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A new method of analysis has been devised for determining the developing laminar flow and corresponding pressure drop in the entrance region of tubes and ducts. The method is formulated in a general manner which applies to ducts of any cross section. Specific application is made for flow in a circular tube and in a parallel-plate channel, and the velocity distribution and pressure-drop results are compared with experimental data and prior analyses. These comparisons lend strong support to the findings of the present analysis.