This article discusses how to derive a closed-form analytical solution describing the profile of unidirectional flow through a class of noncircular tubes. The cross sections of the conduits are a slightly distorted version of regular shapes, like triangles or trapeziums or rectangles, that are commonly seen in microfluidic or heat pipe applications. Hence, the study leads to approximate but useful expression for velocity profiles as well as resistivity for the aforementioned channels. Moreover, the paper shows how to extend the fundamental idea to other arbitrary geometries, providing simple expressions for flow fields that can be used subsequently in various hydrodynamic calculations. The analysis also gives an estimate of error in such a mathematical treatment that is found to be adequately accurate. Thus, the findings will be especially relevant in a number of fields, including microfluidic separation, heat pipe design, and capillary transport optimization.