The pressure-time method allows measuring the flowrate in hydraulic turbines, according to IEC 60041 standard. According to this standard, the applicability of the pressure-time method is limited to a straight pipe with a constant cross section with specific limits for length and velocity. However, low-head hydropower plants usually have an intake with a variable cross section and short length making this method difficult to be applied. In this paper, a test rig has been developed to extend the method's applicability. The test rig is designed for developing flows condition and small measurement lengths for pipes with constant and variable cross section, which could be similar to low-head turbine conditions. For pipe with constant cross section, three measuring lengths of 0.5, 1, and 1.5 m can be obtained on this test rig to study the pressure-time method. For pipe with variable cross section, the method is applied across a concentric reducer with a length of 255 mm, i.e., a 9.46 deg reducing angle. Different flow assumptions for estimation of the head loss and dynamic pressure variation are considered to compare the accuracy of discharge measurement. The results showed that the quasi-steady assumption for friction factor and kinetic energy, along with friction factor correction, increases the method accuracy up to 0.4% compared with the current standard recommendations. Moreover, the Monte Carlo method (MCM) is applied to estimate the transient measurement uncertainty and compared with the Taylor series method (TSM).