214 



TRAKSPORTATION OF DEBRIS BY RUNNING WATER. 



Simple combinations of the quantities, into 

 which it is not necessary to enter, show (1) 

 that with constant depth, capacity increases 

 with width and more rapidly than width, and 

 (2) that with constant width, capacity increases 

 with depth and more rapidly than depth. The 

 rate of increase with depth, if expressed as an 

 exponent, may be as low as 1.2 or as high as 

 2.0. From these premises, a line of reasoning 

 parallel to that of Chapter IV shows that for 

 flume traction, as for stream traction, the 

 function C=f(R) increases to a maximum 

 and then decreases. The value of R corre- 

 sponding to maximum capacity the optimum 

 form ratio can not be determined from obser- 

 vations involving but two channel widths, but 

 its limits can in some cases be indicated. For 

 example, when the capacities conditioned by 

 the same slope and discharge are approximately 

 the same for the two trough widths, it may be 

 inferred that the optimum falls between the 

 values of R associated with the two capacities. 

 Thus for grades (E), coarse sand, with a slope 

 of 2 per cent, the capacities are about the 

 same for the two widths, while the form ratios 

 are 0.032 and 0.096, or one-thirtieth and one- 

 tenth; and it is inferred that the optimum form 

 ratio falls between those fractions. 



From inferences of this sort, used in combi- 

 nation with the general principles of flume 

 traction, a number of tentative conclusions 

 have been drawn. They are of so hypothetic 

 a character that the reasoning connected with 

 them is not thought worthy of record, but the 

 conclusions themselves may perhaps be of 

 some service, until replaced by others of more 

 secure foundation. They are: The ratio of 

 depth to width giving a current the highest 

 efficiency for flume traction (1) is greater for 

 gentle slopes than for steep, (2) is greater for 

 small discharge than for large, (3) is greater for 

 fine debris than for coarse, (4) is greater for 

 rough than for smooth channel beds, and (5) 

 is in general less than for stream traction. 

 The first and second propositions apply also to 

 stream traction. The third is the reverse of 

 the relation determined for stream traction, 

 and its applicability may be limited to condi- 

 tions under which rolling is the dominant mode 

 of transit. By aid of the fifth and fourth 

 Table 31 may be roughly applied to practical 

 problems of flume traction. 



TROUGH OF SEMICIRCULAR CROSS SECTION. 



A few experiments were made with a trough 

 of galvanized sheet iron, 1 foot wide, having a 

 semicircular section. It was given a slope of 

 1 per cent, and in it were tested four grades of 

 debris. The observational data appear in 

 Table 77. The object of the experiments was 

 to determine whether a channel with curved 

 perimeter is more efficient or less efficient 

 than one with rectangular section; the capaci- 

 ties obtained are compared, in the table, with 

 those determined for a flat-bottomed trough 

 of the same width. As the discharge used did 

 not fill the semicylindric trough, the width of 

 water surface was less than 1 foot. The 

 width of channel bed occupied by the load 

 ranged from one-fifth to one-half of the width 

 of water surface. The medial depth of water 

 was greater than in the rectangular channel, 

 and the mean velocity was higher. The higher 

 velocity is a factor favorable to the develop- 

 ment of capacity; the narrower field of traction 

 is an unfavorable factor. The resultant of the 

 two was unfavorable, the capacities for the 

 semicylindric trough being only half as great 

 as for the rectangular. The result is qualified 

 by the fact that the troughs compared were 

 not of the same material, but the disparity of 

 capacities is too great to be ascribed to that 

 factor. 



TABLE 77. Data on flume traction in a semicylindric iron 

 trough of 0.5 foot radius: with comparative data for a rec- 

 tangular wooden trough 1 foot wide. 



The fact that the doubling of the discharge 

 did not double the observed load indicates that 

 the duty of water diminishes as discharge 



