Study on Timing Characteristic of Saxon Bowl and Prediction of Sinking Time

Abstract

There have been many water clocks in history and the Saxons used bowl with a hole in its base is one of them. When the bowl is put into water, it will sink slowly. This paper mainly studies series factors that affect the time bowl sinks, water filling rate and how the bowl measures time by establishing a theoretical model, calculating an approximate expression of water filling rate and using ordinary differential equation group for numerical simulation. The effects of aperture of the orifice, weight of the bowl, external height of the bowl on the sinking time were investigated. The innovation of this paper is to find the depth of water inside the bowl can be used as a timekeeping criterion.