GRAVITY DRAINAGE OF AN OPEN SPHEROIDAL TANK

Abstract

This study simulates the gravity-driven drainage of an open spheroidal tank. A dimensionless parameter λ is introduced that alters the geometry of the tank but not its volume, generating prolate, spherical, and oblate spheroidal variants. The openings in the tank are obtained by cutting its surface with two symmetrical planes, close to the ends, without significantly affecting its capacity. Based on the principles of hydrodynamics, two models are developed: a general numerical model and an approximate analytical model based on Torricelli’s theorem for analyzing the drainage process as a function of geometry and time. Both models are implemented using Python 3.13 code. The results show excellent agreement between the two approaches for a specific range of λ, although the analytical model loses validity near a critical threshold. Under conditions of equal volume and discharge opening, the prolate tank drains faster despite a higher initial fluid level, while the oblate tank, with a lower initial height, drains more slowly. These results may be of particular interest in hydraulic and process engineering for the control of liquid storage and distribution. The implementation in Python 3.13 provides an open-access, fully reproducible, and classroom-applicable educational resource.