WATEB.-POWER OVBRSHOT-WHEELS.] APPLIED MECHANICS. 



829 



meter, and the depth of the buckets, measured towards 

 the centre, two feet. Dividing this depth into two equal 



Tig. 120. 



parts, each one foot, marked by the dotted circle (Fig. 

 121), dividing the circumference of this circle into a con- 

 venient number of equal parts B B equal to the numder 

 Fig. 121. 



of buckets (40 in the diagram), and drawing lines C B A 

 towards the centre of the wheel through the points ot 

 division, we are enabled to determine the form of the 

 buckets. The casing extending between A A is called 

 the sole of a bucket, and is left with a narrow slit open 

 at A for the escape of air from the bucket when the water 

 pours into it. The board A B is called the start, and the 

 inclined part B C the arm of the bucket. Sometimes this 

 inclined part is made in two parts at different degrees of 

 obliquity, like the lines B D, D E ; of which B D 

 would be called the arm, and D E the wrist, the start A B 

 being called the shoulder. These names are doubtless 

 given from the resemblance of the section to the form of 

 a bent arm. The whole circumference of buckets and 

 Holes is called the shrouding. 



On dividing the vertical diameter F G of the mean 

 circle of the shrouding into six equal parts at the points 

 H, I, J, K, L (Fig. 120), and drawing horizontal lines 

 through H and L to meet the circumference, we observe 

 that at the upper line the bucket is filled, and therefore, 

 the weight of its contents begins to act in causing the 

 wheel to revolve, while at the lower line it begins to 

 empty itself, and its action may there be considered to 

 cease ; or whatever effect the water may have beyond 

 this point is BO small that it may be neglected as an 



element of power. The total effect of the water, then, 



in causing the wheel to revolve, may be reckoned to be 

 that of the weight of water contained in ten buckets 

 descending through a height equal to two-thirds of 

 the diameter of the mean circle, viz., 22 x = 15 feet 

 nearly. The diameter of the mean circle is equal to 

 the height of fall ; and we may, therefore, by taking 

 a wheel of just proportions, generally obtain a de- 

 scending weight acting through a vertical height two- 

 thirds of the height of fall ; and the weight itself, 

 consisting of the contents of one-fourth of the total 

 number of buckets. The capacity of those buckets 

 for containing water depends manifestly on the 

 breadth of the wheel or the length of the buckets, as 

 well as then- sectional area. The area of those in 

 the diagram, reckoning up to the level line bounded 

 by the air-slit at their filling-point, and by the lip of 

 the bucket where the discharge begins, may be taken 

 at little above 1J- square foot ; and we may suppose, 

 for facility of calculation, that their length or the 

 breadth of the wheel is 1 foot, giving each bucket a 

 capacity for containing 1J cubic foot of water, 

 weighing about 70 Ibs. The contents of the 10 

 buckets, therefore, weigh 700 Ibs. ; and this weight 

 is constantly moving with the velocity of the wheel. 



In determining the absolute power to drive ma- 

 chinery, we must ascertain the velocity in rela- 

 tion to that with which the water flows from 

 the spout. The circumference of the wheel mnst 



^ move at such a rate that no bucket shall pass 

 the spout without being filled from it. The total 

 circumference of the wheel being 75 feet, divided 



into 40 equal parts, we have, for the distance from lip to 



lip of each bucket, -.? = 1 '888 nearly, or about 1 J foot. 



If the wheel make one revolution per minute, each 

 bucket passes any fixed point in j^jth of a minute, or l 

 second ; and the velocity of any point in the circjim- 



Kel 



ference is -~7) ' about 1J foot per second. 



It has been 



stated, that the most advantageous circumferential velo- 

 city of an overshot- wheel is at the rate of 2 to 3 

 feet per second. Taking 2 feet per second for the case 

 we are discussing, the wheel would make 2 revolutions 

 per minute, and each bucket would pass a fixed point in 

 }ths of a second. As the water issuing from the spout 

 has a certain depth or thickness, some time of the 

 bucket's passage must be deducted in order to ascertain 

 the time allowed for influx of the water. Deducting Jrd 

 of the time, that is, J* from J", we have J* as the time 

 during which the bucket remains under the spout to be 

 filled ; and in this time 1J. cubic foot, the contents of the 

 bucket, must flow from the spout that is, 2 X 1 J = 2J- 

 cubic feet in 1 second. As the spout is 1 foot broad, and 

 we must not reckon the depth of water in it above 

 6 inches or \ a. foot, the sectional area of the water- 

 channel is ^ a square foot, through which 2J cubic feet 

 must flow per second. The velocity of the water must 

 therefore be 2 X 2J = 4 feet per second. Should the 

 velocity of the stream be less than this, either the wheel 

 must move more slowly or the spout must be inclined to 

 meet it at a lower level, so that the water may attain 

 greater velocity from additional fall. Should the velo- 

 city of the stream exceed this, either the wheel must be 

 permitted to move more quickly, or it and the spout 

 must be widened, so as to present greater capacity of 

 bucket and diminish the speed of influx. 



Recurring to the power of the wheel, which we suppose 

 to revolve at the speed of 2 feet per second, or 150 feet 

 per minute, with a force of 700 Ibs. at its circumference, 

 we find the efl'ect to be equivalent to 700 X 150 = 105000 



Ibs. moved 1 foot per minute, -- * = about 3J horse- 



ooOOO 



power. 



Had we estimated it in another way by taking tlio 

 quantity of water issuing from the spout, viz., 2^ cubic 



