510 BAGNOLD [chap. 21 



for as clues to the little understood physical processes underlying the 

 phenomenon as a whole. 



The phenomenon covers sediment transport by wind and by water streams 

 both in nature and in industrial ducts, and by sea currents with or without 

 superimposed fluid oscillations due to surface waves. It also covers turbidity 

 currents, the creep of super-saturated soils, etc., and the flow of slurries. It 

 extends finally to the simple avalanching, under the action of the gravity 

 component alone, of sand down the shp-face of a dune, and of material down 

 the sides of a spoil heap. 



While little serious attempt has been made in the past to investigate the 

 underlying physics, particular aspects of the jihenomenon have been subjects 

 of interest to one or other branch of engineering technology, each for its o^^Tl 

 practical purposes, and have been studied in isolation as separate phenomena. 

 Thus, though a number of separate quantitative theories have been suggested 

 by which the measiu-ed rate of sediment transport may in particular fields be 

 related to definable attributes of the sediment and of the fluid flow, the theories 

 treat of different sets of conditions, assume different attributes to be relevant, 

 and are expressed in different and often conflicting terms and symbols. 



Moreover, since the majority of experiments made have been designed for 

 j)ractical rather than scientific ends, factual data are in most cases insufficient 

 to test the general applicability of theoretical conclusions even within a 

 particular field. 



As a subject for broad general study, the phenomenon as a whole essentially 

 involves the "flow" of dispersed granular solids within fluids, and therefore 

 occupies a much neglected field between solid and fluid physics. So, it is un- 

 likely that a proper understanding of the phenomenon can be attained by any 

 approach based wholly on the concepts of either the one or the other discipline ; 

 or indeed that the physical processes involved can be described in any 

 commonly conventional set of terms and symbols. 



In this connection it will be as well to be clear at the outset as to the meanings 

 to be attached to certain terms currently used in very different senses. 



The term "friction factor" or "friction coefficient" has entirely diff'erent 

 meanings in solid physics and in hydraulics. In solid physics, the limiting 

 friction coefficient signifies the ratio of the shear force or stress, T, needed to 

 be exerted over a plane of static contact between two bodies in order to main- 

 tain relative motion between them to the perpendicular force or stress, P, 

 across that plane (Fig. 2a). The ratio TjP is usually defined as the tangent of 

 the "friction angle" <j), which in the case of a granular mass is a measure of the 

 mean angle of contact betw^een the grains. Thus friction coefficient = T/P = 

 tan ^. 



In hydraulics, on the other hand, the friction factor or coefficient, ca, relates 

 the shear stress over a floAv boimdary not to any fluid stress normal to the 

 boundary, but to the square of some representative flow velocity, u. Thus 

 Cd = Tlpu^, The flow velocity of a fluid is independent of any normal stress it 

 may exert on the flow boundary. 



