WATER-POWER BREAST- WHEELS. ] 



APPLIED MECHANICS. 



831 



employed for obtaining power from a fall of water. I 

 theory, this arrangement appears one likely to prov 

 more effective than that of the wheel, for the weight o 

 water is retained in the buckets, and acts with constan 

 force throughout the whole descent. Practically, how 

 ever, the apparatus is not of so substantial and perma 

 neiit a character as the wheel ; the chain has numerou 

 joints, all subject to wear and decay from rust ; an 

 when they become deranged, the increased friction an 

 inequality of action considerably diminish the efficiency 

 of the apparatus. 



3. The breast-wheel is an arrangement intermediat 

 between the undershot and overahot-wheels. It consist 

 of a wheel fitted with floats or paddle-boards round it 

 circumference, revolving with its lower part in a channe 

 which nearly fits it. Each float has a back-plate or sole 

 so that the wheel is somewhat like an overshot-wheel 

 with buckets open on their outer sides. When a consider 

 able stream of water falls over a height not sufficient tc 

 render an overahot-wheel applicable, and yet greater 

 than would be required for an undershot-wheel, the 

 breast-wheel is applied with great advantage. Th< 

 floats fit as nearly as possible, without rubbing-friction, 

 to the bottom and sides of the channel, or sweep, in 

 which they revolve ; and thus, after passing the poin 

 where the water is delivered upon them, they act ahnosi 

 as close buckets, containing a load of water which urges 

 them onwards. 



At the point where the floats receive the water, some 

 force arises from the impulse or velocity with which the 

 water strikes them, as well as from the mere weight oi 

 their contents. Some millwrights have thought this 

 impulse a most essential element of power, and have 

 therefore contrived the spout so as to throw the water on 

 the floats with great velocity. Others, and among them 

 Smeaton, whose opinions on such matters are always to 

 be received with respect, have arranged the spouts so 

 aa to deliver the water on the wheel at as high a level as 

 possible. By this arrangement the impulse from velocity 

 is lessened, but the height through which the water after- 

 wards acts by weight is increased. 



If we suppose that a certain stream, flowing with a 



velocity of 8 feet per second, and having a fall of 8 feet, 



is applied to driving a breast-wheel 20 feet in diameter, 



having 40 floats (Fig. 124), we may inquire whether it 



Fig. 124. 



be more advantageous to deliver the stream at once on 

 the' wheel, or to slope its course downwards 3 feet before 

 it meets the floats. In the one case we have the impulse 

 due to a speed of 8 feet per second on one float marked 

 9, and the weight of the water contained in eight others, 



marked 1 to 8 inclusive. In the other case we have the 

 impulse due to the increased velocity of stream upon one 

 float marked 7, and the weight of water acting on six 

 others marked 1 to 6 inclusive. Farther, as in the 

 second case the velocity of the delivered water is greater, 

 its stream must be shallower, and therefore it must 

 strike on a less area of float ; and if the wheels move at 

 rates respectively proportional to those of their streams, 

 the same quantity of water being supposed to be delivered 

 in each case, each of the buckets in the second wheel 

 must contain less water than each of those in the first. 

 Let us assume that in each case the wheel revolves at a 

 rate which makes its circumference travel at one-third of 

 the velocity of the stream, which we found to be the 

 most advantageous speed for receiving impulse in the case 

 of undershot- wheels. In the first case the velocity would 



Q 



be 5- = 2 feet per second. In the second case we must 



calculate the velocity of stream due to increased fall. 

 The fall to produce 8 feet per second is 1 foot ; and 

 adding to this the 3 feet of additional fall, we have a fall 

 of 4 feet ; the velocity due to which is 8 times its square 

 root, or 16 feet per second. The circumference of the 



1 fi 



second wheel, then, travels at the rate of = 5 J feet per 



8 



second, twice the velocity of the first ; and if in the first 

 the buckets be exactly filled, in the second they can 

 only be half filled, or need have only half the capacity. 

 If we take the area of float in the first case to be 1 

 square foot, and in the second ^ square foot, the float 

 marked 9 in the first sustains a pressure due to 8 feet 

 per second, the velocity of the water, less by 2| feet 

 per second its own velocity ; that is, to 5J feet per 

 second, equivalent to a column ths of a foot high on 1 

 square foot of area, about Jths x 62^=28 Ibs. moving 

 at the rate of 2j feet per second, or 2$ x 60= 160 feet 

 per minute, which givesa power of 28 X 160=4,480 Ibs. 

 moving at 1 foot per minute. In the second case the 

 float 7 is pressed on by a column sufficient to give 16 

 less by 6J, that is, lOj feet per second, which implies a 

 height of 1{ foot ; and this pressing on i square foot 

 gives 66 Ibs. moving at 5J feet per second, equivalent 

 to 17,920 Ibs. moving at 1 foot per niiuute, 4 times the 

 effect of float 9 in the first case, as might have been 

 surmised, because the velocity is doubled. 



It remains now to compute the effect of the remaining 

 loats in producing power. The total quantity of water 

 issuing is 8 cubic feet per second, or 8 x 62| X 60= 

 30,000 Ibs. per minute. In the first case this keeps 8 

 Buckets continually full, and moves them at 2f feet per 

 second, or 160 feet per minute ; in the second case it 

 ceeps 6 buckets half filled, or 3 buckets quite full, and 

 moves them at 6J feet per second, or 320 feet per minute. 

 As each bucket holds 1 cubic foot, or 62| Ibs. , the power 

 of those in the first case is 8 X 160 X 62^=80,000 Ibs. 

 moving 1 foot per minute ; and of those in the second, 

 3 X 320 X 62^=60, 000 Ibs. Adding to each of these 

 results the power derived from the impulse of the water, 

 we have in the first case 84,480 Ibs. moved through 1 

 oot per minute = 2 '54 horse-power ; in the second case 

 7,920 Ibs., equivalent to 2-36 horse-power. The result 

 s, therefore, in favour of the first case ; and thus 

 Smeaton's view of the circumstances is borne out 



If the flotts be tolerably well fitted to the sweep, so 

 hat there is little loss of water by escape past their 

 dges, the circumferential speed of the wheel should be 

 Considerably more than one-third of that of the stream. 

 A rate as high as two- thirds or three-fourths is practically 

 ttained with advantage. When this is the case, the 

 mpulse from excess of the stream's velocity over that 

 f the float is much diminished, and the principal 

 lement of power is the load of the water contained in 

 be buckets. If, then, the fall of the spout be made 

 ust sufficient to deliver the water supplied by the stream 

 r reservoir, all the rest of the fall is most advantageously 

 pplied in the sweep, care being taken that sufficient 

 all is left to carry off the tail- water with full velocity, 



