Exact computation of waterhammer in a three-reservoir system

The three-reservoir problem is a classic topic in hydraulic engineering. Three pipelines connect three reservoirs at a common junction. The three reservoirs have different elevations and liquid flows from the highest to the lowest reservoir. The main question is: will liquid flow to or from the middle reservoir? The classic problem concerns the calculation of the steady flow rates and hydraulic grade lines in the system. The present paper focuses on unsteady flow in the system. A simple and elegant method is presented that is able to detect exactly all reflections and transmissions of pressure waves at the three-way junction