552 



HYDRODYNAMICS. 



Ovmliot 

 Wheels. 



Overshot 

 wheels. 



PLATE 

 CCCXIX. 

 Fig. 15. 



5ig. 16. 



power is conveyed to the other parts of the machine. 

 When the water is introduced into buckets placed round 

 the circumference of a wheel moving in a vertical plane, 

 so as to put the wheel in motion merely by its weight 

 in the buckets, the wheel is called an overshot wheel, 

 from the water being introduced over or near the sum- 

 mit of the wheel. When the water, after having ac- 

 quired a considerable velocity by its descent along an 

 inclined plane, is made to strike plane surfaces, or float- 

 boards, arranged round the wheel's circumference, so as 

 to put the wheel in motion merely by its impulsive force, 

 it is called an undershot wheel, from the water being in- 

 troduced at or near the under part of its circumference. 

 When the water is introduced neither at the upper nor 

 the lower point of the wheel, but at a point between 

 them, so as to fall upon float boards fixed in the wheel's 

 circumference, and to act both by its weight and by its 

 impulse, it is called a breast wheel. When the water is 

 made to issue from an aperture in the circumference of 

 a wheel in the direction of the tangent, the wheel is 

 said to be driven by the re-action or counter-pressure 

 of the water. We shall now proceed to consider, in se- 

 parate Sections, the best mode of constructing water 

 wheels of these four different forms. 



SECT. I. On the Construction of Overshot Wheels. 



AN overshot wheel of the common kind, is represent- 

 ed in Plate CCCXIX. Fig. 15, where ABCD is the 

 rim of the wheel, having a number of buckets a,b,c, d, 

 arranged round its circumference. When the wheel is 

 in a state of rest upon its axis O, and water is introdu- 

 ced into the bucket c from the horizontal mill course 

 or canal EF, the weight of the water in the bucket, 

 acting at the end of a lever equal to m O, puts the wheel 

 in motion in the direction c d. When the subsequent 

 bucket b comes into the position c, it is also filled with 

 water, and so on with all the rest. When the bucket 

 c reaches the situation of d, its mechanical effect to 

 turn the wheel is increased, being now equal to the 

 weight of water acting at the end of a lever n O, 

 equal to the distance of its centre of gravity d from a 

 vertical line passing through the axis O, so that the 

 mechanical effect of the water in the bucket increases 

 all the way to B, and of course diminishes while the 

 buckets are moving from B to C. 



The buckets, however, between B and C, have not 

 the same power upon the wheel as those between A and 

 B ; for the water begins to fall out of the buckets be- 

 fore they approach to B, and are almost complete- 

 ly empty when they reach the point H. The con- 

 struction of the buckets, therefore, as shewn in the Fi- 

 gure, is very improper, as it not only allows the water 

 to escape before it has reached the point B, where its me- 

 chanical effect is a maximum ; but also to escape com- 

 pletely, long before they have reached the lowest point 

 C of the wheel. The power, therefore, of an overshot 

 wheel must depend principally upon the ferm which is 

 given to the buckets, which should always be fullest 

 when they are at the point B, and should retain the 

 water as long as possible. If the buckets were to con- 

 sist of a single partition in the direction of the radii of 

 the wheel, all the water would escape from the buckets 

 before they passed the point B on a level with the 

 axis O. 



The form of a bucket, which has been regarded as the 

 best, is represented in Fig. 16, by the line DCBAGIKL, 

 where it is represented as composed of three partitions, 

 viz. AB and GI, called the start or shoulder, which lies 



5 



in the direction of the radius ; IX and IK, called the 

 arm, and inclined at an obtuse angle to the radius ; and 

 CD, KL, called the mrtst, and inclined at an angle less 

 than 180 to the arm BC or IK. The depth AG of each 

 bucket is about If of GH ; AB is i of AM ; and the 

 angle ABC is such, that BC and GI "prolonged would 

 pass through the same point H. It ends, however, in 

 C ; so that FC is Jths of GH ; and CD is placed so, that 

 HD is nearly f th of HM. Hence it follows, that the 

 arc FABC is nearly equal to DABC ; so that the quan- 

 tity of water FABC will still continue in the bucket 

 when AD is a horizontal line, which happens when AB 

 forms an angle of about 35 with a vertical line. The 

 preceding construction of the buckets is obviously too 

 complicated, and very little additional power is gained 

 by the angle BCD. Hence the general practice is to 

 continue BC to H, and AB is generally only ^d of GH. 



Such is the general view of the construction of buc- 

 kets, which is given by Dr Robison ; but we cannot 

 agree with him in thinking that this form is the best. 

 It must be obvious, upon the slightest consideration, that 

 the power of the wheel would be a maximum, if the 

 whole of its semi-circumference were loaded with wa- 

 ter. This effect would be produced, if the buckets had 

 the shape shewn in Fig. 17, where ABC is the form of 

 the bucket, AB being in the direction of the radius, and 

 BC part of the circumference of the wheel, and nearly 

 equal to AD. This construction is, however, impracti- 

 cable, as the aperture EC is not large enough either tor 

 the admission or the escape of the water, and when 

 the last portion of the water flows out along BC, it 

 would strike against the bottom DE of the bucket im- 

 mediately above it. We must therefore consider what 

 modification this form should receive, in order to give a 

 free passage to the water at EC. This may be effect- 

 ed, by making BC (Fig. 18.) a little larger than BE, 

 and diminishing AB, so as to make the angle ABC a 

 little greater than 90. In this way an aperture dE 

 will be obtained, of sufficient magnitude both for the 

 introduction and the discharge of the fluid; and the last 

 portion of water will no longer strike against the bottom 

 D d of the upper bucket. When the water is properly 

 introduced by the methods afterwards to be described, 

 this construction will be found to give great additional 

 power to the wheel. Hence we see the reason why 

 the inclination of DC, in Fig. 16, is advantageous, as 

 it is an approximation to the preceding construction. 



The late Mr Robert Burns of Cartside in Renfrewshire, 

 a most ingenious millwright and mechanic, proposed 

 what appeared to be a very great improvement upon the 

 form of the buckets in overshot wheels. It consisted in 

 using a double bucket, as shewn in Fig. 1 9, where LM is a 

 partition almost concentric with the rim, and placed so 

 as to make the inner and outer portions of the bucket 

 hold equal quantities of water. When these buckets 

 are filled ^d, they retain the whole water at 18 from 

 the bottom of the arch, and they retain | of the water 

 at 1 1. Another great advantage of this construction 

 is, that when there is little water to drive the wheel, it 

 may be directed, by a slight adjustment of the spout, 

 into the outer bucket, so as to make up, by the addi- 

 tional length of lever, for the small quantity of wa- 

 ter which is in use. These advantages, however, are 

 found in practice to be counterbalanced by disadvan- 

 tages which cannot be got the better of. The water 

 is found never to fill the inner buckets, and on this ac- 

 count we believe Mr Burns did not put the construc- 

 tion in practice. 



It has in general been assumed by writers on water 



Overshot 



Wncels. 



PLATE 

 CCCXIX. 

 Fig. 16. 



New form 

 of the buc 

 kcts. 



Fig. IT. 



Fig. 18. 



Double 

 bucke 

 contriv 

 by Mr 

 Burns. 



