The Phase-Plane Topology of the Simple Surge-Tank Equation

An investigation of the phase-plane solution curves of the nonlinear differential equation describing the motion of the water level in a simple surge tank operating in conjunction with a turbine governed for constant hydraulic power acceptance. The phase-plane solution picture is developed by determining the form of the solution of the equation near each of its singularities. The picture enables prediction and interpretation of instability and drainage phenomena.