Discharge time of a cylindrical leaking bucket

Abstract

The problem of the discharge time of a cylindrical bucket with a hole in the bottom is solved by means of Bernoulli's equation for non-steady flow.Comparison of the results with experiment and with a simplified analysis using Torricelli's law is made. The measurements were made by high-school students in a laboratory session under guidance of instructors. It is noted that, for large ratios between the radius R of the cylinder and the radius r of the hole, the simple formula for the discharge time of a leaking bucket found by means of Torricelli's law can be used to interpret the experimental results, provided effective parameters for the model are defined.

How can the global temperature increase be explained to students?

“…Let us first consider the hydrodynamic system consisting of a leaking bucket of cross section S as in figure 1. In this figure p t ( ) is the incoming water flux flow rate and q t ( ) is the outcoming flux flow rate expressed by means of Torricelli's equation [14]…”

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“…If the rate of change of the height h of fluid in the tank is small compared to υ 2 then that speed of outflow can be approximated using Torricelli's theorem [9] so that…”

Numerical Model for a Nineteenth-Century Hydrometric Module

“…The Torricelli equation [Eq. (6)] was used to determine the outlet flow, Q, through the discharge valve from the head above it, H; the orifice area, S h ; and a nondimensional discharge coefficient, K d , that depends on the geometry of the orifice (Franchini and Lanza 2013;Blasone et al 2015). The discharge coefficient for a thin-walled circular orifice has been estimated at 0.6 (White 1999).…”