2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/86709We consider pressure-driven, steady state Poiseuille flow in straight channels with various cross-sectional shapes: elliptic, rectangular, triangular, and harmonic-perturbed circles. A given shape is characterized by its perimeter P and area A which are combined into the dimensionless compactness number C = P^2/A, while the hydraulic resistance is characterized by the well-known dimensionless geometrical correction factor alpha. We find that alpha depends linearly on C, which points out C as a single dimensionless measure characterizing flow properties as well as the strength and effectiveness of surface-related phenomena central to lab-on-a-chip applications. This measure also provides a simple way to evaluate the hydraulic resistance for the various shapes.4 pages including 3 figures. Revised title, as publishedFluid DynamicsSoft Condensed Mattertext