Predicting Drag Coefficient of Pneumatic Capsule

Abstract

This research compares various methods for determining the drag coefficient of a capsule moving through a pneumatic capsule pipeline. A theoretical drag coefficient equation is derived using the 1D energy equation, continuity equation, and momentum equation. The equation contains the orifice coefficients of the end disks, which cannot be predicted accurately without knowing the curvature of the edge of the end disks. The equation is compared with other equations and experimental data found in literature. Using the sharp-crested orifice coefficient published in textbooks overpredicts experimental data by >30%. Calibrating the equation to match individual sets of experimental data yields a maximum 14% error. Finally, using the equation and an empirical formula to correct the orifice coefficient as a function of the diameter ratio of the end disks can predict the drag coefficient within 20% of the experimental data. Achieving greater accuracy requires more accurate determination of the ratio of pipe to disk diameter, curvature of the disk edge, or direct measurement of the drag of individual capsules through model or prototype tests.