RELATION OF CAPACITY TO FORM RATIO. 



135 



tion with discharge the evidence is not unani- 

 mous; either it varies inversely under some 

 circumstances and directly under others, or 

 else its proper variation is inverse and data 

 of contrary import are erroneous. The latter 

 view is thought more probable, because in 

 many other connections the controls of slope 

 and discharge follow parallel lines. 



The constant ft, which represents the resist- 

 ance of side walls or banks to the flow of the 

 stream, is also a decreasing function of slope, 

 discharge, and fineness. 



The constant & 2 , which is of the unit of 

 capacity, varies directly with slope and in- 

 versely with fineness, and the evidence as to 

 its variation with discharge is conflicting. As 

 6 2 is the value of capacity when 



- a R) R = 



m+1 



it corresponds to a rather complicated relation 

 between E, m, and a, or R, m, and p; and this 

 relation makes the interpretation of the lack of 

 order among its tabulated values a difficult 

 matter. 



If 6 2 is kft ou t of the account, it is possible 

 to generalize by saying that the constants of 

 equations (54) and (58) vary decreasingly w T ith 

 the conditions which affect capacity increas- 



ingly- 



(61) 



(62) 



THE OPTIMUM FORM RATIO. 



The ratio of depth to width which gives to 

 a stream its greatest capacity for traction is of 

 importance to the engineer whenever he has 

 occasion to control the movement of debris. 

 The title optimum ratio is especially appropriate 

 when his desire is to promote that movement. 



The range of values for the ratio, under lab- 

 oratory conditions, is from 1:2 to 1 : 20. One 

 effect of this wide range, when taken in connec- 

 tion with the variety of conditions by which 

 the ratio is controlled, is to complicate the 

 formulation of practical rules; but this diffi- 

 culty is not insuperable. It is qualified to an 

 important degree by the consideration that 

 capacity, in the region of its maximum, changes 

 very slowly with change of form ratio, so that 



an approximate determination of the ratio has 

 practical value. 



The values of the ratio given in Table 31 are 

 appropriate to the conditions of the Berkeley 

 laboratory that is, they pertain to troughs a 

 few inches or a few feet wide, with smooth 

 vertical sides. It is important to note also that 

 they apply only to transportation of debris 

 over a bed of debris, and not to flume traction, 

 which has a different law. (See p. 213.) 



TABLE 31. Estimated ratios of depth of current to width of 

 trough, to enable a given discharge, on a given slope, to 

 transport its maximum load. 



No way has been found to extend the quan- 

 titative results to rivers. It can hardly be 

 questioned that the optimum ratio for rivers 

 varies inversely with slope, discharge, and 

 fineness of debris, but its absolute amount can 

 not be inferred from the experimental results. 

 River slopes are relatively very small and river 

 discharges are relatively very large, and the 

 two differences affect the ratio in opposite 

 ways. To compute the joint result we should 

 have definite and precise information as to the 

 laws of dependence, but our actual knowledge 

 is qualitative and vague. 



In this connection it is of interest to record a 

 single observation on river efficiency. Where 

 Yuba river passes from the Sierra Nevada to 

 the broad Sacramento Valley its habit is rather 

 abruptly changed. In the Narrows it is nar- 

 row and deep; a few miles downstream it has 

 become wide and shallow. Its bed is of 

 gravel, with slopes regulated by the river 

 itself when in flood, and the same material 

 composes the load it carries. 



In the Narrows the form ratio during high 

 flood is 0.06 and the slope is 0.10 per cent. 

 Two miles downstream the form ratio is 0.008 

 and the slope is 0.34 per cent. Thus the 

 energy necessary to transport the load where 

 the form ratio is 0.008 is more than three times 

 that which suffices where the form ratio is 



