What question did this study set out to answer?

This paper aims to revise the characterization of the Gorelli Extended Siphon (GES) by identifying a missing equation related to fluid behavior during depression.

May 27, 2026Open Access

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The Missing Equation: Inertial Dominance, Controllable Depression and the Limit of Existing Models in the Gorelli Extended Siphon (GES)

Key Points

This paper aims to revise the characterization of the Gorelli Extended Siphon (GES) by identifying a missing equation related to fluid behavior during depression.
Utilized prototype parameters: D = 20 mm, Lc = 70 cm, Li = 10 cm, V = 30 L, Rg = 7.0.
Employed 4th-order Runge-Kutta integration with GCI < 0.03% for simulation.
Developed a four-phase experimental protocol with formal falsification criteria.
Quantified peak inertial force and basin depression profile using simulation.
Identified a critical point where the required volume of fluid aspirated cannot be calculated using existing equations.

Abstract

This paper presents a revised characterisation of the Gorelli Extended Siphon (GES), defined by the parameter Rg = Lc/Li >= 7 with an open/closed variable-control source basin. Using actual prototype parameters (D = 20 mm, Lc = 70 cm, Li = 10 cm, V = 30 L, Rg = 7.0) and 4th-order Runge-Kutta integration (GCI < 0.03%), the simulation quantifies the peak inertial force and basin depression profile. The simulation halts at the point where it must calculate the volume of fluid aspirated by the falling column — a parameter not described by any existing equation. This is the missing equation. A four-phase experimental protocol with formal falsification criteria is provided.

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Cite This Study

Elvio Gorelli (Sat,) studied this question.

synapsesocial.com/papers/6a168a640c924ddd1bd59180 https://doi.org/https://doi.org/10.5281/zenodo.20371848

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