Residential water meters accommodate various methods of power provisioning. Electromagnetic and ultrasonic meters, for example, often rely on a battery-like external power source, whereas mechanical meters harvest energy from water flow through an impeller. Although energy harvesting (EH) minimizes maintenance needs driven by battery depletion/replenishment, placing a physical element into the flow adversely affects water pressure. This intrusive EH/sensing technique is not user-friendly either since the meters with impellers need to be embedded into pipes by skilled personnel. Hence, this paper proposes a non-intrusive sensor system powered by thermoelectric generators (TEGs) for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">plug-and-play</i> water flow rate measurement. This system, equipped with a custom-made energy management unit (EMU), adopts ultrasonic sensors, a task-based computing scheme, and a LoRa module for autonomous sensing and reporting of the flow rate. After summarizing thermoelectricity and delta time-of-flight ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\Delta$</tex-math></inline-formula> ToF)-based ultrasonic sensing theory, we provide the system model and design details with a particular focus on the EMU. Then, we experimentally evaluate the system under varying conditions, demonstrating their impact on average sensing and transmission periods. The results unveil that our proposal can achieve high measurement precision ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\pm 1.4\%$</tex-math></inline-formula> ), comparable to its intrusive and battery-powered counterparts, and thus has the potential of replacing the residential water meters.