关键词: 萨克逊碗, 沉没耗时, 数值计算, 模型评价

Abstract: Saxon bowl is a timing tool of the ancient Saxon. There is a hole in the center of its bottom and the bowl will sink after being placed on the water. We establish a model through Bernoulli equation and boundary layer theory, and then carry out numerical calculation to obtain submergence time, and compare it with experience. The results show that when the outer diameter of the bowl is more than 10 times of the bottom aperture, the model can well describe various experimental results, including the changes of submergence time with the aperture, mass of the bowl and liquid density. The model also reveals two special phenomena. First, with the increase of bowl mass, the submergence time tends to zero. Second, as liquid density exceeds density of the bowl, the bowl will not sink. The main advantages of the model are that it can accurately describe the experimental data and the speed correction term CD has great universality and insensitivity. The main limitation are its description of turbulence and an extreme situation.

Key words: Saxon bowl, sinking time, numerical calculation, model evaluation and discussion