【摘要】 谷超豪等三位教授编著的《应用偏微分方程》教材中对于理想流体的柱对称流和球对称流的动力学方程组的方程组的导出过程相对繁琐,导致学生理解较为困难、教学需要较多课时.本文同样采用隔离物体法,从积分方程出发,利用柱坐标系、球坐标系下的三重积分的计算,借助梯度、散度、拉普拉斯等微分算子在柱坐标和球坐标系下的形式,较快的给出这些流体的动力学方程组.此外,本文还给出了外力的作用对于方程组的影响以及轴对称流的动力学方程组.更多还原

【Abstract】 We discuss the derivation of the hydrodynamic equations of cylindrically symmetric flow and spherically symmetric flow at ideal fluid in the textbook Application of Partial Differential Equation complicated by professor Gu and other two professors. The derivation of these equations in the textbook are relatively complicated, which leads to the difficulty of students’ understanding and the need of more teaching hours. In this paper, we also adopt the method of isolating objects and start with integral equations, by using calculation of triple integral in cylindrical coordinate system and spherical coordinate system, using the forms of differential operators such as gradient, divergence and Laplace operator in cylindrical and spherical coordinates, we can derivate these hydrodynamic equations faster. In addition, the effects of external forces on the equations and the derivation of the dynamic equations of axisymmetric flow are also considered.更多还原