Reservoir Oscillations with Through Flow

The two-reservoir problem with through flow is a common feature in wastewater treatment plants. The start of the through flow may cause water surface oscillations in the reservoirs and velocity variations in the connecting pipe during the initial unsteady phase that may adversely affect the operation and under certain conditions may cause overtopping of the upstream reservoir. The classical solution based on the rigid mass theory is inapplicable as velocity variations within the pipe system are ignored. One-dimensional mass and momentum conservation equations, based on the elastic theory, with a new set of boundary conditions are solved using the method of characteristics to investigate the water surface oscillations in the two reservoirs and minimum velocity in the connecting pipe as a result of the start of a through flow. The impact of a constant or variable friction factor on the velocity and water surface oscillations in the connecting pipe is found to be negligible. The magnitude and the time it takes to establish the through flow are found to be important parameters for the system. Optimum time of linear increase of a given inflow rate to the final steady state discharge is investigated for an actual facility. A ramp time of 40 seconds is found to reduce the maximum water surface level from 40 cm to 9.4 cm and increase the minimum velocity in the system to 85% of the final steady state velocity.