As a typical Cyber-Physical System (CPS), smart water distribution networks require monitoring of underground water pipes with high sample rates for precise data analysis and water network control. Due to poor underground wireless channel quality and long-range communication requirements, high transmission power is typically adopted to communicate high-speed sensor data streams; posing challenges for long term sustainable monitoring. In this paper, we develop the first sustainable water sensing system, exploiting energy harvesting opportunities from water flows. Our system does this by scheduling the transmission of a subset of the data streams, while other correlated streams are estimated using auto-regressive models based on the sound-velocity propagation of pressure signals inside water networks. To compute the optimal scheduling policy, we formalize a stochastic optimization problem to maximize the estimation reliability, while ensuring the system's sustainable operation under dynamic conditions. We develop Data Transmission Scheduling (DTS), an asymptotically optimal scheme; and FAST-DTS, a lightweight online algorithm that can adapt to arbitrary energy and correlation dynamics. Using over 170 days of real data from our smart water system deployment and conducting in-vitro experiments to our small-scale testbed; our evaluation demonstrates that Fast-DTS significantly outperforms three alternatives, considering data reliability, energy utilization, and sustainable operation.