Many studies have aimed to characterize pressurized transient hydraulics. However, it remains difficult to assess the importance of dynamic effects in a robust manner, and modeling is further complicated by the tension between computational efficiency and physical accuracy. To address such challenges for incompressible flows, this article presents an adaptive modeling approach that combines a novel hybrid formulation, termed the hybrid global gradient algorithm (HGGA), with a variable time step (VTS). The HGGA combines the generalized and rigid water column global gradient algorithms, so it can adapt to inertially-dominated flows and those without such effects. Computational efficiency and physical accuracy are balanced by adjusting the formulation according to the simulated hydraulics. Three physically-based indicators are then introduced to characterize unsteady flow: these actively inform the HGGA of how to model a system. Two pipe networks are used to demonstrate the current work. The first illustrates the utility of the inertial indicators, and the second comprises an extended period simulation with the VTS scheme. Although more computationally intensive than conventional modeling, the methodology is shown to provide a better representation of dynamic hydraulics.