The Estimation of Friction Velocity by Hydraulic Parameters Reflecting Turbulent Flow Characteristics in a Smooth Pipe Line

매끄러운 관수로 내 난류흐름특성을 반영한 수리학적 매개변수에 의한 마찰속도의 산정

  • 추태호 (부산대학교 사회환경시스템공학부) ;
  • 손종근 (부산대학교 사회환경시스템공학부) ;
  • 권용빈 (부산대학교 사회환경시스템공학부) ;
  • 안시형 (부산대학교 사회환경시스템공학부) ;
  • 윤관선 (부산대학교 사회환경시스템공학부)
  • Received : 2016.02.04
  • Accepted : 2016.04.01
  • Published : 2016.04.28


Grid(pipe network) design is an important element of Smart Water Grid, which essential to estimate hydraulic parameters such as the pressure, friction factor, friction velocity, head loss and energy slope. Especially, friction velocity in a grid is an important factor in conjunction with energy gradient, friction coefficient, pressure and head loss. However, accurate estimation friction head loss, friction velocity and friction factor are very difficult. The empirical friction factor is still estimated by using theory and equation which were developed one hundred years ago. Therefore, in this paper, new equation from maximum velocity and friction velocity is developed by using integration relationship between Darcy-Weisbach's friction head loss equation and Schlichting equation and regression analysis. To prove the developed equation, smooth pipe data areis used. Proposed equation shows high accuracy compared to observed data. Study results are expected to be used in stability improvements and design in a grid.


Friction Velocity;Friction Factor;Smooth Pipeline;SWG;Turbulent Flow


Supported by : 국토교통부


  1. C. H. Kim, "How to change korean water management system? : Focused on expert's recognition analysis," The Korea Contents Society, Vol. 13, No. 10, pp. 266-277, 2013.
  2. H. Rouse, "Evaluation of boundary roughness," Proceeedings Second Hydraulics Conference, univ. of Iowa Studies in Engrg., Bulletin, No. 27, 1943.
  3. T. M. Walski, "Water supply system rehabilitation," Task Committee on Water Supply Rehabilitation Systems, ASCE, New York, 1987.
  4. D. H. Yoo, "Friction factor for circular pipe with uniform roughness," KSCE Journal of Civil Engineering, Vol. 13, No. 5, pp. 165-172, 1993.
  5. T. H. Choo and S. J. Je, "A study on the maximum velocity and the surface velocity," The Korea Contents Society, Vol. 4, No. 1, pp. 351-355, 2006.
  6. Wang, Yong Ruan, Qi, "A new Explicit Equation for Calculating the Friction Factor for the Turbulent Flow in Pipes," Engineering science, Vol. 8, No. 6, pp. 83-88, 2006.
  7. T. H. Choo and S. K. Lee, "Measurement of discharge using the entropy concept," The Korea Contents Society, Vol. 4, No. 1, pp. 342-346, 2006.
  8. J. W. Kim, A study on the estimation of the mean velocity in closed conduit by using the Chiu's Velocity Equation, M. S. Thesis, Department of Civil Engineering, Pusan University, Busan, Korea, 2009.
  9. C. L. Chiu, "Application of probability and entropy concept in pipe-flow sturdy," Journal of Hydraulic Engineering, Vol. 119, No. 6, p.742, 1993.
  10. D. Joseph and B. H. Yang, "Friction factor correlations for lamina, transition and turbulent flow in smooth pipes," Physica D, Nonlinear phenomena, Vol. 239, No. 14, pp. 1318-1328, 2010.
  11. N. Afzal, A. Seena, and A. Bushra, "Turbulent flow in a machine honed rough pipe for large Reynolds numbers: General roughness scaling laws," Journal of hydro-environment research, Vol. 7, No. 1, pp. 81-90, 2013.
  12. T. H. Choo, H. S. Son, G. S. Yun, H. S. Noh, and H. S. Ko, "The proposal for friction velocity formula at uniform flow channel using the entropy concept," The Korea Contents Society, Vol. 15, No. 2, pp. 499-506, 2015.
  13. B. R. Pearson, P. A. Krogstad, and W. van de Water, "Measurements of the Turbulent Energy Dissipation Rate," Physics of Fluids, Vol. 14, 2002.
  14. W. Szablewski, "Turbulente Drenzs-chichten in Ablosenahe," Z., Angrew. Math., Vol. 49, p.215, 1969.
  15. G. Gust and J. B. Southard, "Effects of weak bed load on the universal law of the wall," Journal of Geophysical Research, Vol. 88, No. C10, pp. 5939-5952, 1983.
  16. I. Nezu and H. Nakagawa, "Turbulence in open-channel flows," Journal of Hydraulic Engineering, Vol. 120, No. 10, pp. 1235-1237, 1994.
  17. A. Gyr and A. Schmid, "Turbulent flows over smooth erodible sand beds in flumes," Journal of Hydraulic Engineering, Vol. 35, No. 4, pp. 525-544, 1997.
  18. L. Prandtl, "The mechanics of viscous fluids, in W.F. Durand (editor-in-chief) : Aerodynamic Theory," Springer-Verlag, Berlin, Vol. 3, div. G, p.142, 1935
  19. H. Schlichting, Boundary-Layer Theory, McGraw-Hill, New York, 1979.
  20. J. Nikuradse, Laws of turbulent flow in smooth pipes, NASA TT F-10, 359, Washington, 1932.
  21. D. H. Yoo, "Pipe friction in transition flow," KSCE Journal of Civil Engineering, Vol. 13, No. 4, pp. 101-109, 1993.