APPLICATION TO NATURAL STREAMS. 



225 



very finest actually move downward with refer- 

 once to the surrounding water. From time to 

 time they may touch the stream bed, but only 

 to be lifted again by the next adequate rush of 

 water. 



Three ways are known in which the veloci- 

 ties of a stream are affected by the suspended 

 load. In the first place, the load adds its mass 

 to the mass of the stream, and as the stream's 

 energy is proportional to the product of mass 

 by slope, and the stream's velocity has its 

 source in this energy, the addition tends to 

 increase velocity. Second, the suspended par- 

 ticles are continually impelled downward by 

 gravity. Also, as the strands of current con- 

 taining them have curved courses, the particles 

 are subject to tangential force, and because of 

 their higher density this force is greater than the 

 force simultaneously developed by the contain- 

 ing water, so that they are impelled through the 

 water. Motion through the water, caused by 

 these two forces, involves work; and this work 

 is a direct consequence of suspension. The 

 energy expended is potential energy, or energy 

 of position, given to the particles by the flo'w- 

 ing water, and its source is the energy of flow. 

 So the work is the measure of the work of the 

 stream in suspending the particles. It may 

 therefore be regarded as a tax on the stream's 

 energy, resulting in reduction of velocity. 

 Third, the imperfect liquid constituted by the 

 combination of water and debris is more viscous 

 and therefore flows more slowly than the water 

 alone. The solid particles do not partake of 

 the internal shearing involved in the differen- 

 tial movements of the current, and by their 

 rigidity they restrain the shearing of water in 

 their immediate vicinity. Moreover, each par- 

 ticle is surrounded, through molecular forces, 

 by a sphere or shell of influence which still 

 further interferes with the freedom of water 

 movement. 



The relative importance of these factors 

 varies with conditions, and no sun pie statement 

 is possible because the influence of each factor 

 follows a law peculiar to itself. The most 

 important conditions affecting the influence of 

 the mass of the load are discharge and slope, 

 while for the work of suspension and for 

 viscosity the important condition is the degree 

 of comminution of the load. 



The mass which the load contributes to the 

 stream is equivalent, in relation to potential 



20921 No. 8614 ^15 



energy, to an increase of discharge, and its 

 product by the stream's slope is proportional 

 to potential energy in the same sense in which 

 the stream's energy is proportional to the pro- 

 duct of discharge and slope. In a series of 

 experiments with loadless streams of water 

 flowing in straight troughs, the mean velocity 

 was found to vary approximately with the 0.25 

 power of the discharge and the 0.3 power of 

 the slope. Under the particular conditions of 

 these experiments 



V m = Q- 2S S- 3 x constant. 

 Differentiating with reference to Q, we have 



d V m = 



C0.3 



X constant . 



The increment to Q being interpreted for pres- 

 ent purposes as the suspended load, we see that 

 the corresponding increment to mean velocity 

 has a magnitude which varies directly but 

 slowly with the slope and inversely but more 

 rapidly with the discharge. 



Each particle in suspension is drawn down- 

 ward through the surrounding water by 

 gravity. It is impelled through the water in 

 an ever-changing direction by tangential force. 

 The average speed of the resultant motions, 

 referred to the surrounding water, . is greater 

 than the constant rate of descent the particle 

 would acquire if sinking in still water. There- 

 fore the work of suspension, measured by all 

 the motions through the water, is greater than 

 the work of simple subsidence, a quantity as to 

 which much is known. The measure of a 

 particle's work of subsidence per unit tune is 

 the product of its mass, less the mass of an 

 equal volume of water, by its fall in unit time 

 by the acceleration of gravity. If we call the 

 mass of the particle M and its velocity of 

 subsidence V,, and assume its density to be 

 2.7, the measure of the work of subsidence is 



The coordinate measure of work for the 

 stream's flow is the product of its mass by its 

 fall in unit time by the acceleration of gravity, 

 and the contribution which the particle, con- 

 sidered as a part of the stream, makes to the 

 work of flow is therefore measured by the 

 product of its mass by the fall of the stream in 



