Regarding Bernoulli’s equation
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Is there such a thing as a control volume in Bernoulli’s equation? Forgot: loveliness:
The conditions for applying Bernoulli’s equation are: along the streamlines, steady state, ideal fluid, incompressible flow field; these points should be kept in mind when using it. The Bernoulli equation provides the parametric relationship between any two points on a streamline, making it convenient to use. There is no need to select control volumes along the flow lines when using it
Control volume, abbreviated as CV: a study area selected when performing mass and energy balance calculations. It seems that there’s no need to select CV for the Bernoulli equation
The Bai Nuli equation uses two cross-sections
The control volume seems to be the system chosen for the purpose of conservation. The Bernoulli equation represents the principle of conservation and transformation of mechanical energy in flow; it describes the quantitative relationship between the volume of fluid flowing in and out of a system and the flow parameters. Theoretically, it is necessary to select a system, but in calculations this system is represented by two cross-sections, one at the upstream end and one at the downstream end
The Bernoulli equation is essentially a simplified form of the equation of conservation of (vector) momentum; it seems to be mentioned in \"Transport Phenomena\"
This Bernoulli equation is derived based on the Euler method (that is, the control volume method), so there should be a control volume.
The Bernoulli equation is the equation of fluid flow
The Bernoulli equation makes use of a control volume in its derivation, but no need to consider such a control volume when applying it, as its size can be chosen arbitrarily.
Since there is no loss of mechanical energy in the flow of an ideal fluid, according to the law of conservation of mechanical energy, and in the absence of any other external forces or conditions acting on the pipeline, the total mechanical energy of 1 kg of ideal fluid entering and leaving the system under consideration must be equal. For more details, refer to the principles of chemical engineering; it is explained clearly there.