Theoretical Analysis of Pressure Drop in the Laminar Flow of Fluid in a Coiled Pipe

Abstract

A series solution with terms depending on the curvature of the pipe is presented for the coiling effect. Because of its slow convergence the series is most useful only at Dean numbers below about 16. However, this is the normal range for viscometry with coiled capillaries. Theoretical analysis is also appropriate in this range because as the excess pressure drop due to coiling decreases it is more difficult to measure accurately by experiment. A previously unreported finding is made, that at very low flows all coiled capillaries yield a lower pressure drop than a straight capillary of the same axial length. However, this does not detract from the utility of coiled capillaries for high precision viscometry.