The hydraulic design of Francis turbines and pump-turbines is an expensive project-specific engineering effort that typically involves a direct iterative exploration of the design space. An inverse design method for turbomachinery has been previously introduced in the literature, and several recent applications have demonstrated its advantages; however, only a commercial implementation of the method is currently available. In this work, an open-source implementation of the inverse design method is introduced. First, the governing equations in cylindrical and curvilinear coordinate systems are derived, consolidating the somewhat inconsistent formulations that are available in the literature. Then, a convergence analysis of the method is performed in order to characterize the behavior of the discretization error and deduce the mesh resolution requirements. A validation of the method output with respect to high-fidelity computational fluid dynamics simulations is then presented; it is demonstrated that the velocity fields are well predicted, the pressure distribution on the blades is reasonably well approximated, and the flow angular momentum extraction is achieved in the prescribed manner. Possible improvements to the open-source implementation of the method are discussed.