Abstract
To study the relationships between the friction factor f and the flow type in a single rough fracture, the formulae of f for both unconfined and confined flows are deduced based on previous studies. The relationships between f and the Reynolds number (Re) for different relative roughnesses are investigated experimentally. The Moody-type diagram, based on the deduced formula of f, is also plotted and the hydraulic characteristics of the flow in a rough fracture are analyzed. Results show that the Moody-type diagram of the experiment has a similar distribution to that of the conventional Moody diagram. It is found that the value of f in the experiment is much smaller than that of the conventional Moody diagram and turbulent flow appears easier for rough fractures, which can be explained by the separation phenomenon in boundary layers. The critical Re ranging from 650 to 700 in rough fractures is concluded based on the experimental results. It also can be concluded that the friction factor f is related not only with the Re and the relative roughness but also with the absolute roughness.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
BAUGET F., FOURAR M. Non-Fickian dispersion in a single fracture[J]. J. Contam. Hydrol., 2008, 100(3-4): 137–148.
TAN Ye-fei, ZHOU Zhi-fang and HUANG Yong. Solute transport in natural fractures based on digital image technology[J]. Journal of Hydrodynamics, 2009, 21(2): 219–227.
TAN Ye-fei, ZHOU Zhi-fang. Simulation of solute transport in a parallel single fracture with LBM/MMP mixed method[J]. Journal of Hydrodynamics, 2008, 20(3): 365–372.
LI Min, DIAO Nai-ren and FANG Zhao-hong. Analysis of seepage flow in a confined aquifer with a standing column well[J]. Journal of Hydrodynamics, Ser. B, 2007, 19(1): 84–91.
ZHANG Qian-fei, LAN Shou-qi and WANG Yan-ming et al. A new numerical method for groundwater flow and solute using velocity field[J]. Journal of Hydro-dynamics, 2008, 20(3): 356-364
LOUIS C. A. A study of groundwater flow in jointed rock and its influence on the stability of rock masse[D]. Ph. D. Thesis, Karlsruhe, France: University of Karlsruhe, 1968.
JAMES B., TAYLOR A. L. and KANDLIKAR S. G. Characterization of the effect of surface roughness and texture on fluid flow-past, present, and future[J]. Int. J. Thermal. Sci., 2006, 45(10): 962–968.
NIKURADSE J. Laws of flow in rough pipes [M]. Berlin: Vereins Deutscher Ingenieure, 1933, 4: 361(in German).
COLEBROOK C. F. Turbulent flow in pipes, with particular reference to the transition region between the smooth and rough pipe laws[J]. J. Inst. Civ. Eng., 1939, 11(4): 133–156.
MOODY L. F. Friction factors for pipe flow[J]. Trans. ASME, 1944, 66: 671–683.
LOMIZE G. M. Flow in fractured rocks[M]. Moscow: Gosenergoizdat, 1951, 127(in Russian).
KANDLIKAR S. G., SCHMITT D. and CARRANO A. L. et al. Characterization of surface roughness effects on pressure drop in single-phase flow in minichannels[J]. Phys. Fluids., 2005, 17(5): 1006061–100606.11.
NAZRIDOUST K., AHMADI G. and SMITH D. H. A new friction factor correlation for laminar, single-phase flows through rock fractures[J]. J. Hydrol., 2006, 329(1-2): 315–328.
TIAN Kai-ming. The properties of the flow in cross fracture[J]. Geol. Sci., 1986, (2): 202–213(in Chinese).
QIAN Jia-zhong, WANG Jia-quan and LI Ru-zhong et al. Formulae for average velocity of groundwater flow and experimental evidence of non-Darcy’s flow through a single fracture[J]. Journal of Hydrodynamics. Ser. B, 2003, 15(6): 56–62.
QIAN Jia-zhong, LIU Yong and WANG Jian-hua et al. Non-LD and tracer test for groundwater flow in a single fracture[J]. Journal of Hydrodynamics, Ser. B, 2006, 18(1): 104–108.
QIAN J. Z., ZHAN H. B. and ZHAO W. D. et al. Experimental study of turbulent unconfined groundwater flow in a single fracture[J]. J. Hydrol., 2005, 311(1-4): 134–142.
IWAI K. Fundamental studies of fluid flow through a single fracture[D]. Ph. D. Thesis, Berkeley, USA: University of California, 1976.
SUN Feng-gen, LUO Shao-he and WANG Xin-yi et al. The average velocity equations in a single fracture [J]. Hydrogeol Eng. Geol., 1996, (4): 25–27(in Chinese).
MUNSON B. R., YOUNG D. F. and OKIISHI T. H. Fundamentals of fluid mechanics[M]. 3rd Edition, NY: John Wiley and Son, 1998.
Author information
Authors and Affiliations
Corresponding author
Additional information
Project supported by the Program for New Century Excellent Talents in Universities (Grant No. NCET-06-0541) the National Natural Science Foundation of China (Grant Nos. 40672154, 40772153).
Biography: CHEN Zhou (1983-), Male, Ph. D. Candidate
Rights and permissions
About this article
Cite this article
Chen, Z., Qian, Jz., Luo, Sh. et al. Experimental Study of Friction Factor for Groundwater Flow in a Single Rough Fracture. J Hydrodyn 21, 820–825 (2009). https://doi.org/10.1016/S1001-6058(08)60218-8
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1016/S1001-6058(08)60218-8