CHAPTER X. REVIEW OF CONTROLS OF CAPACITY. 



INTRODUCTION. 



In the preceding seven chapters the relations 

 of capacity for stream traction to a variety of 

 factors have been examined one at a time. It 

 is now proposed to bring together some of the 

 discovered elements of control. The experi- 

 mental data thus far considered pertain to 

 straight channels, and the factors of control 

 connected with bending channels have not re- 

 ceived attention. Those factors must be in- 

 cluded when the attempt is made to bring 

 laboratory results into relation with river phe- 

 nomena, but as they constitute a category by 

 themselves it is convenient to leave them out 

 of the account in correlating the results from 

 straight -channel work. 



The immediate determinants of capacity are 

 (1) the velocities of the current adjacent to the 

 channel bed, (2) the widths of channel bed 

 through which those velocities are effective in 

 moving debris, and (3) the mobility of the 

 debris constituting the bed and the load. It 

 was not found practicable to measure bed ve- 

 locity, but measurement was applied to its two 

 chief determinants, slope and discharge, and 

 also to its ultimate associate, mean velocity, 

 and these have been discussed separately. 

 Width has entered into the discussion chiefly as 

 an associate of depth in the determination of 

 form ratio. By reason of these and other inter- 

 relations the six controls of capacity which have 

 been discussed slope, discharge, fineness, 

 depth, mean velocity, and form ratio are not 

 independent, and not all should appear in a 

 general equation. Slope, discharge, and fine- 

 ness being accepted as of primary importance, 

 it is feasible to add but one of the others, and 

 choice has been made of form ratio. 



FORMULATION BASED ON COMPETENCE. 



The functions used in discussing the relations 

 of capacity to slope, discharge, and fineness are 

 similar, and each involves a conception of com- 

 petence. Competence enters also the theoiy of 

 186 



the relation of capacity to form ratio, but it 

 enters in a different way. It is convenient to 

 omit at first the form-ratio function and con- 

 sider together the three which are similar. 

 They are: 



(10) 



-(64) 

 (75) 



Each of these equations expresses the law of 

 variation of capacity with respect to one con- 

 dition when the other two conditions are con- 

 stant, and in that sense they are independent ; 

 but there is a mutual dependence of parameters 

 which is of so complete a character that they 

 are essentially simultaneous. The dependence 

 of parameters is more readily stated by means 

 of a specific instance than in general terms. 

 In equation (10) 6,, a, and n are constant so 

 long as Q and Fhold the same values; they do 

 not vary with variation of S. But when the 

 values of Q and F are changed those of l lf a, 

 and n are modified. Through this control of its 

 parameters the equation involves the relation 

 of capacity to discharge and fineness. 



The coefficient 6, is the value of capacity 

 when (S-o) = \;l a when (Q- K ) = l; &< when 

 (F<}>) = 1. Replacing them by Z 5 , as the 

 numerical value of capacity when (S a) = \, 

 (Q-K) = 1, and (F- <) = !, we may combine 

 the three equations into 



The constant J 5 is not of the same unit with 

 either & b 3 , or & 4 . Its dimensions, derived from 

 those of the variables of (91), are L""' 30 M +l T~ l . 



From the experimental data have been com- 

 puted 92 values of n, 20 values of o, and 5 

 values of p. (See Tables 15, 32, and 44.) All 

 these are positive. The following statistical 

 summary gives a general idea of their relative 

 magnitudes. Its figures are not based on the 

 same range of observational data; but the 



