Extension of Bernoulli's theorem on steady flows of inviscid fluids to steady flows of plastic solids |
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| Institution: | 1. Department of Medicine and Radiology, Division of Cardiology, Loyola University Chicago, Chicago, IL, USA;2. Edward Hines Jr. Veteran''s Affairs Hospital, Hines, IL, USA;3. Cedars-Sinai Medical Center, Department of Imaging, USA;4. VA Long Beach HCS, Department of Cardiology, University of California Irvine, USA;5. Beaumont Health, Department of Cardiology, USA;6. Duke University, Department of Medicine and Radiology, USA;7. Emory University, Department of Cardiology, USA;8. St. Paul''s Hospital & University of British Columbia, Department of Radiology, Canada;9. Sanger Heart and Vascular Institute, Department of Cardiology, USA;10. Aarhus University Hospital, Department of Cardiology, Denmark;11. Minneapolis Heart Institute, USA;12. Cardiologico Monzino, Department of Cardiovascular Imaging, Milan, Italy;13. OLV Ziekenhuis Aalst, Cardiovascular Center Aalst, Belgium;14. Leiden University Medical Center, Department of Cardiology, The Netherlands;1. William Beaumont Hospital, Royal Oaks, MI, USA;2. Wakayama Medical University, Wakayama, Japan;3. Aichi Medical University, Aichi, Japan;4. Leiden University Medical Center, Leiden, The Netherlands;5. Department of Radiology, University of British Columbia, Vancouver, BC, Canada;6. Onze-Lieve-Vrouwziekenhuis Aalst, Aalst, Belgium;7. Shin Koga Hospital, Fukuoka, Japan;8. Gifu Heart Center, Gifu, Japan;9. Iwate Medical University, Iwate, Japan;10. Erasmus Medical Center, Rotterdam, The Netherlands;11. Aarhus University Hospital, Aarhus Skejby, Denmark;12. Duke University School of Medicine, Durham, NC, USA;13. Centro Cardiologico Monzino, IRCCS, University of Milan, Milan, Italy;14. Loyola University Medical Center, Maywood, IL, USA;15. HeartFlow, Redwood City, CA, USA;p. University of Southern Denmark, Odense, Denmark;1. Department of Vascular Surgery, Norfolk and Norwich University Hospital, Norwich, Norfolk, UK;2. Department of Radiology, Norfolk and Norwich University Hospital, Norwich, Norfolk, UK |
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| Abstract: | A differential equation is derived which is valid along any streamline in a steady flow of a general continuum where the streamline is also a trajectory of principal stress. For special materials and flow conditions this equation can be integrated to give algebraic relations between variables along the streamline. For inviscid fluids this leads to Bernoulli's famous theorem relating pressure and velocity along any streamline. For three-dimensional ideal flows of Tresca plastic solids and planar ideal flows of general rigid/perfectly plastic solids, it also leads to known results along any streamline. For other special constitutive materials in rigid/plastic solids additional streamline relations are obtained. |
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