2006, Volume 8, Issue 6
Strategic Study of CAE >> 2006, Volume 8, Issue 6
A New Explicit Equation for Calculating the Friction Factor for the Turbulent Flow in Pipes
Department of Chemical Engineering, Fuzhou University, Fuzhou 350002, China
Next Previous
Abstract
The friction factor for the turbulent flow in pipes is the binary nonlinear function of Reynolds number and relative roughness. Calculating friction factor by implicit Colebrook equation have to use iterative algorithm, which is discommodious.The intelligent fitting method for binary nonlinear polynomials was presented in order to obtain a high precise and simple form explicit equation for calculating the friction factor. The binary nonlinear polynomial was firstly transformed into multivariate linear polynomials, and the least squares standard matrix was established. Then the number, the form, the index and the coefficient of polynomials term were searched to obtain the optimum function by genetic algorithms combined with matrix method. Fitting the data calculated by Colebrook equation with the above method, a new explicit equation for calculating the friction factor for the turbulent flow in pipes was obtained. The new equation can reproduce the Colebrook equation with average deviation of 0.5% and the maximum deviation of 1.8% in the range of Reynolds number being 3 000≤Re≤108 and relative roughness being 0≤e/d≤0.05，and it has an average deviation of 2.3 % to the experimental data. The new equation has the advantages such as simple form, high precise, wide range of application, and can be simplified to the equation for calculating the friction factor in the range of smooth pipe and the rough region easily.
Keywords
turbulent flow ; friction factor ; implicit Colebrook equation ; genetic algorithms ; intelligent fitting method ; explicit equation
Figures
图1
图10
图11
图12
图2
图3
图4
图5
图6
图7
图8
图9
References
[ 1 ] Colebrook C F.Turbulent flow in pipe with particularreference to the transition region between the smooth andrough pipe laws[J].J Inst Civil Engrs, 1938~1939, 11:133~156
[ 2 ] Shacham M.Comments on‘An explicit equation forfriction factor in pipe[J].IEC Fundam, 1980, 19:228~229
[ 3 ] Moody L F.Friction factors for pipe flow[J].TransASME, 1944, 66 (8) :671~684
[ 4 ] Churchill S W.Empirical expressions for the shear stressin turbulent flow in commercial pipe[J].AIChE J, 1973, 19 (2) :375~376
[ 5 ] Altshul A D, Kiselev P G.Hydraulics and Aerodynamics[M].2nd ed.Moscow:Strojizdat, 1975:166~196
[ 6 ] Churchill S W.Friction factor equations spans all fluid-flow regimes[J].Chem Eng, 1977, 84 (24) :91~92
[ 7 ] Chen N H.An explicit equation for friction factor in pipe[J].IEC Foundam, 1979, 18 (3) :296~297
[ 8 ] Round G F.An explicit approximation for the frictionfactor Reynolds number relation for rough and smooth pipe[J].Can J Chem Eng, 1980, 58 (1) :122~123
[ 9 ] Barr D I H.Solutions of the Colebrook-White Function forResistance to Uniform Turbulent Flow[M].Proc Inst CivilEngrs, Part 2, 1981, 71
[10] Zigrang D J, Sylvester N D.Explicit approximations to theColebrook s friction factor[J].AICHE J, 1982, 28 (3) :514~515
[11] Haaland S E.Simple and explicit formulas for the frictionfactor in turbulent pipe flow[J].Trans ASME JFE, 1983, 105:89
[12] Manadili G.Replace implicit equations with signomialfunctions[J].Chem Eng, 1997, 104 (8) :129~132
[13] 李春喜, 黄大铿.圆形直管内湍动流体的摩擦因数计算[J].北京化工大学学报, 2000, 27 (24) :19~21 link1
[14] Romeo E, Royo C, Monzon A.Improved explicitequations for estimation of the friction factor in rough andsmooth pipes[J].Chem Eng J, 2002, 86:369~374
[15] 谭天恩, 麦本熙, 丁惠华.化工原理[M], 上册.第二版.北京:化学工业出版社, 1999 link1
[16] 王勇, 阮奇.多元非线性多项式智能拟合法及其应用研究[J].计算机与应用化学, 2004, 21 (1) :157~162 link1
[17] 角仕云, 刘丽亚.实用科学与工程计算方法[M].北京:科学出版社, 2000:178~204 link1
京公网安备 11010502051620号
