- 

 sliot-wheel. A strong boss, E, is fitted on to the main 

 shaft or axle, A, on which the wheel turns. Two sets of 

 arms, C C and D D, extend as radii from this boss, some 

 of them, C, C, supporting the sides, B, of the buckets, 

 and the others, D, D, supporting their bottoms or soles. 

 The buckets or floats, F, F, are bent plates extending 

 across the outer part of the wheel, and terminated at 

 both ends by the casing, B, part of which is supposed 

 to be removed in order to show the form of the buckets 

 and the action of the water on them. The head of 

 water, M, is fronted by a double sluice presenting two 

 openings, I and J, at the lower and upper levels respec- 

 tively, these openings being separated by a casting, G, 

 formed in front to suit the sweep of the wheel. A h.ind- 

 w h.\l and suitable gearing, K, are arranged above the 

 sluice for causing it to slide up or down, and thereby 

 regulating the amount of opening at I and J. Under 

 the wheel the masonry, H, is formed in a curve suited 

 to the motion of the water from the lower opening I, and 

 is made to approach close to the edge of the wheel at L, 

 so that no water may pass without acting on the floats. 

 X is the tail-water, wliich is kept quite under the level 

 of the wheel, so as to give no resistance to its rotation. 

 Hy this construction, the water which issues from the 

 higher opening, J, fills the buckets, and acts by weight 

 to cause them to descend ; while the water which issues 

 from the lower opening I, with the increased velocity 

 due to the head of water in M pressing upon it, rushes 

 into the buckets, and presses the floats onwards, as in an 

 undershot-wheel. 



The terms undershot, overshot, and brcast-wncch, have 

 been applied in a somewhat different way from mat in 

 which we have used them. The term undershot has been 

 used when the water is delivered on the wheel anywhere 

 below the level of is centre, and thus the wheels which 

 we have called breast-wheels would be among the under- 

 slu)t ; the term overshot has been used in those cases only 

 where the spout is actually carried over the summit of 

 the wheel ; and the term breast has been applied to 

 heels where the water is delivered somewhere above 

 the central level. We think, however, that the classifi- 

 cation we have adopted here is more distinct, as it refers 

 not only to the different points whore the water is d.-li- 

 i , but also to differences in the construction of the 

 wheels. Thus, the undershot-w\ieo\ is that which receives 

 the water-pressure on simple paddles or floats immersed 

 in the current, and is acted on by its force only ; the 

 uvcrnhot-wheeil receives the water at a high level in 

 buckets formed in its circumference, and is moved simply 

 by the weight of water contained in them ; the breast- 

 wheel receives the water on paddles or floats nearly 

 fitting a sweep in which they revolve, and is thus put in 

 motion partly by the weight of water lodged on and be- 

 i the floats, and partly by the pressure on the floats 

 arising from the velocity of the current. The peculiar 

 ; ruction of each kind of wheel is adapted to different 

 conditions of the fall of water. 



The undershot-wheel is to be used when there is a 

 mo of water moving with considerable velocity, but 

 nil very little local fall, as in the case of river streams 

 and tidal currents. The velocity of the current of a 

 river arises from numerous little falh, or from a conti- 

 nuous inclination, without any considerable difference of 

 level within a limited space. The velocity of a tidal 

 current, again, arises from the pressure of the tidal wave, 

 or body of ocean water, elevated above its average level 



