1843.] 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



HI 



an overshot wheel, whose diameter is equal to the fall. The velocity of a 

 water wheel working thus, may vary through a larger range without a ma- 

 terial loss of power, and a steady motion is continued to a lower velocity 

 than when it is working in a free race. 



The author finally arrives at the following general practical conclusions : — 



1st. When the depth of water in the reservoir is invariable, the diameter 

 of the water-wheel should never be greater than the entire height of the 

 fall, less, so much of it as may be requisite to give the water a proper velo- 

 city on entering the buckets. 



2nd. When the depth of water in the reservoir varies considerably and 

 unavoidably in depth, an advantage may be obtained by applying a larger 

 wheel, dependent upon the extent of fluctuation and ratio in time, that the 

 water is at its highest and lowest levels during a given prolonged period ; if 

 this be a ratio of equality in time, there will be no advantage ; and hence, 

 in practice, the cases will be rare when any advantage will obtain by the use 

 of an overshot wheel, greater in diameter than the height of fall — minus, 

 the head due to the required velocity of the water reaching the wheel. 



3rd. If the level of the water in the reservoir never fall below the mean 

 depth of the reservoir, when at the highest and lowest, and the average 

 depth be between an eighth and a tenth of the height of the fall, then the 

 average labouring force of the large wheel will be greater than that of the 

 small one ; and it will of course retain its increased advantage at periods of 

 increased depth of the reservoir. 



Dr. Robison's views, therefore, upon this branch of the subject, should, he 

 contends, receive a limitation. 



A positive advantage is obtained by the use of the conduit varying with 

 the conditions of the wheel and fall, of nearly 11 per cent, of the total 

 power. 



The value increases with the wheel's velocity up to 4^ feet per second, or 

 to 6 feet per second, in large wheels. Hence, he argues, that it is practicable 

 to increase the efficiency of the best overshot wheels, as now usually made, 

 at least 10 per cent, by this application. The only objections urged against 

 the use of the conduit are of a practical character, relating to the difficulty 

 of making it fit close, of repair, &e. ; but however these may have applied 

 to the rude workmanship of the older wooden wheels, with wood or stone 

 conduits, they are unimportant, as referring to modern water-wheels made of 

 iron. The conduits may be also made of cast-iron, provided with adjusting 

 screws, and hence of being always kept fitting, readily repaired, and capable 

 of being withdrawn from the circumference of the wheel in time of frost, &c. 



The paper is illustrated by a drawing, showing the elevation and partial 

 sections of the experimental apparatus, and a diagram showing the full size 

 of the loaded arc of each model. 



Mr. Farey observed, that the result arrived at by the experiments, appeared 

 to correspond nearly with those recorded by Smeaton, who had experi- 

 mented upon, and used practically both kinds of wheels. The buckets of 

 the model wheels used in the experiments did not appear to be of the best 

 form, and they were entirely filled with water ; hence an apparent advantage 

 had been obtained, by the use of the circular conduit to retain the water in 

 the buckets. But that would not be realized in practice, for as the form of 

 the bucket regulated the point at which the water quitted it, and it was the 

 practice of the modern millwrights to make the wheels very broad, in order 

 that the buckets should not be filled to more than one-third of their depth, 

 the circular conduits became less useful, and in fact were now seldom used. 

 Smeaton's practice was, to entirely fill the buckets with water, but he never 

 adhered to the slow velocity of revolution which he recommended theoreti- 

 cally in his paper to the Royal Society. 



Mr. Fairbairn had adopted broad wheels with an improved form of bucket, 

 partially filled, and had obtained a more regular motion, particularly at high 

 velocities. 



Mr. Farey promised to present to the Institution, a copy of the method of 

 calculation adopted by Smeaton for water-wheels. 



Mr. Taylor corroborated Mr. Farey's statement of the advantage of using 

 broad wheels, with the buckets of a fine pitch and partially filled ; circular 

 conduits then became unnecessary : this was practised among the millwrights 

 in North Wales with eminent success, and a velocity of six feet per second 

 was given to the wheel. 



Mr. Homersham believed that in Smeaton's latter works he increased the 

 velocity of his wheels to six feet per second. 



Mr. Rennie gave great credit to the author for the ingenuity of the appar- 

 atus with which the experiments were tried, and for the clearness of the 

 tabulated results; but owing to the necessary limited size of the model 

 wheels, he feared the results could not be relied upon for application in 

 practice to large wheels. The experiments of Borda, Bossut, Smeaton, 

 Banks and others, were all liable to the same objection. 



The best modern experiments are those by the Franklin Institute, by Pon- 

 celet, and by Morin. 



The result of these might be taken thus : 



Undershot wheels, the ratio of power to effect varied from 0-27 to 0-30 



Breast wheels „ „ „ n n-45 to 0-50 



Overshot wheels „ „ „ o-60 to 0-H0 



Average „ „ „ H 0-60 



The velocity of the old English water-wheels was generally about three 

 feet per second; the American wheels four feet, and the French wheels six 

 feet : this latter speed was now adopted by the best millwrights in England. 

 Mr. Hughes, at Mr. Oott's factory at Leeds, and Mr. Faiibairn, had found 



advantage from it ; the latter also had a particular contrivance for carrying 

 off the air freely from the buckets. 



It was important to regulate the thickness of the sheet of water running 

 over the shuttle upon the wheel ; four to five inches was found in practice 

 to be the maximum depth allowed. 



The object being to utilize the greatest height of fall and the greatest 

 available quantity of water, by means of properly constructed openings and 

 such sluice-gates as were first introduced by the late Mr. Rennie for the 

 breast-wheels constructed by him, instead of penning up the water in a 

 trough, it was made to flow in a sheet of regular thickness over the top of 

 the shuttle, and by a self-regulating apparatus to adjust itself at all times to 

 the height of the water ; thus obtaining the advantage of the full height of 

 the fall at its surface, and obviating the necessity for the apparatus proposed 

 by Mr. Mallett. 



Mr. Mallett begged to dissent from the validity of the objections which 

 had been made to the practical value of his experiments. With respect to 

 the form of the bucket, that used by him could not, he contended, be called 

 a bad form, although it might be susceptible of improvement ; but as the 

 experiments were altogether comparative, it was foreign to the question 

 whether the form was bad or good, the same having been used in both 

 wheels. 



As it was shown that a certain relation subsisted between two water 

 wheels with the same total descent, but with different diameters, as to their 

 co-efficient of labouring force, a proportional relation would exist with any 

 worse or better form of bucket. The results considered as absolute measures 

 of effect, being obtained with a form of bucket which approached nearer to 

 the best forms now in use, than did those of Smeaton or any other experi- 

 menter, were more applicable to modern practice, and therefore he must con- 

 sider his results, as not without utility. 



With regard to the custom of only partially filling the buckets, it must be 

 remarked that buckets of the best forms begin to spill their contents before 

 arriving at the lowest point of the loaded arc ; the partial filling could, 

 therefore, only palliate the evil which the circular conduit was designed to 

 remedy. He must, however, contend that a positive disadvantage attended 

 the partial filling. A permanent loss of fall was produced equal to the 

 distance between the centres of gravity of the fall, and of the empty portions 

 of the top bucket at the moment it had passed the sluice ; this distance 

 could be but little varied by the fineness of pitch of the bucket, and depended 

 more upon the depth of the shrouding. That there was a constant loss of 

 labouring force by a practical diminution of the effective leverage, or a re- 

 duction in the " moment " of the loaded arc. That as the wheel revolved, 

 the centre of gravity of the fluid contained in each bucket, as it approached 

 the lower portion of the loaded arc, was transferred to a greater distance 

 from the centre of motion even before the contents commenced spilling ; but 

 the angular motion of the centre of gravity of any one bucket was at first 

 that due to its distance from the centre of motion of the wheel, or to its 

 radius ; and as the radius increased, a greater angular velocity would be ac- 

 quired by the water which had changed its position on approaching the 

 lower point of the wheel ; but this increased velocity was given at the ex- 

 pense of the power of the wheel, and hence a partially filled bucket would, 

 he contended, be always attended with a loss of labouring force. To the 

 last objection, a full bucket was not liable. 



From all these reasons, he felt justified in concluding, that the use of the 

 circular conduit was more advantageous than the practice of partially filling 

 the buckets. 



With respect to the shuttle delivering the water over the top, where the 

 head of water and the fall were constant, no advantage could be obtained by 

 the use of a wheel greater in diameter than the total descent ; it was assumed 

 that this form of shuttle would be used in order always to deliver the water 

 as high as possible upon the periphery of the wheel ; but the question was, 

 " If the head be variable, what should be the diameter of the wheel to se- 

 cure the best effect ? " The paper showed that a wheel whose diameter was 

 equal to the total descent, when the head was a maximum, did not always 

 give the greatest average labouring force. The question was therefore inde- 

 pendent of the sort of shuttle used ; it assumed the power of always admit- 

 ting the water upon the wheel at the highest point of the total descent, and 

 sought to establish the best relation between the diameter of the wheel and 

 the whole descent when the head alone was variable, according to givea 

 conditions. The results of this part of the investigation, therelore, while 

 they admitted the full value of Mr. Rennie's shuttle, went further, and 

 pointed out the limits of its useful application. 



He was fully aware of the prejudice which existed agaiust the circular 

 conduit, and once participated in it ; but his atteutiou had been forcibly 

 drawn to it in his practice, and having used them very beneficially upon 

 wheels of 40, 50, and 60 horses' power, which he had constructed for mining 

 purposes, he wished to draw the attention of the profession to the considera- 

 tion of their practical merits when adapted to good wheels. 



Kngltsh Marm.e.— A bed of variegated marble has been discovered in a 

 limestone quarry, belonging to George PyLms, Esq., of Muldleton Tyas, near 

 Richmond, Yorkshire. A small piece has been dressed by a skilful workman ; 

 the pulish is beautiful, and the marble seems likely to be brought into gene- 

 ral use. 



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