Hole Diameter and Sinking Time of Water Clocks

Abstract

Water clocks measure time by controlling the flow of water into a container. Ancient Persians used the sinking time of Fenjaans, bowls with holes in the center, as a metric for time. The relationship between hole diameter and sinking time of cylindrical containers was investigated. A theoretical model was derived using Torricelli’s Law and Archimedes’ Principle. The experimental relationship was found by drilling holes with diameters ranging from 2 to 13 mm in the center of nearly cylindrical stainless-steel containers and measuring their sinking time. It was found that there was a proportional relationship between the sinking time and the inverse square of the hole diameter with a proportionality constant which matched, within uncertainties, the proportionality constant predicted by the theoretical model.