238 



TRANSPORTATION OF DEBKIS BY RUNNING WATER. 



ratio of 1 : 100, and the times consumed in the 

 ratio of 1:360, the ratio of loads (per second) 



wasl: Q or 1:280,000. The results were 

 ooU 



satisfactory; it was found that the successive 

 forms given to the river bed by variations of 

 discharge were repeated in the model. 



The exaggerations of the vertical scale by 

 Reynolds and of the slope by Eger, Dix, and 

 Seifert had the important effect of shortening 

 the time necessary to produce the desired re- 

 modeling of the mobile bed. The absolute 

 proportionality adopted by Froude and recom- 

 mended by Hearson would have entailed a 

 prohibitive consumption of time and might 

 have added a serious complication in connec- 

 tion with the use of very fine debris. 1 



The similarity controlled by Reynold's law 

 was a relation between the wave periods and 

 dimensions of tidal basins and is not closely 

 related to similarity in the control of trac- 

 tional load. The similarities obtained in con- 

 structing the model of the Weser are more in 

 point, because they involve an average rate of 

 movement of debris; but they throw no light 

 on the laws of variation of debris movement* 

 which is the important matter in bridging the 

 interval between our experiment streams and 

 natural streams. After attempting to use 

 various suggestions which came from the 

 adjustments of the Weser model, I have re- 

 turned to the principles of geometric similarity 

 employed by Froude and Hearson. 



Let us assume, as possible or plausible, that 

 the principles developed in the laboratory, 

 together with all parameters which are of the 

 nature of ratios, are independent of the scale 

 of operations and may be applied to streams of 

 far greater magnitude, provided all linear fac- 

 tors are magnified in equal degree. If width 

 and depth are enlarged in the same ratio, the 

 form ratio is unchanged. If longitudinal dis- 

 tance and loss of head are enlarged in the same 

 ratio, the slope is unchanged. If the dimen- 

 sions of the transported particles are enlarged 

 in the same ratio as the linear elements of chan- 

 nel, the linear coarseness is increased, or the 

 linear fineness is reduced in that ratio. 



The natural streams which may be consid- 

 ered as similar to the experimental streams 

 constitute a class of moderate size. The form 



' Such considerations as these affected the selection of materials for the 

 Berkeley experiments land prevented the employment of very gentle 

 slopes. 



ratio for rivers ranges lower than for experi- 

 mental streams, but there is some overlap. 

 The smaller of the form ratios of the laboratory 

 are representative of a considerable number of 

 rivers. The slopes of rivers range lower than 

 for laboratory streams, but here again there is 

 overlap, and the natural streams which are 

 similar in respect to slope are in general such 

 as have coarse debris, so that there may be 

 correspondence in that regard also. The simi- 

 lar natural streams to which hypothesis extends 

 the laboratory results are those of large form 

 ratio and steep slope, carrying coarse debris. 



The primary difference between a large 

 stream and a small one being one of discharge, 

 and our general inquiry being directed to the 

 valuation of capacity for traction, let us seek 

 an expression for the relation of capacity to 

 discharge when similar streams of different size 

 are compared. 



The laboratory data determine control of 

 capacity by slope, discharge, fineness, and form 

 ratio. In similar streams slope and form ratio 

 are constant, and we need consider here only 

 discharge and fineness. As we are comparing 

 the laboratory streams as a group with similar 

 natural streams, also taken as a group, it is 

 advisable to employ a mode of formulation 

 which lends itself to the use of averages, and 

 the most convenient is that of the synthetic 

 index. In 



l ia and 7 to are average values of the synthetic 

 index and may be estimated, from data in 

 Tables 32 and 43, as 1.32 and 0.77. Designat- 

 ing elements of the larger and smaller streams 

 severally by subscripts and , , we have, from 

 the above, 



(113) 



If we designate by L the ratio between a linear 

 dimension of the larger stream and the corre- 

 sponding dimension of the smaller. 



d, 



L 



Calling mean velocity V, bearing in mind that 

 the hydraulic mean radius is a linear dimension 

 of channel, and recalling that the Chezy formula 



