224 



TRANSPORTATION OF DEBRIS BY RUNNING WATER. 



tation of the low stage percentage of load in 

 1879, we obtain an estimate of 12.6 per cent, 

 which is 14 times greater than the observed 

 load, 0.86 per cent. The discrepancy is alto- 

 gether too great to be accounted for by errors 

 in the explicit assumptions, and its explana- 

 tion involves the factor of competence. The 

 stronger currents of flood stages were compe- 

 tent to suspend .heavier particles than were the 

 feeble currents of low stages, and so a part of 

 the load which at high stages reached the mouth 

 of the river at Marysville was at low stages 

 arrested on the way, being deposited in the 

 low-water pools. 



In these cases it is evident that the range of 

 available fineness is determined, through veloc- 

 ity, by discharge, and that the load of debris 

 within the range of adeqiiate fineness is deter- 

 mined by supply. The load appears to bear 

 no relation to capacity, and if the term capacity 

 be used in the broad sense of a stream's ability 

 to suspend material of unspecified fineness, then 

 it is undoubtedly true, not merely of the Yuba 

 but of all rivers, that the suspended load is less 

 than the capacity and depends for its quantity 

 on supply. If, however, capacity be considered 

 with reference to particular degrees of fineness, 

 the case is somewhat different, for a stream 

 may carry a full load of that material for which 

 it is barely competent and at the same time 

 have less than a full load of finer material, and 

 the matter is further complicated by interde- 

 pendencies in virtue of which each element of 

 load tends to limit the capacity for all other 

 elements of load. 



To show the basis for these statements and 

 also to explain certain mutual relations between 

 traction and suspension, it is necessary to give 

 somewhat elementary consideration to the sub- 

 ject of capacity for suspension. 



As already mentioned and implied in various 

 connections, the process of suspension depends 

 on the diversity in direction of the strands of 

 the current. If the lines of flow were parallel 

 to the stream bed, as is sometimes assumed for 

 the sake of simplifying mathematical discus- 

 sions, there would be no suspension. 1 In the 



i There is a theory originating with Dupuit (Etudes sur le mouve- 

 ment des eaux, 1848) that suspension is due, or might be duo in the 

 ideal case of parallel flow lines, to reactions between solid particles and 

 contiguous threads of current having different velocities. Under the 

 postulate that the solid tends to move faster than the liquid, it is shown 

 that the path of least resistance trends obliquely toward the swifter of 

 adjacent threads of current, and therefore obliquely upward. As this 

 theorj retains place in current hydraulic literature, the fact that it is 



sinuous and swirling movements which charac- 

 terize the flow of streams strands of current are 

 continually passing upward and downward and 

 are as continually dividing and blending. Par- 

 ticles of debris too light to resist the lower ele- 

 ments of the current are swept upward and are 

 retained in the body of the stream through a 

 process analogous to the stirring of the domes- 

 tic pot. While thus incorporated they are 

 impelled downward by gravity, and all but the 



ignored in the text of the present paper may call for explanation. I do 

 not accept the postulate and am of opinion also that the reasoning based 

 on it ignores an essential factor. As a full statement and discussion of 

 Dupuit's analysis would occupy mucU space, I will content myself 

 with a statement of my own view. A good abstract of h is theory, by 

 E. II. Hooker, may be found in Am. Soc. Civil Eng. Trans., vol. 38, pp. 

 246-247, 320-322. 



In various discussions of the subject the velocities are treated as 

 "absolute" that ts, they are referred to the fixed walls and bed of the 

 channel. As the only possible reactions between the solid particles and 

 contiguous water are through relative velocities, it is better to focus 

 attention on those by referring them to the center of the particle. Let 

 us assume that the solid particle A , figure 70, is immersed in a current 



FIODBE 70. Diagram of forces. 



of which the parallel rectilinear filaments increase gradually in "abso- 

 lute" velocity from below upward, and let us assume that at some 

 instant it moves with the velocity and direction of the filament which 

 is at the same level. Barring extraneous forces, it will continue indefi- 

 nitely in the same direction and with the same velocity. The filament 

 above moves, with reference to the particle, in a direction indicated by 

 the arrow; the filament below moves in the opposite direction. Their 

 relative velocities are the same, except for a possible difference of the 

 second order of magnitude. The two filaments tend to draw the upper 

 and lower parts of the particle in opposite directions, and the result Is 

 rotation. This is the only result dependent on the fact that the particle 

 is solid. Now introduce the factor of density. The particle is denser 

 than water. It is also part of a stream which is flowing, and the impulse 

 It receives from gravity is greater than it would receive if it had the 

 density of water. The component of gravity in the direction of flow, 

 AB, acting on the excess of mass, draws the particle in the direction of 

 flow. This component is proportional to the slope of the stream, which 

 is a small fraction. At the same time the component of gravity normal 

 to the direction of flow, A C, also draws the particle, which is equally 

 free to move through the water in that direction. Its actual accelera- 

 tion has the direction of their resultant, AO, which is vertically 

 downward. 



Dupuit's postulate was suggested and supported by the observed 

 fact that a body floating down a stream moves faster than the visible 

 current. BeYard demonstrated experimentally that the differential 

 motion is due to the propulsion of the body by strands of current below 

 the surface. See Annales des ponts et chauss&s, 6th ser., vol. 12, pp. 

 830-835, 1886. 



