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Gravity-driven capillary viscometers (GDCVs) are used to obtain the viscosity function of non-Newtonian fluids from measurements of the instantaneous fluid height in the overhead reservoir. The reliability of this viscometry depends on two main aspects: the accomplishment of the required flow condition in the apparatus and the appropriate conversion of raw data into rheometric functions. This work presents a rigorous theoretical analysis of the GDCV, thus providing criteria to achieve accurate measurements. The equations describing the rheometric flow in a GDCV are deduced from the basic laws of momentum and mass conservation. From these equations, the flow dynamics of the apparatus is studied and the constraints required to attain a quasi-steady-state flow are established. Under these conditions, the rheometric functions are written in terms of the instantaneous fluid height. In addition, a method to process experimental data of non-Newtonian fluids is proposed, which can handle the ill-posed problem associated with the determination of the viscosity function in this viscometry. © 2004 American Institute of Physics.