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We describe an unsteady pressure-driven capillary viscometer, in which the liquid under test is forced through a capillary tube by compressed-air pressure. The principle of operation involves measurement of the driving pressure versus time that decays progressively as the fluid flows and covers continuously a broad shear rate range in a single measurement. The viscosity is determined by curve fitting of the experimental data to the explicit expression for the transient pressure as a function of time. A laboratory bench test shows the validity of the theoretical approach for viscosity determination of both Newtonian and non-Newtonian liquids.