Author  Santos, Leonardo Sioufi Fagundes dos 
Abstract  This work discusses the energy density distribution in an ideal gas and the consequences of Bernoulli's equation and the corresponding relation for compressible fluids. The aim of this work is to study how Bernoulli's equation determines the energy flow in a fluid, although Bernoulli's equation does not describe the energy density itself. The model from molecular dynamic considerations that describes an ideal gas at rest with uniform density is modified to explore the gas in motion with nonuniform density and gravitational effects. The difference between the component of the speed of a particle that is parallel to the gas speed and the gas speed itself is called 'parallel random speed'. The pressure from the 'parallel random speed' is denominated as parallel pressure. The modified model predicts that the energy density is the sum of kinetic and potential gravitational energy densities plus two terms with static and parallel pressures. The application of Bernoulli's equation and the corresponding relation for compressible fluids in the energy density expression has resulted in two new formulations. For incompressible and compressible gas, the energy density expressions are written as a function of stagnation, static and parallel pressures, without any dependence on kinetic or gravitational potential energy densities. These expressions of the energy density are the main contributions of this work. When the parallel pressure was uniform, the energy density distribution for incompressible approximation and compressible gas did not converge to zero for the limit of null static pressure. This result is rather unusual because the temperature tends to zero for null pressure. When the gas was considered incompressible and the parallel pressure was equal to static pressure, the energy density maintained this unusual behaviour with small pressures. If the parallel pressure was equal to static pressure, the energy density converged to zero for the limit of the null pressure only if the gas was compressible. Only the last situation describes an intuitive behaviour for an ideal gas. 
Keywords 
Bernoulli's equation
Bernoulli's equation for compressible fluid kinetic theory ideal gas energy density pressure temperature 
xmlui.dri2xhtml.METS1.0.itemcoverage  Bristol 
Language  English 
Date  2018 
Published in  European Journal Of Physics. Bristol, v. 39, n. 3, p. , 2018. 
ISSN  01430807 (Sherpa/Romeo, impact factor) 
Publisher  Iop Publishing Ltd 
Extent   
Origin 

Access rights  Closed access 
Type  Article 
Web of Science ID  WOS:000427371800002 
URI  https://repositorio.unifesp.br/handle/11600/55619 
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