Objective Traditional rapid evaluation methods for small-hole leakage on the sidewall of cylindrical tanks often assume a constant discharge coefficient. This leads to significant deviations under small-aperture and low-Reynolds-number conditions. To improve the evaluation accuracy of leakage flow rate, drainage time and liquid level state, this study develops an evaluation method for leakage parameters to support quick judgment during the initial stage of accidents.

Methods An experimental apparatus was set up to simulate small-hole leakage on the sidewall of atmospheric cylindrical tanks. Using tap water as the test medium, variable liquid-level leakage experiments were systematically conducted across eight different aperture sizes. Key data—including leakage flow rate, drainage time, and jet range—were acquired, with the experimental Reynolds number ranging from 4×10³ to 2.5×10⁴. On this basis, the dynamic variations of the discharge coefficient with respect to aperture size and Reynolds number were analyzed, and a discharge coefficient correction model was established and integrated into the drainage process calculations. Finally, a Multilayer Perceptron (MLP)-based jet range prediction model and a liquid level inversion model were constructed using aperture size, liquid level, and effective head as input variables. Cross-validation was adopted to verify the generalization ability of the models, enabling rapid inversion of the internal tank state based on external leakage characteristics.

Results Within the 3–10 mm aperture range, the discharge coefficient was not constant but was jointly influenced by orifice geometric features and the Reynolds number. For small apertures (3–4 mm), the mean discharge coefficient was approximately 0.885, which was 36％–45％ higher than the mean value (0.61–0.65) of the classic sharp-edged orifice theory. After adopting the corrected discharge coefficient, the prediction error for drainage time within the effective inversion interval (liquid level: 200–500 mm) for small apertures (3–4 mm) decreased from roughly 33％–37％ to less than 2％. Throughout the entire drainage process, drainage time decreased following a power-law trend as aperture size increased, yielding a fitting exponent of −1.954 and a coefficient of determination R² of 0.999 8. The R² of the jet range prediction model reached 0.983. In the small-aperture sensitive region, the Mean Absolute Percentage Error (MAPE) was reduced from the traditional theoretical range of 11％–18％ to 1.5％–3.5％. The overall MAPE of the liquid level inversion model was 1.91％.

Conclusion This study develops a rapid evaluation framework for small-hole leakage on the sidewall of cylindrical tanks, comprising three modules: discharge coefficient correction, jet range prediction, and liquid level inversion. The framework collaboratively outputs key parameters including leakage flow rate, residual liquid level, drainage time, and impact distance. Applicable to low-viscosity, single-phase liquid leakage under atmospheric pressure, this method provides a technical reference for rapid emergency decision-making and digital safety assessments during the initial stage of leakage accidents.