FLUME TRACTION. 



201 



It may be observed in passing that the re- 

 corded speed of the particles is on the average 

 75 per cent of the mean velocity of the water, 

 the ratio being gi eater as the velocity is greater 

 and as the depth is less. A higher ratio would 

 of course be found if the speed of particles 

 were to be compared with that of the lower part 

 of the current. The percentage might be less 

 than 75 if the stream were fully loaded. 



In watching the traction of mixed debris it 

 was observed, as already mentioned, that the 

 larger particles traveled faster than the smaller. 

 As it is difficult in such an observation to avoid 

 giving attention largely to the more active par- 

 ticles, the observation applies especially to those 

 which roll, but there is probably a similar con- 

 trast between the speeds of less active parti- 

 cles also. In an experiment with glass balls of 

 different sizes it was found that the larger were 

 rolled by the current somewhat faster than the 

 smaller. 



In attempting to understand the more rapid 

 propulsion of the larger particles it is natural 

 to compare the phenomenon with the more 

 familiar fact that in the absence of water a 

 large stone or ball will descend an incline with 

 greater speed than a small one, but there is an 

 important difference between the two cases. 

 The object descending a dry incline is impelled 

 by gravity, acting directly, and part of the 

 resistance comes from the fluid in which it is 

 immersed, whereas the rolling debris pebble is 

 impelled chiefly by the moving fluid which 

 surrounds it. The advantage in speed accruing 

 to the larger pebble in flume traction is prob- 

 ably connected with the fact that the velocities 

 of the current increase from the bottom 

 upward. If the velocities were all the same 

 the pressures applied to similar pebbles of 

 different diameter would be proportional to 

 their sectional areas, or to the squares of their 

 diameters; but because of the gradation of 

 velocities the increase of pressure in conse- 

 quence of increase of diameter is more rapid 

 than the increase of the square of the diameter. 

 The chief resistance to the forward movement 

 of the pebble is engendered at its contact with 

 the bed and is of the nature of rolling resistance. 

 For uniform speed, the rolling resistance of a 

 wheel is proportional to its downward pressure 

 divided by its diameter; and since in the case 

 of the pebble the pressure is proportional to 

 the cube of the diameter, the rolling resistance 

 is proportional to the square. Increase in size 

 of the rolling pebble is thus accompanied by 



increase of both propulsive force and rolling 

 resistance, the increment to propulsive force 

 being somewhat the larger; and the equality of 

 force and resistance is restored by an increase 

 of speed, which has the effect of reducing the 

 propulsive force and increasing the resistance. 1 

 The reduction of propulsive force is connected 

 with the fact that that force is determined at 

 each instant by the velocities of the water, not 

 as referred to the fixed bed, but as referred to 

 the moving pebble. 



The analysis of forces might be further de- 

 veloped, but the foregoing brief outline serves 

 to indicate a mechanical principle underlying 

 the observed fact that a current rolls large 

 particles more swiftly than small. The princi- 

 ple is of fundamental importance in account- 

 ing for certain contrasts between the laws of 

 flume traction and those of stream traction. 



The discrimination of traction and suspen- 

 sion, usually easy in the experiments with 

 stream transportation, was difficult in the 

 flume work. The zone of saltation grew 

 deeper with progressive increase of slope until 

 it occupied the whole depth of the stream. 

 Further increase of slope, with increase of load, 

 made the cloud of particles denser, but there 

 seemed no way of telling when the condition 

 became that of a flowing mixture of water 

 and sand. 



COLLECTIVE MOVEMENT. 



To the general fact that in flume traction 

 the particles of the load either roll or slide in 

 continuous contact with the fixed bed or else 

 skip from point to point along it, there are two 

 noteworthy exceptions. 



When the transported debris includes par- 

 ticles which are small compared to the projec- 

 tions constituting the roughness of the bed, 

 some of the debris finds lodgment among the 

 projections. The roughness of the bed is thus 

 diminished and the process of transportation 

 is modified. The bed comes to be constituted 

 in part of the fixed summits of projections and 

 in part of mobile debris, and the process be- 

 comes a blending of flume traction proper and 

 stream traction. When such conditions existed 

 in the experiments it was found that the capacity 

 was essentially that due to stream traction. 



i The formula given by W. J. M. Rankine, in his " Applied mechanics " 

 and elsewhere, for the rolling resistance of a wheel is R -|a+6(t) 3.28)} 



where R is resistance, Q gross load, r radius of wheel, v velocity in ft. /sec., 

 and a and b constants. The experimental values of a and b are such as to 

 give velocity only a moderate influence on the resistance. 



