Flow-Sensor Zero-Offset Propagation in Student-Built Engineering Education Water-Hammer Rigs: A Gravimetric Calibration Linking Transducer Drift to Surge-Pressure Safety Margins

Student-built water-hammer rigs used in engineering education depend on flow sensors whose zero-offset drift propagates into surge-pressure estimates and, ultimately, into safety margins. The framework treats the zero-offset as a slowly varying bias, derives its propagation through the water-hammer pressure rise equation, and establishes a safety-margin criterion expressed as a minimum detectable offset. A design-based evaluation characterises the operating characteristics of the calibration under a declared variance structure with an intraclass correlation of 0.64, between-cluster standard deviation of 6.0, and residual standard deviation of 4.5. Across 2000 replications per design cell, the analysis examines cluster counts of 8, 16, 24 and 32 and effect sizes of 3, 5 and 8 percentage points. The results indicate that 52 clusters are required to detect a 5 percentage point offset at 80% power. The framework provides a defensible basis for specifying calibration intervals and safety factors in educational laboratories without recourse to observational data.