On the Navier-Stokes equations for water
In general, the existence of entropy imposes restrictions on the constitutive functions in the Navier-Stokes equations. In this paper, it is shown that if the energy per unit mass is a function of the temperature T only, then the pressure p is an arbitrary function of the density ρ multiplied by the...
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| Format: | Article |
| Language: | English |
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Institute of Fundamental Technological Research Polish Academy of Sciences
2014-03-01
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| Series: | Archives of Acoustics |
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| Online Access: | https://acoustics.ippt.pan.pl/index.php/aa/article/view/672 |
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| author | S. Piekarski |
| author_facet | S. Piekarski |
| author_sort | S. Piekarski |
| collection | DOAJ |
| description | In general, the existence of entropy imposes restrictions on the constitutive functions in the Navier-Stokes equations. In this paper, it is shown that if the energy per unit mass is a function of the temperature T only, then the pressure p is an arbitrary function of the density ρ multiplied by the temperature T.
However, for many fluids with the properties radically different than ideal gases (the best example here is water) the pressure as a function of ρ and T is not of the form p0(ρ)T. Therefore the energy density per unit mass in the Navier-Stokes equations for water should depend also on the mass density and the explicit form of this dependence requires further discussion. |
| format | Article |
| id | doaj-art-92e928149bfb4986b6ec8e8717da0bf6 |
| institution | DOAJ |
| issn | 0137-5075 2300-262X |
| language | English |
| publishDate | 2014-03-01 |
| publisher | Institute of Fundamental Technological Research Polish Academy of Sciences |
| record_format | Article |
| series | Archives of Acoustics |
| spelling | doaj-art-92e928149bfb4986b6ec8e8717da0bf62025-08-20T02:39:19ZengInstitute of Fundamental Technological Research Polish Academy of SciencesArchives of Acoustics0137-50752300-262X2014-03-01312On the Navier-Stokes equations for waterS. Piekarski0Institute of Fundamental Technological Research Polish Academy of SciencesIn general, the existence of entropy imposes restrictions on the constitutive functions in the Navier-Stokes equations. In this paper, it is shown that if the energy per unit mass is a function of the temperature T only, then the pressure p is an arbitrary function of the density ρ multiplied by the temperature T. However, for many fluids with the properties radically different than ideal gases (the best example here is water) the pressure as a function of ρ and T is not of the form p0(ρ)T. Therefore the energy density per unit mass in the Navier-Stokes equations for water should depend also on the mass density and the explicit form of this dependence requires further discussion.https://acoustics.ippt.pan.pl/index.php/aa/article/view/672Gibbs identitythermodynamicsconstitutive functions for water |
| spellingShingle | S. Piekarski On the Navier-Stokes equations for water Archives of Acoustics Gibbs identity thermodynamics constitutive functions for water |
| title | On the Navier-Stokes equations for water |
| title_full | On the Navier-Stokes equations for water |
| title_fullStr | On the Navier-Stokes equations for water |
| title_full_unstemmed | On the Navier-Stokes equations for water |
| title_short | On the Navier-Stokes equations for water |
| title_sort | on the navier stokes equations for water |
| topic | Gibbs identity thermodynamics constitutive functions for water |
| url | https://acoustics.ippt.pan.pl/index.php/aa/article/view/672 |
| work_keys_str_mv | AT spiekarski onthenavierstokesequationsforwater |