At present, underwater electric pulsed discharges are used in a wide range of modern applications. During the development of a system for generating underwater acoustic pressure pulses, a numerical model is an essential tool for guiding the design and interpreting the data. Developing a complex one-dimensional numerical code, like those presented in the literature, requires a substantial dedicated effort. Unfortunately, previous work trying to use simple and elegant theoretical models developed many decades ago reported a fundamental issue, apparently related to the input data. The present work performs a detailed analysis of the real meaning of the voltage measured across an underwater discharge and clarifies the correct way the power input to a simple two-phase model should be calculated. Based on accurate measurements, a phenomenological methodology to obtain the input data is demonstrated, with theoretical predictions obtained from the simple two-phase model being successfully compared with the experimental evidence obtained from both the present work as well as from other reliable data presented in the literature.