希罗喷泉动力学分析

Dynamics analysis of Heron’s fountain

本文构建了一个希罗喷泉系统,利用修正后的非定常伯努利方程及连续性方程,在层流与非定常的基本假设下,解出其动力学方程;使用Mathematica软件并结合实验参数进行数值求解,推导了喷射高度随时间的理论变化关系,并探讨了喷射瓶的相对放置高度、横截面积、喷射管道直径以及喷口高度等参量对喷泉高度的影响.同时运用Tracker软件追踪喷泉高度,建立了空气弹簧的模型,完成了理论与实验的相互验证.

In this paper, a Heron’s fountain is constructed. The modified unsteady Bernoulli equation and the continuity equation are used to solve the dynamic equation under the laminar and unsteady basic assumptions. A mathematic software is used to combine the experimental parameters with the numerical solutions. The relationship between the height of the jet and the time is deduced theoretically. Its relationship with the height of the bottle on the right side, the cross-sectional area, the height of the fountain outlet, and the diameter of the pipe is also discussed. At the same time, tracker software is used to track the maximum jet height of the fountain, and the model of the air spring is established to complete the mutual verification of theory and experiment.