140 



THANSPORTATION OF DEBRIS BY RUNNING WATER. 



with reference to grade of debris and channel 

 width. 



TABLE 33. Values of the discharge constant, K, computed 

 from the discharges and capacities of Table 32. 



The tabulated values of K show great irreg- 

 ularity. It is not difficult, however, to recog- 

 nize a tendency to grow larger in passing from 

 finer debris to coarser; and there is also, 

 though it is ill defined, a tendency to increase 

 with increasing width. The cause of the first- 

 mentioned tendency is readily understood, 

 because relatively coarse debris requires a 

 relatively swift current to move it; and the 

 reality of the second also finds support when 

 the conditions affecting competent discharge 

 are considered. 



Postulating, initially, a channel of some 

 particular width, containing a stream of which 

 the discharge is barely competent, let us assume 

 that the width is increased. In spreading to 

 the new width the stream loses depth and 

 velocity, and its velocity is no longer compe- 

 tent. That the velocity may again become 

 competent the discharge must be increased. 

 Thus it is in general true that competent dis- 

 charge increases with increase of width. In 

 the cross section of a broad laboratory current, 

 figure 48, a medial portion, AA, is unaffected 



FIGURE 48. Ideal cross section of a stream in the experiment trough, 

 illustrating the relation of competent discharge to width. 



by side-wall resistance and has competent 

 velocity. Two lateral portions, AB, have less 

 than competent velocity. Let us imagine 

 these lateral portions replaced by narrower 

 divisions, AD, in which velocities are the same 

 as in AA. The effective width for the main- 

 tenance of competent velocity is then DD = 



w 2 BD. If now width and discharge be 

 increased or diminished, with maintenance of 

 competent velocity, the quantity 2 BD is 

 unaffected, so that it may be regarded as a 

 constant. Velocities being, by hypothesis, 

 uniform through the whole space DD, the dis- 

 charge is proportional to the width of that 

 space. 



Q c <x w & constant (65) 



This result assumes a channel so wide that a 

 medial portion is unaffected by side-wall resist- 

 ance. It may not be true for narrower chan- 

 nels. If it were to be refined, the constant 

 would be found to be a function of depth (com- 

 pare p. 129); but in applying its principle to 

 the values of no aUowance was made for 

 that factor. 



On the theory that K is closely related to 

 competent discharge and has similar properties, 

 and with the assumption that (65) may be 

 applied to narrow channels as weU as broad, the 

 principle of (65) was used in adjusting the 

 tabulated values of K in relation to width of 

 channel. The formula assumed was 



K <x w 0.2 



The value of the constant was arbitrarily 

 fixed, after several trials, no criterion for selec- 

 tion being discovered except the harmony of 

 results. 



With the aid of this formula it was possible 

 to combine the data of Table 33 in such way as 

 to afford a better view of the relation of K to 

 grade, or fineness ; and this was done. By mul- 

 tiplication or division, each value was reduced 

 to its equivalent for a channel width of 1 foot, 

 and means were taken. These means appear 

 in the second line of Table 34. They were com- 

 pared with the mean diameters of particles for 

 the several grades, the comparison being made 

 on logarithmic section paper. In figure 49, 

 showing this plot, the numbers indicate 

 weights. While the plotted points do not fall 

 well into line, they leave no question that the 

 value of K rises as the debris becomes coarser. 

 On the assumption that the function is a power 

 function, a straight line was drawn to represent 

 it; and by this line the mean values of K were 

 adjusted. Values for the other trough widths 

 were then computed. These appear in Table 32. 



