RELATION OP CAPACITY TO VELOCITY. 



159 



/w,//v. The values of I w /Iv<t listed 

 in Table 48 are therefore estimates of the rela- 

 tive variation of mean velocity in relation to 

 slope, and they have the same quality as the 

 corresponding values of /, and JVQ. They are 

 subject to the limiting conditions of constant 

 discharge, fineness, and width, and they are av- 

 erages of variability for practically the entire 

 range of conditions realized in the laboratory, 

 with the exception of those in the immediate 

 neighborhood of competence. For this range 

 of conditions mean velocity varies, on the 

 average, as the 0.38 power of the slope. 



This result is comparable with the generali- 

 zation embodied in the Chezy formula, which 

 makes mean velocity vary with the 0.5 power 

 of the slope. The two are not inconsistent 

 because they pertain severally to loaded and 

 loadless streams. In a loaded stream increase 

 of slope augments load and thus develops 

 rapidly a factor of resistance from which the 

 loadless stream is free. Velocity, being lim- 

 ited by resistances, develops less rapidly when 

 the conditions are such that the resistances 

 develop more rapidly. 



THE SYNTHETIC INDEX WHEN SLOPE IS 

 CONSTANT. 



For a selected slope, values of V m may be 

 found in Table 14 which agree as to width of 

 channel and grade of debris and differ only as 

 to the discharges with which they are asso- 

 ciated; and in Table 12 may be found the cor- 

 responding values of capacity. Such pairs of 

 values, when occurring in series of two to five, 

 constitute data for the computation of values 

 of Iva. To cover the entire range of tabulated 

 data without needless repetition choice was 

 made of slopes 0.6, 1.0, 1.4, and 2.0 per cent. 

 The data associated with these slopes gave 66 

 values of the index, the values being essen- 

 tially independent except in a few instances. 

 They are shown in Table 49. From them were 

 derived the sets of partial means arranged in 

 Table 50, the method of derivation being that 

 described in connection with Table 47. 



The means show that Iva varies inversely 

 with slope, the variation being of moderate 

 amount. They leave little question that it 

 varies inversely with fineness, though the evi- 

 dence is somewhat conflicting. They indicate 



also a direct variation with trough width, the 

 opposite tendency being indicated only by the 

 means for the greatest widths. The plots of 

 the data, not here reproduced, show that the 

 index varies inversely with discharge. 



TABLE 49. Values of lys, the synthetic index of relative 

 variation for capacity in relation to mean velocity, when 

 slope is constant. 



TABLE 50. Partial means based on Table 49, illustrating 

 the control of IYS by slope, fineness, and width. 



