The objective of this paper is to investigate the reliability of the mathematical model used for estimating the U-Oscillating Water Column (U-OWC) response in the time domain. This device is a wave energy harvester belonging to the family of Oscillating Water Columns. It comprises a water column, an air chamber with a self-rectifying turbine and a vertical U-shaped duct connecting the water column to the open wave field. The model used for describing the water column oscillations is based on the application of the unsteady Bernoulli equation for a real fluid and involves the determination of energy losses occurring over the entire duct length. The reliability of this mathematical model is assessed against experimental data. For this purpose, a U-OWC experimental model is installed in a benign natural basin, the Natural Ocean Engineering Laboratory NOEL. The experimental model is exposed to waves stochastically characterized. Thus, its response is described by relevant statistics. The paper shows that the current mathematical model may yield relevant overestimations of the system response. This relates to the approximate representation of the head losses, which are based on the Darcy-Weisbach formula traditionally employed in the analyses of steady flows. For overcoming these limitations, the paper proposes the utilization of the instantaneous acceleration-based model, which includes unsteady head losses proportional to the water column inertia. In this context, the model shows a general good agreement with the experimental measurements and demonstrate a superior capability of predicting the U-OWC response in all the processed records.