Laminar tube flow through an abrupt contraction

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Abstract
The general equations of motion were solved numerically for the laminar isothermal flow of Newtonian fluids from a large tube of circular cross section through an abrupt contraction into a coaxial tube of smaller diameter and through the flow‐development region of the smaller tube. The ratio of the diameter of the large tube to that of the smaller tube was varied from one to eight (the latter in one case). Solutions were obtained for the case where the larger tube is real, with no slip at the wall, and for the case where it is a frictionless “stream” tube. The results are presented as charts giving excess pressure losses attributable to contracted and developing flow in terms of equivalent smaller‐tube diameters as functions of the tube‐contraction ratio and the Reynolds number, which was varied from 0.01 to as high as 500 in one case. Both radial‐ and axial‐velocity profiles are presented. The computed results are shown to be in satisfactory agreement with some experimental data. The results are presented in a manner convenient for use in the design of equipment in which contracted Newtonian flow occurs, such as fiber spinnerettes and heat exchangers, and in the analysis of experimental data for contracted flow.