Fixture-Resolved Water Monitoring and Leak Localization via Transmission-Line Modeling and Active Time-Domain Reflectometry of Residential Plumbing

A Technical Disclosure

Abstract

We describe a method for inferring, from a single instrumented point on a dwelling’s main water supply, (i) which plumbing fixture is drawing water and (ii) the presence and physical location of leaks. The dwelling’s pipe network is modeled as a branched acoustic transmission line: pressure and volumetric flow play the roles of voltage and current, the distributed inertance and compliance of the water-filled pipe set a characteristic impedance and wave speed, viscous friction sets the attenuation, and a leak appears as a shunt admittance to a pressure sink at a specific location. Each fixture terminates a branch of distinct length and load impedance, so opening a fixture measurably changes the driving-point complex impedance Zin(ω) observed at the main and produces a reflection whose time-of-flight localizes the fixture. We describe both passive inference (from the pressure transients fixtures generate when their valves actuate) and, as the distinguishing element of this disclosure, active interrogation, in which a controlled transducer injects a known excitation and the system measures Zin(ω) or performs time-domain reflectometry (TDR) to obtain range to each active fixture or leak directly. We give the governing equations, the transfer-matrix (ABCD) and scattering-matrix network formulations, a complete and reproducible reference simulation of a model dwelling, and an enumeration of practical embodiments and variants, including methods addressing the dominant real-world error sources (trapped air, pipe-material variability, and simultaneous fixture use). The purpose of the disclosure is to make these methods and their variants freely available.