Case studies for solving the Saint-Venant equations using the method of characteristics: pipeline hydraulic transients and discharge propagation

Hydraulic transients occur during a change from one equilibrium state to another, for example, in flows. The pipeline project should provide the head and discharge in any operating states, e.g., sudden valve opening or closure. Among the various numerical approaches for the calculation of pipeline transients, the method of characteristics (MOC) is advantageous This study aims to present a hydraulic transitory study as MOC applications for solving the Saint- Venant equations in two case studies: 1) in a penstock of a small hydropower system as a simple pipeline in the case of valve-closure in the downstream boundary with a reservoir in the upstream boundary; and 2) for discharge propagation into a channel by velocity and depth of the flow channel along space evaluation. The main data for the first case study consisted of a design head that is 182 meters, a turbine discharge of 13.82 m super(3)/s, a diameter of 4 meters and length pipe (penstock) of 2,152.50 meters. Regarding the second case study, the entry hydrogram was given to a rectangular channel with a width of 6.1 meters, length of 3,048 meters, slope of 0.0016 meters, and exhibited uniform flow with nominal depth of 2.44 meters. The characteristic curve of the discharge in the downstream extremity is Q = 158.(y - 3.25) super(32). The proposed methodology by Chaudry [5] concerning the development of hydrodynamic models was used. The obtained results for first case study showed that the simulated values for valve pressure while varying turning the valve between 4 and 12 seconds results in maximum values of pressures that oscillated between 219.97mca and 212.39 mca (4s) and 196.42mca and 190.86mca (12s). For the second case study, the values of discharge, velocity, and depth for x=0 and elapsed time of 850s were, respectively, 127.70m super(3)/s, 3.87m/s, and 5.36m. For x=0 and an elapsed time of 1,230s, the values were 87.92m super(3)/s, 4.49m/s, and 3.21m. Therefore, the MOC numerical approach has been confirmed to be useful for several engineering purposes, including cases of hydraulic transients and discharge propagation in hydraulic systems