194 



TRANSPORTATION OF DEBRIS BY RUNNING WATER. 



portional to the discharge [load] of sand, C, 

 may be represented by the expression hC. We 

 have then : 



0= ( V b 2 - 0.25 2 ) = m( F b 2 - O.oe)- - - (4) 



The value of the m will be sought from obser- 

 vation, which will correct in a measure for the 

 introduction of F$ into the equation without 

 allowance for the speed of the grains, etc. 

 Subtraction of 0.06 ceases when the sands are 

 prevented by suspension from rubbing on the 

 bottom; therefore the formula becomes 

 C=mV b 2 for velocities above a certain limit. 

 (It is readily understood that m, like a, is only 

 approximately constant.)" 



The rate at which dunes advance has been 

 measured, in the French rivers, in relation to 

 the velocities of the associated currents. It 

 rises with F 6 until the critical velocity is 

 reached, and then drops as the change is made 

 from rolling to suspension. The advance of 

 dunes, depending on the fall of grains into the 

 eddy (fig. 10) when they have been rolled to 

 the crest, is affected by the introduction of 

 suspension because then only a part of the 

 traveling grains are received by the eddy. 



Observations made on the Loire give as the 

 limiting bed velocity for transportation [com- 

 petent velocity for transportation], F 6< , = 0.25 

 meters per second. According to an engineer 

 who has discussed those observations [H. L. 

 Partiot ?], the corresponding surface velocity, 

 V,, is equal to ^JO.ll; and the formula for the 

 rate of advance of the dunes, 



Rate of advance = 0.00013 (F S 2 -0.11) .(5) 



is good for all values of V s up to 1.016. One 

 might base on this a formula for load in rela- 

 tion to surface velocity, but the formula would 

 be incomplete unless developed so as to take 

 account of the depth; and it is best for the 

 present to adhere to equation (4), which con- 

 nects load with bed velocity. 



Lechalas, however, for a temporary purpose, 

 uses formulas of Darcy and Bazin to connect 

 F b with V s , under certain assumptions as to 

 depth, and with their aid computes for the 

 Loire the critical bed velocity, V bcc , at which 

 suspension of the sands begins. F i)0( , = 0.55 



meters per second. This is the velocity cor- 

 responding to F s = 1.016, the surface velocity 

 which limits the applicability of formula (5). 

 The following table contains the observa- 

 tional data on dunes of the Loire and compares 

 the observed rates of dune advance with rates 

 computed by formula (5). 



TABLE 63a. Data on subaqueous dunes of the Loire. 



In later passages Lechalas recognizes the 

 variations of velocity in passing from one 

 vertical to another of the same stream section 

 and makes (4) the formula for a division, one 

 unit wide, of the cross section. Thus modified, 

 it is applied in a variety of ways to practical 

 engineering problems of the Loire. 



DISCUSSION. 



Lechalas's classification of transportation 

 processes differs from that adopted for our 

 work in that he makes saltation, at least 

 verbally, a part of suspension. I am led, how- 

 ever, by a study of the more detailed descrip- 

 tions of his colleague Partiot, to believe that 

 the line practically drawn between rolling and 

 suspension differs in small measure only from 

 the line we have drawn between traction and 

 suspension. 



The lower critical velocity of Lechalas is the 

 exact equivalent of our velocity competent for 

 traction, and his upper critical velocity corre- 

 sponds approximately to our velocity compe- 

 tent for suspension. The two attempts at 

 formulation likewise agree in giving promi- 

 nence to the factor of competence. They 

 differ in the mode of using that factor, and 

 they are actuated by different preconcep- 

 tions. 



