水击基本方程的改进

Improvement of fundamental equation of water hammer

本文首先指出了当前用于水击计算的数学模型中的连续性方程式在恒定流时不能成立的问题,并通过进一步的理论推导,得到了新的水击波速计算公式和新的连续性方程。新的水击波速计算公式表明水击波速并非是一个常量,它的大小随流体动能沿程变化率与压强势能沿程变化率之比的变化而变化,同时也随管道断面相对变化量与压强相对变化量之比的变化而变化。新的连续性方程改善了老方程存在的不合理现象。本文还通过对水击现象的计算比较,进一步说明了老方程的确存在不合理现象,而新方程的计算结果是合理的。最后,分析指出了当前用于水击计算的连续性方程式在恒定流时不能成立的原因所在。

The problem of continuity equation in current mathematical model for water hammer does not conform to the reality is pointed out. A precise formula for water hammer wave speed and a new continuity equation are deduced from the fundamental equations of hydrodynamics. The new formula indicates that the wave speed is not a constant, it changes with the variation rates of dynamic energy and potential energy of pressure in the process of propagation. At the same time, the wave speed varies with the ratio of relative variation of pipe cross section to relative variation of pressure. The new continuity equation solves the problem of incorrect hammer calculation result by using the current equation. The validity of the new formula is verified by the comparison of calcuation result with the actual process of hammer.