8vo, cloth, 128. 6d. 



THE NEW FOKMTJLA FOE MEAN VELOCITY OF DISOHAEGE 



OF eivhes and canals. 



By W. R. KUTTER. 



Translated from Articles in the ' Cultur-Ing^nieur,' by Lowis D'A. Jackson, A.I.C.E., Author of 

 ' Hydraulic Manual and Statistics,' ' A Curve Book,' ' Simplified Weights and Measures,' &c. 



ZsTOTIOES OIF THE I=I2,ESS. 



" About a year ago, ■when reviewing the very im- 

 portant investigations of Captain Cvmningham, R.E., 

 on the flow of water in the Ganges Canal, we referred 

 to the above work of Herr Kutter, and expressed a 

 wish that the Institution of Engineers should at least 

 publish an abstract, if no translator or publisher could 

 be found to present English engineers with the whole 

 work, 



" As a result of our suggestion the present transla- 

 tion has been made, and we welcome its appearance 

 none the less that the duty of translation has been 

 assumed by an engineer whose previous studies in the 

 same field render him undeniably competent and 

 trustworthy. 



We have frequently had occasion to ridicule the 

 superstitious reverence with which too many of our 

 so-called hydraulic engineers regard the nostmms of 

 old authorities in their particular branch of science, 

 and we may now the more properly take occasion to 

 state that we consider the present work to be a specific 

 against infection from these old sources of mischief. 

 One minute's glance at the tables will dispel at once 

 and for ever a host of illusions, and a careful reading 

 of the whole work will prove most valuable to students, 

 and interesting to all. 



" The most convenient, and consequently the most 

 generally employed, formulag for the flow of water in 

 open channels are of the form 



v = c \/ rs 



where v is the mean velocity, r the hydraulic mean 

 depth, s the fall of the water in a length of unity, 

 and c the experimental coefiicient. Now, in a given 

 channel, and within certain limits of variation in the 

 depth and surface fall of the water, the value of c 

 remains practically constant, and it lias been but too 

 commonly assumed that it will similarly remain con- 

 stant when applied to other channels widely differing 

 in section and fall. Thus in Beardmore's tables, one 

 value of c does duty for all the cases tabulated, and 

 the author has taken care to notify that the same 

 value will apply to cases outside the limits of his 

 tables, since he says the latter may be readily extended 

 if it be remembered that to get double the discharge 

 you require four times the fall, and so on. What years 

 of laborious research have been wasted in the past, and 

 would be spared in the future, were such an assump- 

 tion only approximately true ! But unhappily it is 

 about as unwarranted an assumption to take a constant 

 value for c as it would be to assume a constant length 

 for a degree of longitude. The latter will vary but 

 little within certain limits of latitude, and the former 

 ■will similarly vary but little within certain limits as 

 regards depth of water, fall of the channel, and condi- 

 tion of its surface. 



"We are of opinion, therefore, that the present 

 translation of Kutter's work has appeared none too 

 soon, and that it wiU fill a long-standing void injthe 

 literattu-e of hydraulic science." — Engineering. 



" The fact that the erosion of the bed and destruction 

 of the works of the Ganges Canal were due to the 

 reliance placed by Colonel Cautley, R.E., in common 

 ■with the majority of the English engineers of the day, 

 on the velocity-formula of Dubuat, which proved, in 

 this instance, mischievously misleading, is a proof of 

 the great practical importance that attaches to a 

 thorough knowledge of hydraulic law, in so far as it 

 is at present ascertained. Considerable gratitude is 

 therefore due to the enterprise, whether it be that of 

 the author or that of the publisher, which has led to 

 the publication of a book which must have been so 

 costly to print as Kutter's ' Hydraulic Tables,' which 

 are reproduced in a clear and intelligible form by the 

 translation of Mr. Jackson. The public addressed by 

 such a work is not large ; but to that public it has an 

 indispensable value. Herr Kutter has brought the 



new formula; of D'Arcy and Bazin, and the new 

 formula of the American engineers, Humphreys and 

 Abbot, to the test of a tabulated series of experiments 

 collected from very wide observation. From a com- 

 parison of eighty-five measurements of discharge in 

 Swiss rivers, it appears that the formula of D'Arcy 

 and Bazin give velocities within 4 per cent, of those 

 actually observed ; while the formula of Chezy-Eytel- 

 wein gives a velocity of 252, and that of Humphreys 

 and Abbot a velocity of 46, against an observed velo- 

 city of 181, on the average of the experiments. The 

 American formula is based on measurements of the flow 

 of the Mississippi and its affluents, where the volume 

 is immense and the inclination of the bed is very small. 

 It appears, from what we have above stated, that the 

 application of such a formula to the flow of water 

 under other conditions is entirely out of the question. 

 The subject is of too technical a nature for us further 

 to pursue ; but we are able thoroughly to recommend 

 the book ; and that the more so because, in spite of 

 the extreme importance of the subject, both as relates 

 to our own country and to India, hydraulic engineering 

 is not a branch of the art and science of the engineer, 

 as to which Great Britain can ■with any truth be said 

 to occupj' a leading, or even a satisfactory, position. 

 Herr Kutter's work, which appeared in 1870, was 

 immediately translated into French, Dutch, and Italian. 

 English engineers are indebted to Mr. Jackson for the 

 manner in which he has translated it into their own 

 tongue." — Athe^iceum. 



" This translation will be of interest to aU engiDeers 

 in India who are familiar with the large work, ' Hy- 

 draulic Manual and Statistics ' of the translator, now 

 translated into Russian. HydrauUc engineers of every 

 description, from the engineer of experience down to 

 the extra assistant commissioner, who tries to find out 

 how much irrigation water may be conveyed in a small 

 trench of supply, will be glad to learn something of 

 the way in which the only trustworthy formula for 

 calculating discharges of water in open channels of 

 every size and inclination, and in any material, has 

 been eventually arrived at. It has been deduced from 

 experimental observations on rivers of all sizes, up to 

 the Mississippi down to trenches a few inches wide, 

 with inclinations from those scarcely appreciable do^wn 

 to the steep gradient of Swiss torrents ; and allowance 

 is made for every material of surface, from smooth 

 curbstone, planed and unplaned timber, rubble, earth, 

 and grass-covered and pebble-impeded mud. The 

 tables given in this work enable the formula to be 

 applied in practice in metrical measures, with the 

 least amoimt of work : the diagram answers the same 

 purpose, both for metrical and for English measures. 

 The application of this formula and tables for English 

 measures having been already fully carried out in Mr. 

 Lowis Jackson's ' Hydraulic Manual,' this translation 

 may be considered as a useful adjunct to it." — AUen's 

 Indian Mail. 



" ' The New Formula for Mean Velocity of Discharge 

 of Rivers and Canals ' is an English translation by 

 Mr. Lowis Jackson, A.I.C.E., from a German work 

 by Herr Kutter, ■^\ hich has already circulated widely in 

 many parts of Europe. Hydraulic science in England 

 appears to have lagged far behind other branches of 

 engineering, in which our countrymen have kept the 

 lead of other nations for years past. Even the great 

 field which India has offered to our engineers seems in 

 this respect to have been but indifferently worked, 

 owing, in great measure, to faulty theories and defec- 

 tive or mistaken methods. The new fonuula claims to 

 point the way to more successful applications of hy- 

 draulic science in the future, and the claim is certainly 

 supported by the good opinions of some experienced 

 judges in this cotmtry, as weU as others, not forgetting 

 -Home Xews. 



London: E. & F. N. SPON, 48, Charing Cross. 

 New York : 446, Broome Street, 



