FLUME TRACTION. 



215 



increases, but the data are too few to give 

 confidence to the inference. The three capaci- 

 ties with a discharge of 0.363 ft. 3 /sec. indicate 

 a minimum in the curve of C=f(F), thus sup- 

 porting the generalizations already made from 

 the results with rectangular troughs. 



The low efficiency here found for an open 

 channel having a circular arc for its perimeter 

 suggests that the cylindric form commonly 

 given to closed conduits for the hydraulic con- 

 veyance of debris may not be the most efficient. 



A second suggestion is connected with the 

 fact that the semicylindric trough, while it nar- 

 rows the field of traction, at the same time gives 

 a high velocity to the water. It thus concen- 

 trates the available force and energy on the 

 narrow field. Though the result is not favor- 

 able to capacity, it may be favorable to com- 

 petence. When but a small load is to be trans- . 

 ported, the practical problem may be one of 

 competent velocity ; and such a trough appears 

 well adapted to the production of competent 

 velocity with economy of discharge and slope. 



SUMMARY. 



Iii the transportation of d6bris in flumes 

 much of the movement is usually by rolling 

 and sliding. This is especially true if the cur- 

 rent is gentle or the debris coarse. With a 

 very swift current or with fine debris the par- 

 ticles travel by a series of leaps, and with the 

 finest debris the load is suspended. When the 

 conditions are such that the principal move- 

 ment is by rolling and sliding, the capacity of 

 the current increases with the coarseness of the 

 debris transported, this law holding good up 

 to the limit of coarseness at which the current 

 is barely competent to start the particles. 

 When the conditions are such that the princi- 

 pal movement is by saltation, the capacity of 

 the current increases with the fineness of the 

 debris, the law holding good up to and prob- 

 ably beyond the critical fineness at which the 

 current is competent to carry the debris in 

 suspension. 



Under all conditions the capacity is increased 

 by steepening the slope, and the increase of ca- 

 pacity is more rapid than the increase of slope. 

 The capacity may vary with a power of the 

 slope as low as the 1 .2 power, or with one higher 

 than the second. A general average for the 

 experimental determinations is the 1.5 power. 



Under all conditions the capacity is increased 

 by enlarging the discharge. It may be in- 

 creased in the same ratio, in a higher ratio, or 

 in a somewhat lower ratio. 



The highest capacity is associated with the 

 smoothest channel bed. Progressive increase 

 of roughness reduces capacity progressively un- 

 til the texture of the bed becomes coarser than 

 the debris of the load. The mode of transpor- 

 tation then passes from flume traction to stream 

 traction. Under like conditions of slope, dis- 

 charge, and character of debris, flume traction 

 gives higher capacities than stream traction. 



Rectangular or box flumes have higher ca- 

 pacity than semicylindric flumes of similar 

 width. Up to a limit, which varies with con- 

 ditions, the capacity is enlarged by increasing 

 the width of channel at the expense of depth of 

 current. The ratio of depth to width which 

 gives highest efficiency has not been well cov- 

 ered by the experiments, but it is believed to 

 be rarely greater than 1:10 and often as small 

 as 1 : 30. For large operations the determina- 

 tion of width will usually represent a compro- 

 mise between efficiency and the cost of con- 

 struction and maintenance. 



As most of the experiments were made with 

 sorted debris, each grade being nanowly 

 limited as to range in the size of its particles, 

 and as most practical work is with aggregations 

 having great range in size, the loads and 

 capacities here reported need qualification. By 

 experiments with mixtures of the laboratory 

 grades it was found that the load carried of a 

 mixture is greater than the load of any one of 

 its important components taken separately. 

 It is in general true that the capacities for com- 

 plex natural grades of debris are greater than 

 the tabulated capacities for the laboratory 

 grades they most nearly resemble. 



COMPETENCE. 



The experiments in flume traction were prac- 

 tically limited in their range by phenomena of 

 competence, and these limitations were of use 

 in determining values of a, K, and <f>, but no 

 effort was made to observe competence di- 

 rectly and precisely. There are, however, a 

 few observations by others, which may properly 

 be assembled here, although it is not practicable 

 to use them as checks on our work. Our in- 

 definite data pertain to slope and discharge, 



