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Drag Force Acting on a Body Moving in Viscous Fluid

  • L. P. Yarin
Chapter
Part of the Experimental Fluid Mechanics book series (FLUID, volume 1)

Abstract

Drag force is one of the most important factors that determine dynamics of solid bodies moving in viscous fluids. The knowledge of this force is essential for a number of applications in engineering, in particular, for the evaluation the engine power to ensure a desirable velocity of the airplanes, ships, etc., as well as for analyzing the behavior of solid particles, droplets and bubbles in two-phase flows. Numerous experimental and theoretical investigations dealing with drag of bodies of different shapes moving with low and high velocities in viscous fluid were performed during the last three centuries.

Keywords

Reynolds Number Functional Equation Spherical Particle Drag Force Drag Coefficient 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Anton TR (1987) The lift force on a spherical body in rotation flow. J Fluid Mech 183:199–218CrossRefGoogle Scholar
  2. Batchelor GK (1967) An introduction to fluid dynamics. Cambridge University Press, CambridgezbMATHGoogle Scholar
  3. Basset AB (1961) A treatise on hydrodynamics, vol 2. Dover, New YorkGoogle Scholar
  4. Bearman PW, Dowirie MJ, Graham JMP, Obasaju ED (1985) Forces on cylinders in viscous oscillatory flow at low Kenlegan-Carpenter numbers. J Fluid Mech 154:337–356zbMATHCrossRefGoogle Scholar
  5. Berlemont A, Desjonqueres P, Gouesbet G (1990) Particle Lagrangian simulation in turbulent flow. Int J Multiphas Flow 16:19–34zbMATHCrossRefGoogle Scholar
  6. Boothroyd RG (1971) Following gas-solids suspensions. Chapman and Hall, LondonGoogle Scholar
  7. Boussinesq J (1903) Theorie Analytique de la Chaleur. L’ Ecole Polytechnique, ParisGoogle Scholar
  8. Bridgman PW (1922) Dimensional analysis. Yale University Press, New HavenGoogle Scholar
  9. Chang EJ, Maxey MR (1994) Unsteady flow about a sphere at low to moderate Reynolds number. Part 1. Oscillatory motion. J Fluid Mech 277:347–379zbMATHCrossRefGoogle Scholar
  10. Chang EJ, Maxey MR (1995) Unsteady flow about a sphere at low to moderate Reynolds number. Part 2. Accelerated motion. J Fluid Mech 303:133–153zbMATHCrossRefGoogle Scholar
  11. Clift R, Grace JR, Weber ME (1978) Bubbles, droplets and particles. Academic, New YorkGoogle Scholar
  12. Dandy DS, Dwyer HA (1990) A sphere in shear flows at finite Reynolds number: effect of shear on particle lift, drag and heat transfer. J Fluid Mech 216:821–828CrossRefGoogle Scholar
  13. Derjaguin BM, Levi SM (1964) Film coating theory. The Focal Press, LondonGoogle Scholar
  14. Dwyer HA (1989) Calculation of droplet dynamics in high temperature environments. Prog Energ Combust Sci 15:131–158CrossRefGoogle Scholar
  15. Fendell FE, Sprankle ML, Dodson DS (1966) Thin-flame theory for a fuel drop in slow viscous flow. J Fluid Mech 26:267–280zbMATHCrossRefGoogle Scholar
  16. Graham JMR (1980) The forces on sharp-edged cylinders in oscillatory flow at low Kenlegan-Carpenter numbers. J Fluid Mech 97:331–346CrossRefGoogle Scholar
  17. Hadamard JS (1911) Movement permanent lend d’une sphere liquid et visqueuse dans un liquid visqueux. C.R. ACAD Sci Paris 152:1735–1738zbMATHGoogle Scholar
  18. Happel J, Brenner H (1983) Low Reynolds number hydrodynamics. Martinus Nijhoft, The HagueGoogle Scholar
  19. Huntley HE (1967) Dimensional analysis. Dover Publications, New YorkGoogle Scholar
  20. Karanfilian SK, Kotas TJ (1978) Drag on sphere in steady motion in a liquid at rest. J Fluid Mech 87:85–96CrossRefGoogle Scholar
  21. Kassoy DR, Adamson TC, Messiter AF (1966) Compressible low Reynolds number flow around a sphere. Phys Fluids 9:671–681zbMATHCrossRefGoogle Scholar
  22. Kenlegan GH, Carpenter LH (1958) Forces on cylinders and plates in an oscillating fluid. J Res Nat Bur Standard 60:423–440Google Scholar
  23. Lamb H (1959) Hydrodynamics, 6th edn. Cambridge University Press, CambridgeGoogle Scholar
  24. Landau LD, Lifshitz EM (1987) Fluid mechanics, 2nd edn. Pergamon, New YorkGoogle Scholar
  25. Landau LD, Levich VG (1942) Dragging of a liquid by moving plate. Acta Physicochimica USSR 17:42–54Google Scholar
  26. Levich VG (1962) Physicochemical hydrodynamics. Prentice-Hall, Englewood CliffsGoogle Scholar
  27. Loitsyanskii LG (1967) Laminar Grenzschichten. Academic-Verlag, BerlinGoogle Scholar
  28. Loitsyanskii LG (1966) Mechanics of liquids and gases. Pergamon, OxfordGoogle Scholar
  29. Maxey MR, Riley JJ (1983) Equation of motion for a small rigid sphere in a nonuniform flow. Phys Fluids 26:863–888CrossRefGoogle Scholar
  30. McLaughlin JB (1991) Inertia migration of small sphere in linear shear flows. J Fluid Mech 224:261–274zbMATHCrossRefGoogle Scholar
  31. Mei R, Lawrence CJ, Adrian RJ (1991) Unsteady drag on sphere of finite Reynolds number with small fluctuations of the free stream velocity. J Fluid Mech 223:613–631CrossRefGoogle Scholar
  32. Mei R (1992) An approximate expression for the shear lift force on a spherical particle at the finite Reynolds number. Int J Multiphas Flow 18:145–147zbMATHCrossRefGoogle Scholar
  33. Mei R (1994) Flow due to an oscillating sphere: an expression for unsteady drag on the sphere at finite Reynolds number. J Fluid Mech 270:133–174zbMATHCrossRefGoogle Scholar
  34. Odar F, Hamilton WS (1964) Forces on a sphere accelerating in viscous fluid. J Fluid Mech 18:302–314zbMATHCrossRefGoogle Scholar
  35. Oseen CW (1910) Uber die Stokes’ Formuel, und uber eine verwen die Aufgabe in der Hydrodynamik. Ark Mth Astronom Fus 6(29):1–20Google Scholar
  36. Oseen CW (1927) Hydrodynamik. Akademise Verlagsgesellichaft, LeipzigzbMATHGoogle Scholar
  37. Rybchynski W (1911) Uber die fortschreitendl Bewegung einer flussingen Kugelin einem Zahen Medium. Bull Inst Acad Sci Cracovie ser. A 1:40–46Google Scholar
  38. Saffman PS (1965) The lift on small sphere in a shear flow. J Fluid Mech 22:385–400zbMATHCrossRefGoogle Scholar
  39. Saffman PS (1968) Corrigendum to ‘the lift on a small sphere in a slow shear flow’. J Fluid Mech 31:624–624CrossRefGoogle Scholar
  40. Schlichting H (1979) Boundary layer theory. McGraw-Hill, New YorkzbMATHGoogle Scholar
  41. Sedov LI (1993) Similarity and dimensional methods in mechanics, 10th edn. CRC Press, Boca RatonGoogle Scholar
  42. Shih CC, Buchanan HJ (1971) The drag on oscillating flat plates in liquids at low Reynolds numbers. J Fluid Mech 48:229–239CrossRefGoogle Scholar
  43. Soo SL (1990) Multiphase fluid dynamics. Science Press and Gower Technical, BeijingGoogle Scholar
  44. Stokes GC (1851) On the effect of internal friction of fluids on the motion of pendulums. Trans Cambridge Philos Soc 9:8–106Google Scholar
  45. Yalin MS (1972) Mechanics of sediment transport. Pergamon Press, OxfordGoogle Scholar
  46. Yarin LP, Hetsroni G (2004) Combustion of two-phase reactive media. Springer, BerlinGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • L. P. Yarin
    • 1
  1. 1.Dept. of Mechanical Engineering Technion CityTechnion-Israel Institute of TechnologyHaifaIsrael

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