Accurate flow measurement is critical for hydraulic systems because it represents a crucial parameter in the control of fluid power systems and enables calculating hydraulic power when combined with pressure data, which is valuable for applications such as predictive maintenance. Existing flow sensors in fluid power systems typically operate invasively, disturbing the flow and providing inaccurate results, especially under transient conditions. A conventional method involves calculating the flow rate using the pressure difference along a pipe via the Hagen-Poiseuille law, which is limited to steady, laminar, incompressible flow. This paper presents a novel soft sensor with an analytical model for transient pipe flow based on two pressure signals, thus eliminating the need for an actual volumetric flow sensor. The soft sensor was derived in previous research and validated with a distributed parameter simulation. This work uses a constructed test rig to validate the soft sensor with real-world experiments. The results highlight the potential of the soft sensor to accurately and computationally efficiently measure transient pipe volumetric flow based on two pressure signals.