Tank-reservoir drainage as a simulation of the recession limb of karst spring hydrographs

Drainage of a cylindrical water-filled tank-reservoir has been analysed by different physical models, providing relative discharge-time equations. The process has been simulated (1) in a condition of free-flow discharge, where no energy is lost during the process, and (2) where friction forces and water viscosity take effect. Simulation (1) is considered to be a Torricelli reservoir, characterised by a linear decrease of discharge; (2) is based on Darcy’s law or on Poiseuille’s law, where discharge decreases exponentially with time, giving a straight line in the semilogarithm plot. For the Darcy’s law simulation, the tank tube was filled with sand. The cylindrical water-filled tank-reservoir drainage analysis has been applied to simulation of the actual shape of karst spring hydrographs. It has been determined that the recession coefficient, α, is proportional to a hydraulic constant, c, which represents the hydraulic characteristics during the baseflow recession, and α is inversely proportional to the product of the water-table area with the effective porosity. This product expresses the area of the aquifer filled by free-flowing water along the water table and can vary during the aquifer drainage.