RELATION OF CAPACITY TO VELOCITY. 



161 



discharge, and the changes in capacity are 

 those due to changes of discharge. When 

 depth is constant the changes of velocity are 

 caused by concurrent changes of slope and 

 discharge, and the changes in capacity are 

 intermediate between those caused by slope 

 alone and by discharge alone. 



TABLE 53. Comparison of synthetic indexes of relative vari- 

 ation for capacity and mean velocity, -under the several con- 

 ditions of constant discharge, constant depth, and con- 

 stunt slope. 



It is profitable to consider the same facts 

 also in relation to depth of current. Postulate 

 an initial status, with a particular discharge 

 and slope, determining a certain velocity, 

 depth, and capacity. First, increase the slope 

 until the velocity is doubled. The capacity is 

 increased, let us say (borrowing mean I v <t 

 from the table) to 15.8 times its initial amount. 

 At the same time the depth is reduced one- 

 half. Second, after returning to the initial 

 status, increase slope and discharge by such 

 amounts as to double the velocity without 

 changing the depth. The capacity grows 

 (mean Ivd) to 12.8 tunes its original amount. 

 Third, starting from the initial condition as 

 before, increase the discharge until velocity is 

 doubled. The capacity grows (mean 7 K ) to 

 9.2 times its original amount; and the depth 

 is at the same time increased, being more than 

 doubled. Thus, for the same (doubled) mean 

 velocity, the capacity is greater as the depth 

 is smaller. Mean velocity is more efficient for 

 traction as depth is less. 



Now, the primary direct cause of stream 

 traction is bed velocity. A concurrent cause 

 theoretically exists in the component of gravity 

 parallel to the slope, acting directly on the 

 load, but for all ordinary stream slopes this 

 factor is negligible. Slope and discharge are 

 (essentially) indirect causes and are causes 

 only in so far as they occasion bed velocity. 

 They also determine mean velocity, and, from 



one point of view, mean velocity may be said 

 to control capacity by controlling bed velocity. 



Let us assume, for the moment, that bed 

 velocity determines capacity irrespectively of 

 depth. Then the variations of capacity above 

 described imply corresponding variations of bed 

 velocity, and, as the mean velocity does not 

 change, we may infer that the ratio of bed ve- 

 locity to mean velocity is a function a de- 

 creasing function of depth. 



This proposition is, to say the least, worthy 

 of consideration, but it fails of demonstration 

 because the assumption which paved the way 

 for it is not valid. It is not true that the rela- 

 tion of capacity to bed velocity is independent 

 of depth. In the first place, change of depth, 

 when not accompanied by change of mean ve- 

 locity, causes change in the mode of traction. 

 Within the range of the above hypothetic con- 

 ditions may occur both the dune rhythm and 

 the antidune rhythm; and at least one of these 

 has an influence on capacity. Moreover, these 

 rhythms involve diversity of velocity from 

 point to point along the bed, so that " bed ve- 

 locity" has not a simple definition. 



In the second place, the load, or the work of 

 traction, reacts on the vertical distribution of 

 velocities. In figure 54 the line ABO is as- 



FIGCBE 54. Ideal curves of velocity in relation to depth, illustrating 

 their relation to the zone of saltation. zero of velocity (horizontal) 

 and of distance from the bottom (vertical). 



sumed as the vertical velocity curve of a stream 

 flowing in a straight conduit and bearing no 

 load. A'B'C, identical except as to vertical 

 dimensions, is assumed as the curve correspond- 

 ing to the same mean velocity in a current one- 

 half as deep. Introducing, now, the condition 

 of traction, we may represent the upper limit 

 of the zone of saltation by the line DE. The 

 potential velocities within the zone are evi- 

 dently quite different for the two depths of cur- 

 rent, and they give advantage, for traction, to 

 the shallower current. The work of saltation 

 tends to retard the lower filaments of current 

 and through these the higher filaments, reduc- 



20021 8 No. 8614- 



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