Predicting Incipient Velocity of Capsules in Pipe

An equation for predicting the incipient velocity of capsules given in a previous paper was analyzed for sources of errors and ways to improve. It is shown that substantially better predictions can be achieved by: (1) using a better formula to determine the lift coefficient; (2) determining the static contact friction coefficient between the capsule and the pipe accurately; (3) using a contraction coefficient somewhat larger than that for sharp-edged capsules; (4) using more accurate values of the capsule-to-pipe diameter ratio; and (5) using a DarcyWeisbach resistance coefficient somewhat larger than for hydraulically smooth pipe. The equation for predicting the incipient velocity of single capsules in pipe is also modified for predicting the incipient velocity of a capsule train in pipe. A formula is developed to determine the extra roughness of the capsule train caused by the rough junctions between neighboring capsules. The formula enables more accurate prediction of the incipient velocity of capsule trains than is possible without using the formula.