Slip Point of Beds in Solid-Liquid Pipeline Flow

In view of the relatively low mean velocities which give optimum efficiency for pipelines transporting granular solids, it is important to study the conditions for which stationary deposits occur in pipes. The limit of deposition is the slip point, at which the force driving the bed exceeds the coefficient of friction times the total normal force exerted by the bed grains against the pipe wall. Although the state of intergranular stress in the deposit is generally indeterminate, it is shown that near the slip point it is a reasonable assumption that the granular pressure at the periphery of the bed follows a hydrostatic distribution. Experimental verification of this assumption was obtained from two types of tests, one involving flow conditions in a recirculating system and the other the slipping of deposits in a tilting pipe. The relationship derived for the hydrostatic distribution of granular pressure shows that the pressure gradient at the slip point is directly proportional to the underwater weight per unit volume of bed, and increases with the angle subtended by the deposit.