关于欧拉方程和伯努利方程适用条件的探讨

DISCUSSION ON THE APPLICABLE CONDITIONS OF EULEREQUATION AND BERNOULLI EQUATION

从动量守恒和能量守恒出发,详细地阐述了欧拉方程和伯努利方程的推导过程。从两个方程的推导过程可以清楚地看到,欧拉方程适用的充要条件是黏性偏应力张量的散度为零,流体黏度为零只是欧拉方程成立的充分条件而非必要条件。伯努利方程除了需要适用欧拉方程外,还需要满足流体正压、质量力有势、流动定常的条件,如果需要保持系统的总能量守恒,则正压流体条件需改为等熵流动条件。

Based on the conservation of momentum and energy,the derivation of Euler equation and Bernoulli equation was described in detail.From the derivation of the two equations,it can be clearly seen that the necessary and sufficient condition for Euler equation is that the divergence of the viscosivity stress tensor is zero,and that the fluid viscosity is zero is only a sufficient condition but not a necessary condition for Euler equation to be established.In addition to requiring Euler equation to apply,Bernoulli equation still needs to satisfy the conditions such that the fluid is barotropic,the mass force is potential,and the flow is steady.If the total energy of the system needs to be preserved,the condition of barotropic fluid should be changed to that of isentropic flow.