. Journal. nd has nothingto do with the mysterious d3~n, which Prof. Reynolds has im-ported. Kutters formula will be referred to later on. The open-channel experiments are located on the DiagramNo. I. by calculating what the discharges would have been ifthe experiments had been with pipes of the observed hydraulicradius and with the observed velocities, and the logarithms ofthe discharges so found are plotted together with the logarithmsof the observed slopes. This is necessary, because the sectionalareas in open channels bear no fixed proportion to the hydraulicradii. It only involves the usu
. Journal. nd has nothingto do with the mysterious d3~n, which Prof. Reynolds has im-ported. Kutters formula will be referred to later on. The open-channel experiments are located on the DiagramNo. I. by calculating what the discharges would have been ifthe experiments had been with pipes of the observed hydraulicradius and with the observed velocities, and the logarithms ofthe discharges so found are plotted together with the logarithmsof the observed slopes. This is necessary, because the sectionalareas in open channels bear no fixed proportion to the hydraulicradii. It only involves the usual assumption that the theory 234 A NEW FORMULA FOR THE FLOW OF WATER of the hydraulic radius is equally true for pipes and irregularchannels. It is better to do this than to plot the logarithms ofv and B, because the experimental points become morescattered on the diagram, and render it easier to detect anysymmetry. Velocity lines can be added very easily, and whenn = 2, they come out on slopes of a? to Fig. 1 <0 LM = 2 4 ? x p LP = x _g P M= 2 3 OPLP=n p If n = 2 OP=2LP = 2 x Referring to Fig. 2, L and M are two experimental points,whose distance apart we may call 2 + x, for A is proportional to E2andV „ „ R* also Q = A V .. Q „ „ K2+* Let L P = x and P M = 2; ? = n, soifw = 2, thenOP = 2LP LP = 2x consequently O M is on a slope of x to 1. This is only true when n = 2; but it is a very convenientcoincidence. The process of sifting the evidence as to the slopes of thevelocity lines is a very laborious one, and need hardly be de-scribed in detail. It will be sufficient to state that, after a IN PIPES AND OPEN CHANNELS. 235 careful examination of a large number of lines representing avelocity of 4 feet per second, the author concluded that for thelarger values of K they varied from ? 58 to about 80 to 1, andthat they would meet at a point on the diagram, the co-ordinates of which would be 6*9015 on the axis of log Q and6 • 16758 on the axis of log S, which c
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