160 ADXISSIONS AND ELECTIONS. [Minutes of Associafe IlIe1r~71err. HORACEALLEN, Stud. Inst.C.E. GEOXGEDALLAS MARSTOX, Stud. Inst. JAMES ATEINSON. C.E. ARTHUR BARCLAY. CHARLESEDWARD MASTERMAN. CHARLESWILLIADX BARNETT. JOHXNETHVEN. FELICIANOMENDES DE MESQUITA \vILLIAM BURTON8bVILLE IIILLS, BARROS. Stud. Inst. C.E. WILLIAM BASHALL, Jun., Stud.Inst. WILLIAU PCRCELLOWEILL, Stud. C.E. Inst. C.E. PERCYBENHAB~, Stud. Inst.C.E. CAHILOGUILLERXO PARDO,Stud. EDWARDROBERT BIRCH, B.A., B.E., Inst. C.E. Stud. Inst. C.E. CHARLES DONALD NAPIERPAREEL HARRYBIRD. HENRYPARKES, Stud. Inst. C.E. WILLIAMNISBET BLAIR, Stud. Inst. WILLIAM MORROPEARSE. C.E. CHARLESBERKELEY PENLINGTOB, CARL RODERIQUELOUIS MENNI BONN. Stud. Inst. C.E. THOXASSMITH BRIGHT,Stud. Inst. WILLIADIFRANK PETTIGREW, Stud. C.E. Inst. C.E. CHARLESEDWIX BROWN. WILLIAXHEXRY RADFORD. WILLIAMHENRY BURR. WILLIAXREID. JAMESBUTLER. PETERROBERTS. ALBERTHAVELOCK CASE. HENRY GEORGEARCHIBALD ROUSE. ALFRED CREER. HEXRYROYLE. FITZHERBERT RUXTOXDESPARD. ROBERT ALLENWILLIAM SNINNERTON. HEXRYFRANCIS DOREY, Stud. Inst. ALBERTHARRISON TURNER. C.E. PERCYJOHN WATES. QEORGEHOLLAND ERSKINE, Stud. Inst. THOMASDUNClN WEIR, Stud.Inst. C.E. C.E. HARRYF~ANCIS. I~AU~IICEFITZGER.4LD WILSON, Stud. JAMESFRENCH. Inst. C.E. ROBERTMACNISH GALE. JOHN i%CKWORTH WOOD. RICHARDHACK. FREDERICKADLARD WRIGHT, Stud. GEORGE HOWARDHARBISON. Inst. C.E. LLOYDHASSELL, Stud. Inst. C.E. ROBERTW.4DE WRIGHT, Stud. Inst. PERDINANDHUDLESTON. C.E. WILLIAMOWEN LGCAS. Associate. WILLIAVWAKEFORD. ‘‘ Speed on Canals.” BY FEANCISROUBILIAC CONDER, M. INST.C.E. THEamount of resistance tothe propulsion of vessels through narrowchannels, due to the size, the form, andthe surface of the channel,has not hitherto been fully studied. Thatthis Downloaded by [ University of Liverpool] on [15/09/16]. Copyright © ICE Publishing, all rights reserved. PLATE 1 e% 120'.0" X 20'.0' FORT H AND C LVD E. 1768. GLOSTER AND BERKLEY. 1793. CALEDONIAN. 1803. WILTS AND BERKS. GLASGOW, AND PAISLEY. 1796. AMSTERDAM. 31865. 1803. 45'"'' X 5'.0" 50'.0"x R'.O' GRANDJUNCTION. MONKLAND 17 DD. NORTH HOLLAND. 1770. 1825. K.CONDER, DEL? DownloadedF by [ University of Liverpool] on [15/09/16]. Copyright © ICE Publishing, all rights reserved. Proceedings.] CONDER ON SPEED ON CANALS. 161 resistanceincreases in some ratio tothe diminution of free mater-way is known. In the ‘Minutes of Proceedings’will be found the statement that asteamer which attained a speed of from 16 to 18 miles an hour at sea, could not make more than from 8 to 9 miles per hour in the narrowest part of the Clyde ; 1 and that a boat which had a speed of 10 miles per hour in the Liffey, could not make more than 7 miles per hour in the Royal Irish Canal.2 The instant acceleration of a boat on passing into deeper water, which was mentioned in the debate cited, is well known to all boating men. But no formula for determining the proportion is to be found in engineering text books. It was the advice of the Author, on being consulted on one of the most important hydraulic projectsof the day, that there should be instituted, in the firstplace, so thorough an investigation of the mainscientific questions involved as to leave no point open to hostiIecriticism. Among the specialsteps recommended to this end was “ the commencement of a series of experiments for deter- mining the form of cross:section best suited for canal navigation.” The recommendation nothaving beencarried out, the Author has endeavoured to apply to theelucidation of the question certain known facts as to the movement of water in channels of various forms, and as to the movement of vessels in open waters. As to the first, the experiments of Darcy and Bazin have been chiefly of use; and as to the second, those of the late Mr. W. Froude, N. Inst. C.E., on the wave-making resistance of ships. Since the commencement of the inquiry, its importance hasbeen accentuated by the extraordinarydegree of attention that has been excited bythe Suez Canal, and by the remarkablephenomenon of the retardation effected in thepassage of vessels, although not amount- ing to an average of five each way per day. The average time occupied in actual movement through the canal hasincreased from seventeen hours pership in1876, to eighteen hours sixteen minutes in 1881, and to eighteen hours fifty-seven minutes in 1882; the speed slackening from 5 * 88 to 5 -47and 5 27 miles per hour. The time passed in the canal by each ressel has risen from thirty-nine hours in 1876, to fifty-three hours forty-six minutes in 1882. And a very recent Report cites three cases of English mail steamers detained for seventy-one hours each in the canal. It is thus un- deniable that the question of canal capacity for transport assumes * Minutes of Proceedings Inst. C.E., vol. xxvi., p. 20. * Ibid., vol. xxvi., p. 32. TILe Times, 20th September, 1883. [THE INST. C.E. VOL. LXXVI.] M Downloaded by [ University of Liverpool] on [15/09/16]. Copyright © ICE Publishing, all rights reserved. 162 CONDER ON SPEED ON CANALS. [Minutes of a foremost rank among the practical engineering problems of the day. In theabsence of direct experiment, the only method available for the purpose of research is the comparative method. By this, mathematical considerations may beillustrated toa certain extent; and it may be at all events hoped to get so far as to determine where direct experiment becomes indispensable. A vessel in its progress is continually displacing a mass of water equal to its own submerged bulk. This mass is usually calcu1at.ed as proportional to the greatest immergedcross-section of the vessel ; an approximationsufficiently close for the presentinquiry. In open water, the vacuum that would otherwise be left in the wake of the vessel is filled by the water rushing infrom all sides. It is unnecessarynow toinquire how this movement of thewater affects the speed of the vessel, as the ordinary performance of the latter inopen water is taken as the unit of comparison. Whenthe movement of a vessel takesplace in a restricted channel, the case is altered. There is no longer an indefinite supply of water all round thevessel to rush into the hollow at the wake. That hollow is filled, eitherby water which follows the movement of the vessel through the canal, or by that which Aows as a counter current, being driven by the head due to the wave caused by the vessel. The first of these two actions is so limited that it may be neglected except in river navigation. The back- ward current, taken alone. will be directly as the speed and as the cross-section of the vessel, and inversely as the free water-way, or excess of t,he cross-section of the canal over that of the vessel. Thus a vessel moving through a restricted channel has to on- counter an opposing current which is a function of her own move- ment. Her speed will be the resultant of her proper motion and of that of the current, inso far asit affects her, and willbe, roughly speaking, the difference of the two speeds. It is thus possible to obtain, subject to further elucidation, a general formula for the retardation of a vessel in a canal due to the back-current produced by her own movement. Let A = the cross-section of the canal ; a= 7) 7, ,) ,) vessel; A n = -. a’ V = the speed in open water ; y = the back-current in thecanal ; X = the speed of the vessel in thecanal. Downloaded by [ University of Liverpool] on [15/09/16]. Copyright © ICE Publishing, all rights reserved. Proceedings.] CONDERON SPEED CANALS.ON 163 Then v=x+y, X and, as the free water-way is equaln - to 1, y = -- n - 1’ therefore v=x+- X 12- 1 (1) Let, for example, 12 = 4. Then v=x+3,X and x=2v. It results, however, from the experilncnts of Darcy and Bazin, as well as from theory, that not only must the area of the channel be regarded, but also its form, and the special nature of the wetted surface. Of all forms of channel, according to this authority, the semi-circular is that which offers least resistance to the flowof water ; as it is also that of which the hydraulic radius is the largest, in proportion to the area. Butthe hydraulic radius, or the areadivided by thewet n perimeter, = is approximately the same for a semi-circle and G,- 2 for a semi-ellipse of equal area. It will be at once admitted that, if an ellipse be taken of which the axes are, forexample, as 6 to 1, it would be rash to assume that the flow of water would be the samethrough two equal semi-elliptical sections, on0 withthe minor axis vertical, and the other with it horizontal. The peri- phery ineach case would be exactlythe same, and thus theordinary formula, as dependent on the hydraulic radius, would be the same, and the volume and weight of water would be the same. But the hydrostatic pressure on the periphery, and therefore the frictional resistance, would be very different. Here, then, is a case where present forlnulas are inadequate fully to investigate the question of speed. For convenience of navigation, the top width of a canal may be generally taken as from 7 to 10 times its depth; and, with the reserve just mentioned, the formula of the hydraulic radius maybe applied to a semi-elliptical section of this proportion as if it were a semi-circle. With this allowance, the formulaabove given, correctedfor any difference of thehydraulic radius, as below exemplified, may be applied to those few facts which are attain- able in the absence of further experiment. The Suez Canal (Fig. 1) has a depth of 26 feet; a bottom width of 72 feet; sides sloping at 2 or 2& to l to within 5 feet of the water-line, and a top width of 326 feet.