Experiments in Fluids

, 59:65 | Cite as

Friction coefficient of an intact free liquid jet moving in air

  • P. M. Comiskey
  • A. L. Yarin
Research Article


Here, we propose a novel method of determining the friction coefficient of intact free liquid jets moving in quiescent air. The middle-size jets of this kind are relevant for such applications as decorative fountains, fiber-forming, fire suppression, agriculture, and forensics. The present method is based on measurements of trajectories created using a straightforward experimental apparatus emulating such jets at a variety of initial inclination angles. Then, the trajectories are described theoretically, accounting for the longitudinal traction imposed on such jets by the surrounding air. The comparison of the experimental data with the theoretical predictions shows that the results can be perfectly superimposed with the friction coefficient \({C_{{\text{fd}}}}=5R{e_d}^{{ - 1/2 \pm 0.05}}\), in the \(621 \leqslant R{e_d} \leqslant 1289\) range, with Red being the Reynolds number based on the local cross-sectional diameter of the jet. The results also show that the farthest distance such jets can reach corresponds to the initial inclination angle \(\alpha =35^\circ\) which is in agreement with already published data.



This work was financially supported by the US National Institute of Justice (NIJ 2017-DN-BX-0171).


  1. Arato EG, Crow DA, Miller DS (1970) Investigations of a high performance water nozzle. The British Hydromechanics Research Association. Tech. Rep. p 1058Google Scholar
  2. Ashgriz N, Yarin AL (2011) Capillary instability of free liquid jets. In: Ashgriz N (ed) Springer handbook of atomization and sprays: theory and applications, Springer, Heidelberg, Chap. 1, pp 3–53CrossRefGoogle Scholar
  3. Basaran OA (1992) Nonlinear oscillations of viscous liquid drops. J Fluid Mech 241:169–198CrossRefzbMATHGoogle Scholar
  4. Bilanski WK, Kidder EH (1958) Factors that affect the distribution of water from a medium- pressure rotary irrigation sprinkler. Transaction of the ASAE 1:19–28CrossRefGoogle Scholar
  5. Clanet C (1998) On large-amplitude pulsating fountains. J Fluid Mech 366:333–350MathSciNetCrossRefzbMATHGoogle Scholar
  6. Clanet C, Lasheras JC (1999) Transition from dripping to jetting. J Fluid Mech 383:307–326MathSciNetCrossRefzbMATHGoogle Scholar
  7. Comiskey PM, Yarin AL, Kim S, Attinger D (2016) Prediction of blood back spatter from a gunshot in bloodstain pattern analysis. Phys Rev Fluids 1:043201CrossRefGoogle Scholar
  8. Comiskey PM, Yarin AL, Attinger D (2017a) Hydrodynamics of back spatter by blunt bullet gunshot with a link to bloodstain pattern analysis. Phys Rev Fluids 2:073906CrossRefGoogle Scholar
  9. Comiskey PM, Yarin AL, Attinger D (2017b) High-speed video analysis of forward and backward spattered blood droplets. Forensic Sci Int 276:134–141CrossRefGoogle Scholar
  10. Comiskey PM, Yarin AL, Attinger D (2018) Theoretical and experimental investigation of forward spatter of blood from a gunshot. Phys Rev Fluids (submitted)Google Scholar
  11. de Borda JC (1766) M ́emoire sur l’ ́ecoulement des fluides par les orifices des vases. M ́em Acad Sci (Paris), 579–607Google Scholar
  12. Federal Bureau of Investigation (2005) Crime in the United States. United States Department of Justice. Accessed 19 Jan 2018
  13. Federal Bureau of Investigation (2014) Crime in the United States. United States Department of Justice. Accessed 19 Jan 2018
  14. Freeman JR (1889) Experiments relating to hydraulics of fire streams. Transac Am Soc Civil Eng XXI: 303–461Google Scholar
  15. Glicksman LR (1968) The cooling of optical fibres. Glass Technol 9:131–138Google Scholar
  16. Hanson D (2004) Bloodstain pattern analysis: recreating the scene of the crime. Law Enforc Technol 31:84, 86–88, 90Google Scholar
  17. Hatton AP, Osborne MJ (1979) The trajectories of large fire fighting jets. Int J Heat Fluid Flow 6:37–41CrossRefGoogle Scholar
  18. Hatton AP, Leech CM, Osborne MJ (1985) Computer simulation of the trajectories of large water jets. Int J Heat Fluid Flow 6:137–141CrossRefGoogle Scholar
  19. James SH, Kish PE, Sutton TP (2005) Principles of bloodstain pattern analysis: theory and practice. CRC Press, Boca RatonCrossRefGoogle Scholar
  20. Kochin NE, Kibel IA, Roze NC (1964) Theoretical hydromechanics. Wiley, NewzbMATHGoogle Scholar
  21. Kolbasov A, Comiskey PM, Sahu RP, Sinha-Ray S, Yarin AL, Sikarwar BS, Kim S, Jubery TZ Attinger D (2016) Blood rheology in shear and uniaxial elongation. Rheol Acta 55:901–908CrossRefGoogle Scholar
  22. Lamb H (1959) Hydrodynamics. Cambridge University Press, CambridgezbMATHGoogle Scholar
  23. Lin SP, Reitz RD (1998) Drop and spray formation from a liquid jet. Annu Rev Fluid Mech 30:85–105MathSciNetCrossRefGoogle Scholar
  24. Lissaman PBS, Shollenberger CA (1970) Formation flight of birds. Science 168:1003–1005CrossRefGoogle Scholar
  25. Murzabaev MT, Yarin AL (1985) Dynamics of sprinkler jets. Fluid Dyn 20:715–722CrossRefGoogle Scholar
  26. Rayleigh Lord FRS (1878) On the instability of jets. Proc Lond Math Soc 10:4–13MathSciNetCrossRefzbMATHGoogle Scholar
  27. Rouse HR, Howe JW, Metzler DE (1951) Experimental investigation of fire monitors and nozzles. Transac Am Soc Civil Eng 77:1147–1175Google Scholar
  28. Rutland DF, Jameson GJ (1971) A non-linear effect in the capillary instability of liquid jets. J Fluid Mech 46:267–271CrossRefGoogle Scholar
  29. Schlichting H (1979) Boundary layer theory. McGraw-Hill, New YorkzbMATHGoogle Scholar
  30. Tafreshi HV, Pourdeyhimi B (2003) The effects of nozzle geometry on waterjet breakup at high Reynolds numbers. Exp Fluids 35:364–371CrossRefGoogle Scholar
  31. Theobald C (1981) The effect of nozzle design on the stability and performance of turbulent water jets. Fire Saf J 4:1–13CrossRefGoogle Scholar
  32. Trettel B, Ezekoye OA (2015) Theoretical range and trajectory of a water jet. In: Proceedings of ASME 2015 international mechanical engineering congress and exposition. Rep. IMECE2015-52103Google Scholar
  33. Tuck EO (1976) The shape of free jets of water under gravity. J Fluid Mech 76:625–640CrossRefzbMATHGoogle Scholar
  34. Wahl TL, Frizell KH, Cohen EA (2008) Computing the trajectory of free jets. J Hydraul Eng 134:256–260CrossRefGoogle Scholar
  35. Wonder AY (2001) Blood dynamics. Academic Press, LondonGoogle Scholar
  36. Yarin AL (1992) Flow-induced on-line crystallization of rodlike molecules in fibre spinning. J Appl Polymer Sci 46:873–878CrossRefGoogle Scholar
  37. Yarin AL (1993) Free liquid jets and films: hydrodynamics and rheology. Longman Scientific & Technical and Wiley, HarlowzbMATHGoogle Scholar
  38. Yarin AL (2011) Bending and buckling instabilities of free liquid jets: experiments and general quasi-one-dimensional model. In: Ashgriz N (ed) Springer handbook of atomization and sprays: theory and applications, Chap. 2. Springer, Heidelberg, pp 55–73Google Scholar
  39. Yarin AL, Pourdeyhimi B, Ramakrishna S (2014) Fundamentals and applications of micro- and nanofibers. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  40. Yarin AL, Roisman IV, Tropea C (2017) Collision phenomena in liquids and solids. Cambridge University Press, CambridgeCrossRefzbMATHGoogle Scholar
  41. Ziabicki A (1976) Fundamentals of fibre formation. Wiley, LondonGoogle Scholar
  42. Ziabicki A, Kawai H (1985) High-speed fiber spinning. Wiley, New YorkGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mechanical and Industrial EngineeringUniversity of Illinois at ChicagoChicagoUSA

Personalised recommendations