openKARST: From detailed karst conduit dynamics to simplified hydraulic flow dynamics

In this work we employ openKARST, which has been developed to simulate free-surface and pressurized dynamics in large conduit networks. The solver is designed to model transient flood waves as well as steady flow states under mixed flow conditions. Turbulence is represented via Darcy–Weisbach friction, with support for classical correlation function as Churchill and Colebrook-White. A particle-tracking and advection-diffusion module allows to model tracer transport and travel-time analyses. Verification and validation against analytical benchmarks and applications to large cave networks, such as the Ox Bel Ha system, demonstrates the numerical robustness. In this work we introduce a steady-state analysis workflow that condenses complex network solutions into simpler hydraulic metrics. Using conduit-specific Reynolds numbers and friction factors based on high fidelity simulations, we quantify how effective resistance evolves from partial filling to pressurized conditions with discharge, viscosity and diameter along karst conduits. To recover the observed trends without running full simulations, we propose a simple steady-state approximation in which the longitudinal water surface is represented by a generalized water depth profile, where cross-sectional hydraulics follow circular partial-filling geometry. This reduced model enables to compute conduit-averaged Reynolds numbers and friction factors and further provides conduit profiles that can be compared directly to simulated distributions, including regimes influenced by pressurization. Hence, this work offers a practical bridge between complex network hydraulics and compact predictive relationships to enable systematic exploration of parameter space and upscaling.