Hydropower is a clean and sustainable energy resource developed since the late 19th century. To specify the hydraulic performance characteristics of hydraulic turbines, the volumetric flow rate as one of the few basic quantities should be determined. Discharge represents the most difficult quantity to measure. A good measurement accuracy and estimation is difficult to estimate compared to the power and head, especially in low head machines. Despite the developments in discharge measurement techniques, this part of the hydraulic machine performance tests is often a major challenge. The pressure-time method is one of the discharge measurement techniques, which is studied in this PhD thesis. Most of the researches, to improve the accuracy of this method, are performed experimentally, whilst limited one-dimensional numerical simulations are done on this method. Therefore, detailed investigation of this method has been difficult. The studies conducted in this thesis are divided in two experimental and numerical parts. Because the flow physics in the pressure-time method is a combination of decelerating flow with variable rate and water hammer phenomenon, at the first experimental studies are performed considering unsteady constant rate decelerating and accelerating flows. The results helped to better understanding the studies in the second part concerned with numerical simulations. In the second part, the physical phenomenon behind the water hammer and constant rate decelerating and accelerating flows is studied. Then the physical characteristics of the flow in the pressure-time method is investigated in detail based on the time variation of the wall shear stress and the γ parameter. The γ parameter represents the difference between the turbulence structure in a transient accelerating or decelerating flow and the one in the quasi-steady condition. It is demonstrated that for the pressure-time method, part of the flow decrease excursion can be characterized as quasi-steady and the rest is unsteady. The dominance of inertia and turbulence dynamics is investigated to evaluate the wall shear stress in the part of the excursion with the unsteady assumption. It is found that the inertia has a dominant effect during the excursion. The evaluation of the effective forces in the flow rate calculation in a straight pipe showed that the wall shear stress is a good approximation of the losses calculation and the other terms can be neglected. To extend the applicability of this method outside the limitations of the IEC41 standard, variable pipe cross-section and different friction loss calculation are also studied. A new method for the loss calculation in the penstocks with variable cross section is proposed.  The errors induced by the proposed method are in an acceptable range provided that the contraction angle is less than ϴ=10°. The evaluation of the important forces showed that the variation of the momentum flux is the most significant term in the flow rate estimation in a pipe with a contraction. Then, the wall shear stress is the second most significant.