This paper proposes a linear model that relates the pressure head variations at the downstream end of an inverted siphon to the flow rate variations at two ends. It divides the pressure head variations in the inverted siphon into low-frequency part and high-frequency part. The two parts are caused by the deformation of the siphon wall and the reflection of acoustic wave, respectively. In order to build a simplified relation between wall deformation and low-frequency pressure head variations, the Preissmann slot method (PSM) is adopted in this paper. The linear model can also be used in other forms of structures, such as pipes and tunnels, where a pressurized flow condition is present. In comparison with simulation results using the finite volume method, the linear model shows an L2 norm of 0.177 for a large-scale inverted siphon and 0.044 for a PVC pipe. To this end, the linear model is adopted to model a large-scale inverted siphon in a virtual water delivery system. Simulation results show that the inverted siphon can reduce water fluctuations. An equation to quantify this effect is proposed based on the linear model.

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