Abstract: A computer software program provides an algorithm that solves for unknown demands (and junction pressures) within a modeling system that uses a generalized, unified loop-node formulation. The program can be used to calculate the available demand (i.e., the amount of water that is to be supplied) according to the nodal pressure. Both nodal heads and flows are simultaneously solved using a gradient algorithm, which allows, in accordance with the present invention, the model to simulate situations where a change in pressure affects the quantity of water used. Criticality analyses for segments of a system in such pressure dependent scenarios can also be performed using the software program of the present invention.