The implementation of robust hydraulic control in water supply networks relies upon the utilisation of redundant flow estimation methods. In this paper, we propose a novel model-based flow estimation method for diaphragm-actuated globe valves based on three pressure signals, namely the valve inlet pressure, valve outlet pressure and control chamber pressure (the 3P flow estimation method). The proposed flow estimation method relies upon the accurate determination of a valve stem position based on a force-balance analysis for the diaphragm of a valve, the measured pressure differential across a valve and the flow coefficients of a valve (, ). A novel stem position estimation model for diaphragm-actuated globe valves has been formulated and experimentally validated. The non-linear parameterised valve stem position estimation model results in multiple solutions. We combine advances in signal processing with support vector machine classification to find a correct solution. We compare the proposed flow estimation method with a method that uses stem position sensor measurements of a valve and two pressure signals. A unique set of experimental data have been acquired for performance validation. We derive uncertainty bounds for the proposed flow estimation method and demonstrate its application for robust pressure control in water supply networks.