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Stokes flow of a Newtonian fluid through oil and gas production tubing of uniform diameter is studied. Using a direct simulation on computer-aided design of discretised conduits, velocity profiles with gravitational effect and pressure fields are obtained for production tubing of different inner but uniform diameter. The results obtained with this new technique are compared with the integrated form of the Hagen–Poiseuille equation (i.e., lubrication approximation) and data obtained from experimental and numerical studies for flow in vertical pipes. Good agreement is found in the creeping flow regime between the computed and measured pressure fields with a coefficient of correlation of 0.97. Further, computed velocity field was benchmarked against ANSYS Fluent; a finite element commercial software package, in a single-phase flow simulation using the axial velocity profile computed at predefined locations along the geometric domains. This method offers an improved solution approach over other existing methods both in terms of computational speed and accuracy.