Using the concepts of dilatant suspension behavior introduced by Bagnold, an equation has been derived for the hydraulic gradient necessary to transport solids in a two-dimensional channel where suspension arises from the Bagnold dispersive stress.The equation has been tested for the case where a stationary bed of solids exists and the empirical constant in the equation is found to agree with that obtained by Bagnold for shear in an annulus.The equation bears a strong resemblanre to that verified experimentally for circular pipes by Abbott.crc exists a considcrablc body of experimental knowledge Th concerning the flo\v of suspensions of solids in pipelines, but thc correlations which have been proposed(',*' arc basically empirical.Lf'hat is not generally realized by engineers with a passing familiarity with the field of thc flo~v of solids suspensions, is that thcre exists a scparatc body of theorctical and scmicnipirical knowlcdge with a position analogous to that of hydrodynamics in fluid mechanics. This h d y of theorctical and semi-cnipirical knowlcdgc is primarily thc work of Bagnold'R-6). Bagnold did not confinc his attention to thc niore fundamental aspects of the problcm. Indeed, the first steps in thc application of fundaincntal principles to practical problcnis wcrc made h!. Bagnold in his consideration of the transport of solids in open channels and the transport o f dcscrt sands by wind. T h e purpose of this series of investigations is to continue his work with particular rcfcrcncc t o the transport of suspensions in closed pipclincs.Previous Work ( a ) Fundamental Concepts: Prchably the niost important of Bagnold's series of cxperimcnts \vas that(5J in which a suspension of solid particles was sheared in the annular spacc separating two coaxial cylinders. Thc shcar stress necessary to prevent movement of the inner cylinder \\'as mcasurcd, togcthcr with thc dispcrsivc stress o r pressure, characteristic of dilatant SIISpensions, resulting froni the process of monicntum transfer bctwccn successive layers of the niixturc of fluid and solids.Since this dispersive stress acts nomially to the plane of shearing, Bagnold was able to explain how solid particles in a con\ fluid could remain suspended undcr conditions whcrc the suspending action of fluid turhulcncc \vas insufficient.A t solids concentrations grcatcr than 10-1 5% by volume.