228 



TRANSPORTATION OF DEBRIS BY RUNNING WATER. 



factor due to the weight (W) of the load and 

 varying directly with the slope and inversely 

 with the discharge, minus a factor due to the 

 work of suspension and varying directly with 

 the diameter of particles, minus a factor due 

 to viscosity and varying inversely with the 

 diameter if the particles are minute and 

 directly with the diameter if they are larger. 



It was convenient in the discussion to regard 

 the whole suspended load as of one grade, but 

 the result may be applied to any individual 

 particle. For the actual stream with diversi- 

 fied load the equation might be written 



F= V m + Wf^S, $) - 



. .(Ill) 



An investigation of the influence of suspended 

 matter on viscosity has recently been made by 

 Eugene 0. Brigham and T. C. Durham. 1 The 

 materials used by them were powders so fine 

 that their tendency to settle in the water did 

 not interfere with the conduct of the experi- 

 ments. The work of suspension was therefore 

 so small a factor as to be negligible. Various 

 mixtures of water and powder were allowed to 

 flow through a vertical capillary tube, impelled 

 by their own weight, and the time of trans- 

 mission for a determinate volume was noted. 

 The time for a mixture containing 100 parts 

 of water to 2.15 parts, by weight, of clay was 

 found to be 15 per cent greater than the time 

 for clear water; or the average velocity, within 

 a slender tube, was reduced 15 per cent by the 

 addition of the clay. If we assume the flow 

 lines to have been parallel, as was probable, 

 the theoretic increment of velocity due to the 

 weight added by the clay was 1.6 per cent; if 

 the flow lines were sinuous, the theoretic incre- 

 ment was less. The loss of velocity due to 

 increased viscosity was therefore somewhat 

 greater than 15 per cent and may have been 

 as much as 16.6 per cent. Had the experiment 

 been so arranged as to involve sinuous or tur- 

 bulent flow, it would apply more cogently to 

 the phenomena of rivers, but without that 

 adjustment it serves to show that when the 

 suspended material is exceedingly fine the loss 

 of velocity through added viscosity is very 

 much greater than the gain of velocity because 

 of added weight. 



The size of the particles was not reported, 

 but the fact that the rate of settling was in- 



i Am. Chem. Jour., vol. 46, pp. 278-297, Mil. 



appreciable suggests that their size may have 

 fallen below that corresponding to a minimum 

 influence on viscosity. Some light is thrown 

 on this point by the results obtained with other 

 fine powders. Interpolation from the reported 

 data gives the following comparative estimates 

 of the loss in velocity from the suspension of 

 the same volumes of three substances: Infu- 

 sorial earth, 3 per cent; graphite, 12 per cent; 

 clay, 15 per cent. Of these the infusorial earth 

 was coarsest, remaining in suspension largely 

 because differing little in density from the 

 water, while the graphite was a commercial 

 variety said to be permanently suspended. An 

 independent determination by L. J. Briggs and 

 Arthur Campbell 2 gave a loss in velocity of 

 7 per cent, the material being a clay which 

 "would not remain in a state of permanent 

 suspension." The comparative data render it 

 probable that the clay causing a retardation 

 of 15 per cent was so finely divided as to give 

 great effect to the molecular forces of the shell 

 of influence. 



The data from infusorial earth are useful in 

 correlating the various factors which modify 

 the stream's velocity. Assuming that the dia- 

 tom tests composing the earth sample were 

 similar to those figured in geologic textbooks, 

 I have estimated the velocity of subsidence of 

 particles having the same size but as dense as 

 ordinary river silt and find that it corresponds 

 to the critical velocity computed for the Mis- 

 sissippi at flood stage. That is, a suspended 

 silt so fine as to have a large viscosity effect, so 

 that a charge of 2.15 per cent reduces velocity 

 by 3 per cent, is at the same time able, through 

 its work of suspension, to consume all the 

 energy it contributes to the current through 

 its addition of mass. A finer silt would retard 

 more by increasing viscosity, and a coarser silt 

 would retard more through the work of sus- 

 pension. 



The available data are not fully demonstra- 

 tive, but they render it highly probable that, 

 under all conditions, streams are retarded by 

 their suspended loads. If that be true, there 

 is a capacity for suspension coordinate with 

 capacity for traction. For each grade of sus- 

 pended debris, and with any particular slope 

 and discharge, it is possible by increasing 

 the load so to retard the current that it is 



* Unpublished; communicated in lettw. 



