Torricelli’s Law in Fractal Space–Time Continuum

Didier Samayoa, Liliana Alvarez-Romero, José Alfredo Jiménez-Bernal, Lucero Damián Adame, Andriy Kryvko and Claudia del C. Gutiérrez-Torres ()
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Didier Samayoa: Instituto Politécnico Nacional, SEPI-ESIME Zacatenco, Unidad Profesional Adolfo López Mateos, Mexico City 07738, Mexico
Liliana Alvarez-Romero: Instituto Politécnico Nacional, SEPI-ESIME Zacatenco, Unidad Profesional Adolfo López Mateos, Mexico City 07738, Mexico
José Alfredo Jiménez-Bernal: Instituto Politécnico Nacional, SEPI-ESIME Zacatenco, Unidad Profesional Adolfo López Mateos, Mexico City 07738, Mexico
Lucero Damián Adame: Computational Robotics Department, Universidad Politécnica de Yucatán, Carretera Mérida-Tetiz, Km. 4.5, Ucú 97357, Mexico
Andriy Kryvko: Instituto Politécnico Nacional, SEPI-ESIME Zacatenco, Unidad Profesional Adolfo López Mateos, Mexico City 07738, Mexico
Claudia del C. Gutiérrez-Torres: Instituto Politécnico Nacional, SEPI-ESIME Zacatenco, Unidad Profesional Adolfo López Mateos, Mexico City 07738, Mexico

Mathematics, 2024, vol. 12, issue 13, 1-13

Abstract: A new formulation of Torricelli’s law in a fractal space–time continuum is developed to compute the water discharge in fractal reservoirs. Fractal Torricelli’s law is obtained by applying fractal continuum calculus concepts using local fractional differential operators. The model obtained can be used to describe the behavior of real flows, considering the losses in non-conventional reservoirs, taking into account two additional fractal parameters α and β in the spatial and temporal fractal continuum derivatives, respectively. This model is applied to the flows in reservoirs with structures of three-dimensional deterministic fractals, such as inverse Menger sponge, Sierpinski cube, and Cantor dust. The results of the level water discharge H ( t ) are presented as a curve series, showing the impact and influence of fluid flow in naturally fractured reservoirs that posses self-similar properties.

Keywords: Torricelli’s law; fractal continuum; Menger sponge; Sierpinski cube; discharge velocity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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