理想流体伯努利方程的协变性初探

A preliminary study on the covariance of the Bernoulli equation for ideal fluids

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DOI 10.12208/j.sdr.20250237
刊名
Scientific Development Research
年,卷(期) 2025, 5(6)
作者
作者单位

山东省济南市长清第一中学 山东济南

摘要
理想流体的伯努利方程是理想流体机械能守恒定律的体现,但是伯努利方程的协变性在力学教学界没有取得共识,也是流体力学中的一朵乌云。相对性原理不是一个物理理论,而是对于物理理论的一个要求,违背相对性原理的理论都是错误的,为此笔者先从矢量力学角度利用动能定理和机械能守恒定律推导了伯努利方程,然后证明了惯性力都是保守力,接着从分析力学角度分析了伯努利方程,最后得出伯努利方程具有伽利略变换的不变性,验证了机械能守恒定律对于所有参照系都协变,满足相对性原理的要求。
Abstract
The Bernoulli's equation for ideal fluids is the embodiment of the law of conservation of mechanical energy for ideal fluids. However, there is no consensus in the mechanics teaching community regarding the covariance of the Bernoulli equation, which also stands as a "dark cloud" in fluid mechanics. The principle of relativity is not a physical theory itself, but a requirement for physical theories—any theory that violates the principle of relativity is erroneous. To address this, the author first derived the Bernoulli equation from the perspective of vector mechanics using the work-energy theorem and the law of conservation of mechanical energy. Subsequently, it was proven that all inertial forces are conservative forces. Then, the Bernoulli equation was analyzed from the standpoint of analytical mechanics. Finally, it was concluded that the Bernoulli equation is invariant under Galilean transformations, verifying that the law of conservation of mechanical energy is covariant across all reference frames and thus meets the requirements of the principle of relativity.
关键词
伯努利方程;伽利略变换的不变性;动能定理;机械能守恒定律;分析力学
KeyWord
Bernoulli equation; Invariance under Galilean transformation; Kinetic energy theorem; Law of conservation of mechanical energy; Analytical mechanics
基金项目
页码 83-92
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李学生. 理想流体伯努利方程的协变性初探 [J]. 科学发展研究. 2025; 5; (6). 83 - 92.

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