Transcription of Fluid Mechanics - Tufts University
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Fluid Mechanics - Tufts University
Fluid Mechanics . Based on CHEM_ENG 421 at Northwestern University NEWTON'S LAWS | 1. TABLE OF CONTENTS. 1 Newton's Laws .. 3. Inertial Frames .. 3. Newton's Laws .. 3. Galilean Invariance .. 3. 2 Mathematical Description of Fluid Flow .. 4. Fields and Forces .. 4. Continuity Equation .. 4. The Stress Tensor .. 4. Newton's Law of 6. Generalized Gauss' Theorem .. 6. Newton's Equation of Motion for a Fluid .. 7. Navier-Stokes Equation .. 8. Simplifying the Navier-Stokes Equation .. 9. Reduced Pressure ..9. Reynolds Number ..9. Approximate Solutions of the Navier-Stokes Equation ..9. 3 Forces and Torques: Sphere in Stokes Flow .. 11. Problem Setup .. 11. Force Due to Tangential Stress .. 11. Force Due to Viscous Normal Stress .. 13. Force Due to Pressure .. 14. Total Force on the Sphere from the Fluid .. 15. 4 One-Dimensional Flow in Viscous Fluids .. 16. Poiseuille 16. Stokes Flow around a Sphere: Trial Solutions .. 17. Plate Suddenly Set in Motion: Time-Dependent Flow.
Two kinds of forces are typically considered in the study of fluid mechanics. The first is long-range “body forces” such as gravity, usually known per unit mass ( ⃗) or per unit volume (e.g. ⃗). The second is surface “contact forces” due to the short-range action of fluids on fluids (or solids) across an imaginary (or real)
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