伯努利方程教学设计中的若干问题1)

针对流体力学课程中伯努利方程内容的教学设计,分析了伯努利方程演示实验中的常见误解,提供了伯努利方程的不同推导方法,讨论了方程中压强项的物理意义,并将伯努利方程进一步联系拓展,以加深学生的理解认识,建立科学严谨的分析方法。伯努利方程的推导是我们认识该方程最基本的出发点,在运用伯努利方程对演示实验解释时一定要注意伯努利方程的适用条件,且综合考虑流体黏性、卷吸等因素的影响。大多数中文教材和英文教材关于伯努利方程中压强项的物理意义解读不同,由伯努利方程推导过程可知,方程中的压强项具有势能的特性,这一特性仅对流体成立。通过建立伯努利方程与其他知识点的联系,对比了可压缩和不可压缩伯努利方程的形式,加深了学生对伯努利方程的理解认识。

SEVERAL ISSUES IN BERNOULLI EQUATION'S INSTRUCTIONAL DESIGN$^{1)}$

In view of Bernoulli equation's instructional design in fluid mechanics, this paper analyzes some common misunderstandings in demonstration experiments of Bernoulli equation, provides different derivation methods of Bernoulli equation, discusses the physical meaning of the pressure term, and further expands this lesson, so as to deepen the students' understanding and establish scientific analysis method. The derivation of Bernoulli equation is the basis. When using Bernoulli equation to explain the demonstration experiment, we must pay attention to the applicable conditions of Bernoulli equation, and comprehensively consider the influence of fluid viscosity, entrainment and other factors. Most textbooks in Chinese or English give different physical interpretations of the pressure term in Bernoulli equation. Based on the derivation of Bernoulli equation, it can be seen that the pressure term in the equation has the property of potential energy, which is true only for fluid. By establishing the relationship between Bernoulli equation and other knowledge points and comparing compressible and incompressible Bernoulli equation, students can acquire a better understanding of Bernoulli equation.