<p>For Water Distribution Networks (WDS) to be sustainably operated, hydraulic reliability, leak detection, and energy-efficient operation are essential. Although the data-driven hydraulic modeling problem has been advanced by recent developments in Graph Neural Networks (GNNs), the existing solutions are black-box predictors that lack the ability to directly enforce the physical conservation laws, which makes them less robust, interpretable, and reliably performing. The research proposes PI-HydroGNN, a physics-informed spatiotemporal graph learning framework for water distribution system monitoring and control. The framework integrates established modeling components within a unified architecture and incorporates hydraulic mass balance, energy conservation, and pressure-dependent leakage dynamics directly into the optimization objective, improving physical consistency and robustness. Three benchmark networks (Net3, C-Town, and Anytown) with stochastic demand variations and artificial leakage scenarios over a 60-day horizon are used in the extended period EPANET simulations to evaluate the framework. Compared to the data-driven baselines, PI-HydroGNN achieves 9.6% savings in pump energy use, an F1-score improvement of 0.922 for leakage detection, and a 39.9% reduction in pressure prediction RMSE, while also decreasing pressure violation rates by 68.9%. The model demonstrates strong generalization across benchmark networks under varying demand and leakage conditions. The findings show that a high-quality and functionally well-integrated digital twin for WDS operation can be obtained by incorporating physical principles into graph-based learning. PI-HydroGNN demonstrates strong potential for digital twin applications in water distribution system management.</p>