CHAPTER VIIL RETATION OF CAPACITY TO DEPTH. 



INTRODUCTION. 



As a condition controlling capacity for trac- 

 tion, depth has several distinct aspects; and the 

 nature of its control depends altogether on the 

 character of associated conditions. Three as- 

 pects will here be considered. They all assume 

 that size of debris and width of channel are 

 constant, and they are severally characterized 

 by the limiting conditions of constant discharge, 

 constant slope, and constant mean velocity. 

 In examining the nature of the controls, and in 

 comparing them with one another and with 

 other controls, use will be made of the syn- 

 thetic index; and the method of discussion will 

 be similar to that of the preceding chapter. 

 The symbols for the synthetic index, under the 

 three limiting conditions, will be severally 



Ida, Ids, and I dr . 

 WHEN DISCHARGE IS CONSTANT. 



A stream of constant discharge, flowing in a 

 channel of constant width, can change its depth 

 only by changing its mean velocity, and depth 

 and velocity vary in opposite senses. What- 

 ever the ratio by which the mean velocity is in- 

 creased or diminished, the depth diminishes or 

 increases in the same ratio. It follows that 

 the law of change for capacity in relation to 

 mean velocity is the inverse of the law of change 

 for capacity in relation to depth. So far as 

 these laws are expressed by values of the syn- 

 thetic indexes, 



*d = ~ IVQ- 



Independent computations of I dQ are there- 

 fore unnecessary, as the values of Irq in Tables 

 46, 47, and 48 need only change of sign to 

 become the corresponding values of 7 d . The 

 following summary statement of the general 

 features of the control of capacity by depth 

 is but a condensation and adaptation of the 

 statement on pages 157-158. 



Under the condition of constant discharge 



capacity varies inversely with depth. Its rate 



of variation is more than twice the rate at 



which it varies with slope of channel. The 



164 



rate responds to changes in discharge, slope of 

 channel, fineness of debris, and form ratio, 

 diminishing as those factors increase (with 

 possible exception as to form ratio). 



Depth, when subject to the condition of con- 

 stant discharge, varies inversely with slope. 

 Estimates of the average rate of variation are 

 contained in the last column of Table 48. 



WHEN SLOPE IS CONSTANT. 



A stream flowing down a constant slope, in 

 a channel of constant width, and transporting 

 debris of a particular grade changes its depth 

 when the discharge is changed. The depth is 

 greater as the discharge is greater. The 

 capacity for traction also is greater as the 

 discharge is greater. Therefore the capacity 

 varies in the same sense as the depth. 



Table 54 contains 68 values of I ds , com- 

 puted from data of Tables 12 and 14. The 

 method of derivation was identical with that 

 already described for Table 49, with the excep- 

 tion that values of depth were used instead of 

 values of mean velocity. 



TABLE 54. Values of I ds , the synthetic index of relative vari- 

 ation for capacity in relation to depth of current, when slope 

 is constant. 



