141 



THE CIVIL ENGINEER AND ARCHITECrS JOURNAL. 



[Ma^ 



man, vet, were it to cease, the eirtli wouM be shortly deluged. Not 

 only 1\k particles of the ocean, but of tln' air, are subject to its in- 

 fluence,— the magnet acknowledges it, and every particle composing 

 and surrounding this heterogen'-ous mass. If geographers, geolo- 

 gists, and astronomers look at the constant changes which take place 

 on the surface of the earth, anl in the appearance of the heavenly 

 bodies, in accordance with this general law of nature, they cannot for 

 a moment question its existence. 



ON THE MEASUREMENT OF WATER DELIVERED 



THROUGH LARGE (OR WIDE) ORIFICES. 



By M. MoRiN. 



(Communicated lo the Academic des Sciences, Paris.) 



In experiments on hydraulic motive powers, the most delicate por- 

 tion, and that most subject to error, is the measurement of the quan- 

 tity of water expended. Local circumstances, forms, or shapes, the 

 arrangement of Hood-gites, exert on that quantity great influence, 

 which, as yet, has been too little studieil, and the inexact apprecia- 

 tion of which has frequentlv led the m:)st conscientious observers into 

 serious errors, to which may b^ attributed, very frequently, the mani- 

 fest exaggeration of certain results announced with the most perfect 

 sincerity. 



In order to avoid such errors, an 1 to establish with some certainty , 

 or at least with a sufficient approximation to it, the ratio of useful 

 effect produced by the motive powers submitted to experiment, to 

 th? absolute amount of water expanded, I endeavoured to determine 

 upon a mode of measurement beyond the reach of controversy, which 

 was somewhat difficult. 



For this purpose, I first reflected whether I could measure, with 

 sufficient exactness, the quantity of water supplied by an overshot- 

 wheel sluice fixed at the head of a channel or race, in whicli the mo- 

 tive powers to be subjected to experiment were to be placed. 



This sluice is equal in width to the head-race, constructed of mi- 

 sonrv; it is inclined from above downwards at an angle of above G 5 

 degrees to the horizon; its upper edge has an acute angle up-stream, 

 anl is rounded off down-stream ; it is 3 inches thick. Two racks, 

 each of 2 inches wide, reduce the clear width to 6 ft. 7 in. 



In order to estimate the volume or qumtitv of water that passed 

 over this sluice, the tail-race, which was constructed of masonry, with 

 a rectangular section, was closed below by a vertical dam of plank, in 

 which were made three openings; to these were fitted sluices of 

 about 0-300 m. (1 foot) square, of thin sheet iron, of about 0-005 ra. 

 (-j% in.) in thickness, sliding in front of the orifices, wdiich were formed 

 with sliarp edges. These iron sluices were, by means of screws, 

 worked by hand ; rods with marks showing the level, were placed in 

 front of the overshot-wheel sluice and the iron sluices, in order to 

 show and to verily tli^ invariableness of the levels. 



From this short description, it may be readily conceived that by 

 making siinu'taneous observations at the overshot-wheel sluice, and 

 at the regulating orifice, the supjily, or quantity delivered by the two 

 kinds of orifices, might be calculated, by means of the very precise 

 results of the experiments of Messrs. Poncelet and Lesbros, and which 

 were evidently applicable, with all desirable exactness, to the case ia 

 question. 



But these experiments, undertaken on canals of great dimensions, 

 which had vast oasins, subject to the effects of the winds, and whose 

 level it was difficult to regulate perfectly by means of an ordinary mill 

 sluice, could not possess a degree of exactness comparable to that of 

 experiments made under mure favourable circumstances. In order 

 to examine into the whole together, and to disengage the results from 

 accidental influences, we have re-produced them by a graphic con- 

 struction, taking the values of the charge (or head of water) H, on top 

 of the sluice, as abscissa, and those of the co-efficient of the supply or 

 delivery as ordinates. 



In examining the table of the results, and, above all, the curve 

 .ndiich represents them, it is seen that the values of the co-efficient of 

 the supply or delivery increase rapidly witli those of the charge H, 

 on the ground-sill of the orifice, from H = 0-03 m. (12 inches), and 

 0'04 m. (15i inches), up to H=0'10 m. (4 inches), aterm beyond which 

 they still continue to increase, bat more and more slowly. 



If, to compare these results obtained with a sluice of 6 ft. 7 in. in 

 width, equ il to that of the head-race, and placed in the before-men- 

 tion*d circumstances, with those which relate to a sluice of 0-20 m. 



(nearlv 8 inches) wide, to complete contraction, we determine, by 

 means of the figure, the values corresponding with Ihe charge* ob- 

 served; in this last ease, the following table may be formed, which is 

 limited to the charge! with which we have operated : 



It is seen tiiat for small charges, this sluice of 0-08 m. (3 inches) 

 thick, produces a notable diminution in the supply or delivery, although 

 the contraction may be nearly annulled on the vertical sides of the 

 orifice. This effect is an dogous to that observed by Messrs. Poncelet 

 and Lesbros on small overfalls passing through a shute. We know, 

 in fact, that, in the cases in which the contraction is nearly null on 

 the sides, these observeis found the following values of m : 



Charges on the upper 

 side of the overfall. 



Values of m. 



0-04 m. 

 0-246 



0-06 m. 

 0-271 



0-10 m. 

 0-308 



0-15m. 0-21 m. 

 0-324 



These values, which, for small charges, made a very near approach 

 to those we have obtained, show that the diminution of the suppiv or 

 delivery depends, in both cases, on the same cause — on the resistance 

 of the side or wall of the sluice, or of the shute. We notice, in fact, 

 that in small charges, the fluid vein wets and follows the surf ice of 

 the sluice ; but in proportion to the increase of the cAar^e, this in- 

 fluence of the sides or walls di iiinishes, and soon, indeed, the fluid 

 vein detaches itself completely from the upper edge, which is sharp 

 up-stream, and the resistance of the surface of the sluice ceases to b ^ 

 felt, whilst at the same time the suppression of the lateral contraction 

 continues to exert an increasing influence on the augmentation of the 

 supply or quantity delivered ; whence it results that the co-efficient 

 of the supply or delivery increases. 



Such is the natural and sim[)le explanation that inay be given of the 

 smallness of the values of the co-elfieieat of the suppiv or delivery f jr 

 the small charges, and of their mignituJe for the larg? cAjr^cS ob- 

 served in our experiments. 



Notwithstanding the care taken in the execution of these experi- 

 ments, the local causes and circumstances mentioned did not permit 

 us to approximate nearer than yjth or Tj^th ; but the sketch shows, 

 nevertheless, by taking them as a whole, the gradual and continual 

 progress of the increase of the co-etficient of the supply or delivery, 

 and, until new and more precise researches are made, 1 think we may, 

 in applications to an dogous cases, adopt with sufficient accuracy for 

 practice, the values deduced from the sketch, for the co-efficient of 

 the supply or delivery, viz. : — 



Charges on the Sill of the Ocerfall, — in metres. 



0-04, 0-05, 006, 007, 0-08, OO'J, O'lO, 012, 0-14, 016, 0-18, f)-2lt, 



falues of the Co-efficient m., — in metres. 



0-264, 0-.113, 0-.'i3J, 0393, 0-41H, 0-437, 0-448, 0-460, 0-467, 472, 0-477, 0-482 . 



These values, which, for charges exceeding 0-10 m. (4 inches), are 

 much greater than those which have been, up to this time, adopted 

 for similar cases, show that sluices, arranged like that made use of by 

 us, which is the case with many horizontal wheels, deliver more water 

 than is generally admitted to be the case ; and that, in experiments 

 on hydraulic motive powers, we are liable, for want of a good method 

 of measurement, to estimate the suppiv or delivery of water at one- 

 sixth or one-seventh below the real amount, and, on the other hand, 

 very much to overvalue the useful effect. 



Experiments on an Orijice mith the Charge on the Summit. 



Although the ensemble of the results obtained with the overshot 

 water-wheel sluice, enables us to determine with sufficient exactness, 

 at least for practice, the amount of water actually supplied or de- 

 livered in the experiments proposed, on hydraulic motive powers, I 

 have thought it best to in ike use, for this purpose, of an orifice with 

 the cAar^'e on the summit, so tint the li.;ight, and, conaequeully, the 



