Analysis of Water Leakage from a Right-Circular Cylinder Tank

This study delves into the mathematical modeling of water leakage from a right-circular cylinder tank with an orifice at its base. The objective is to determine the height of water in the tank, denoted as ‘h,’ at any given time ‘t’ after an initial height ‘H’ is set. The analysis involves differential equations and integration to derive the expression for ‘h(t)’. In this paper focuses on the mathematical analysis of water leakage from a right-circular cylinder tank standing vertically. The tank features a circular hole at its base, through which water escapes. The primary objective is to develop a mathematical model that describes how the water level within the tank changes over time, given an initial height ‘H.’ This analysis employs principles of fluid dynamics and differential equations to derive a solution. The findings have implications for engineering applications related to fluid containment systems and leak rate prediction.