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# -*- coding: utf-8 -*- Copyright (C) 2016, Caleb Bell <Caleb.Andrew.Bell@gmail.com>
Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.'''
except ImportError: # pragma: no cover import difflib fuzzy_match = lambda name, strings: difflib.get_close_matches(name, strings, n=1, cutoff=0)[0]
'friction_laminar', 'transmission_factor', 'material_roughness', 'nearest_material_roughness', 'roughness_Farshad', '_Farshad_roughness', '_roughness', 'HHR_roughness', 'oregon_smooth_data', 'Moody', 'Alshul_1952', 'Wood_1966', 'Churchill_1973', 'Eck_1973', 'Jain_1976', 'Swamee_Jain_1976', 'Churchill_1977', 'Chen_1979', 'Round_1980', 'Shacham_1980', 'Barr_1981', 'Zigrang_Sylvester_1', 'Zigrang_Sylvester_2', 'Haaland', 'Serghides_1', 'Serghides_2', 'Tsal_1989', 'Manadilli_1997', 'Romeo_2002', 'Sonnad_Goudar_2006', 'Rao_Kumar_2007', 'Buzzelli_2008', 'Avci_Karagoz_2009', 'Papaevangelo_2010', 'Brkic_2011_1', 'Brkic_2011_2', 'Fang_2011', 'Blasius', 'von_Karman', 'Prandtl_von_Karman_Nikuradse', 'helical_laminar_fd_White', 'helical_laminar_fd_Mori_Nakayama', 'helical_laminar_fd_Schmidt', 'helical_turbulent_fd_Schmidt', 'helical_turbulent_fd_Mori_Nakayama', 'helical_turbulent_fd_Prasad', 'helical_turbulent_fd_Czop', 'helical_turbulent_fd_Guo', 'helical_turbulent_fd_Ju', 'helical_turbulent_fd_Mandal_Nigam', 'helical_transition_Re_Seth_Stahel', 'helical_transition_Re_Ito', 'helical_transition_Re_Kubair_Kuloor', 'helical_transition_Re_Kutateladze_Borishanskii', 'helical_transition_Re_Schmidt', 'helical_transition_Re_Srinivasan']
157.5, 179.4, 206.4, 228, 270.9, 315.2, 358.9, 402.9, 450.2, 522.5, 583.1, 671.8, 789.8, 891, 1013, 1197, 1300, 1390, 1669, 1994, 2227, 2554, 2868, 2903, 2926, 2955, 2991, 2997, 3047, 3080, 3264, 3980, 4835, 5959, 8162, 10900, 13650, 18990, 29430, 40850, 59220, 84760, 120000, 176000, 237700, 298200, 467800, 587500, 824200, 1050000] 0.4815, 0.4182, 0.3655, 0.3237, 0.2884, 0.2433, 0.2077, 0.1834, 0.1656, 0.1475, 0.1245, 0.1126, 0.09917, 0.08501, 0.07722, 0.06707, 0.0588, 0.05328, 0.04815, 0.04304, 0.03739, 0.03405, 0.03091, 0.02804, 0.03182, 0.03846, 0.03363, 0.04124, 0.035, 0.03875, 0.04285, 0.0426, 0.03995, 0.03797, 0.0361, 0.03364, 0.03088, 0.02903, 0.0267, 0.02386, 0.02086, 0.02, 0.01805, 0.01686, 0.01594, 0.01511, 0.01462, 0.01365, 0.01313, 0.01244, 0.01198] '''Holds a tuple of experimental results from the smooth pipe flow experiments presented in McKEON, B. J., C. J. SWANSON, M. V. ZAGAROLA, R. J. DONNELLY, and A. J. SMITS. "Friction Factors for Smooth Pipe Flow." Journal of Fluid Mechanics 511 (July 1, 2004): 41-44. doi:10.1017/S0022112004009796. '''
r'''Calculates Darcy friction factor for laminar flow, as shown in [1]_ or anywhere else.
.. math:: f_d = \frac{64}{Re}
Parameters ---------- Re : float Reynolds number, [-]
Returns ------- fd : float Darcy friction factor [-]
Notes ----- For round pipes, this valid for Re < 2320.
Results in [2]_ show that this theoretical solution calculates too low of friction factors from Re = 10 and up, with an average deviation of 4%.
Examples -------- >>> friction_laminar(128) 0.5
References ---------- .. [1] Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006. .. [2] McKEON, B. J., C. J. SWANSON, M. V. ZAGAROLA, R. J. DONNELLY, and A. J. SMITS. "Friction Factors for Smooth Pipe Flow." Journal of Fluid Mechanics 511 (July 1, 2004): 41-44. doi:10.1017/S0022112004009796. '''
r'''Calculates Darcy friction factor according to the Blasius formulation, originally presented in [1]_ and described more recently in [2]_.
.. math:: f_d=\frac{0.3164}{Re^{0.25}}
Parameters ---------- Re : float Reynolds number, [-]
Returns ------- fd : float Darcy friction factor [-]
Notes ----- Developed for 3000 < Re < 200000.
Examples -------- >>> Blasius(10000) 0.03164
References ---------- .. [1] Blasius, H."Das Aehnlichkeitsgesetz bei Reibungsvorgängen in Flüssigkeiten." In Mitteilungen über Forschungsarbeiten auf dem Gebiete des Ingenieurwesens, edited by Verein deutscher Ingenieure, 1-41. Berlin, Heidelberg: Springer Berlin Heidelberg, 1913. http://rd.springer.com/chapter/10.1007/978-3-662-02239-9_1. .. [2] Hager, W. H. "Blasius: A Life in Research and Education." In Experiments in Fluids, 566–571, 2003. '''
r'''Calculates Darcy friction factor using an exact solution to the Colebrook equation, derived with a CAS. Relatively slow despite its explicit form.
.. math:: \frac{1}{\sqrt{f}}=-2\log_{10}\left(\frac{\epsilon/D}{3.7} +\frac{2.51}{\text{Re}\sqrt{f}}\right)
Parameters ---------- Re : float Reynolds number, [-] eD : float Relative roughness, [-]
Returns ------- fd : float Darcy friction factor [-]
Notes ----- The solution is as follows:
.. math:: f_d = \frac{\ln(10)^2\cdot {3.7}^2\cdot{2.51}^2} {\left(\log(10)\epsilon/D\cdot\text{Re} - 2\cdot 2.51\cdot 3.7\cdot \text{lambertW}\left[\log(\sqrt{10})\sqrt{ 10^{\left(\frac{\epsilon \text{Re}}{2.51\cdot 3.7D}\right)} \cdot \text{Re}^2/{2.51}^2}\right]\right)}
Some effort to optimize this function has been made. The `lambertw` function from scipy is used, and is defined to solve the specific function:
.. math:: y = x\exp(x)
\text{lambertW}(y) = x
For high relative roughness and reynolds numbers, an OverflowError is raised in solution of this equation.
Examples -------- >>> Colebrook(1E5, 1E-4) 0.018513866077471648
References ---------- .. [1] Colebrook, C F."Turbulent Flow in Pipes, with Particular Reference to the Transition Region Between the Smooth and Rough Pipe Laws." Journal of the ICE 11, no. 4 (February 1, 1939): 133-156. doi:10.1680/ijoti.1939.13150. ''' # 9.287 = 2.51*3.7; 6.3001 = 2.51**2 # 1.15129... = log(sqrt(10)) # log(10) = 2.302585...; 2*2.51*3.7 = 18.574 # 457.28... = log(10)**2*3.7**2*2.51**2 /(2.30258509299404590109361379290930926799774169921875*eD*Re - 18.574*lambert_term)**2)
r'''Calculates Darcy friction factor using a solution accurate to almost machine precision. Recommended very strongly. For details of the algorithm, see [1]_.
Parameters ---------- Re : float Reynolds number, [-] eD : float Relative roughness, [-]
Returns ------- fd : float Darcy friction factor [-]
Notes ----- This is a highly optimized function, 4 times faster than the solution using the LambertW function, and faster than many other approximations which are much less accurate.
The code used here is only slightly modified than that in [1]_, for further performance improvements.
Examples -------- >>> Clamond(1E5, 1E-4) 0.01851386607747165
References ---------- .. [1] Clamond, Didier. "Efficient Resolution of the Colebrook Equation." Industrial & Engineering Chemistry Research 48, no. 7 (April 1, 2009): 3665-71. doi:10.1021/ie801626g. http://math.unice.fr/%7Edidierc/DidPublis/ICR_2009.pdf '''
r'''Calculates Darcy friction factor using the method in Moody (1947) as shown in [1]_ and originally in [2]_.
.. math:: f_f = 1.375\times 10^{-3}\left[1+\left(2\times10^4\frac{\epsilon}{D} + \frac{10^6}{Re}\right)^{1/3}\right]
Parameters ---------- Re : float Reynolds number, [-] eD : float Relative roughness, [-]
Returns ------- fd : float Darcy friction factor [-]
Notes ----- Range is Re >= 4E3 and Re <= 1E8; eD >= 0 < 0.01.
Examples -------- >>> Moody(1E5, 1E-4) 0.01809185666808665
References ---------- .. [1] Winning, H. and T. Coole. "Explicit Friction Factor Accuracy and Computational Efficiency for Turbulent Flow in Pipes." Flow, Turbulence and Combustion 90, no. 1 (January 1, 2013): 1-27. doi:10.1007/s10494-012-9419-7 .. [2] Moody, L.F.: An approximate formula for pipe friction factors. Trans. Am. Soc. Mech. Eng. 69,1005-1006 (1947) '''
r'''Calculates Darcy friction factor using the method in Alshul (1952) as shown in [1]_.
.. math:: f_d = 0.11\left( \frac{68}{Re} + \frac{\epsilon}{D}\right)^{0.25}
Parameters ---------- Re : float Reynolds number, [-] eD : float Relative roughness, [-]
Returns ------- fd : float Darcy friction factor [-]
Notes ----- No range of validity specified for this equation.
Examples -------- >>> Alshul_1952(1E5, 1E-4) 0.018382997825686878
References ---------- .. [1] Winning, H. and T. Coole. "Explicit Friction Factor Accuracy and Computational Efficiency for Turbulent Flow in Pipes." Flow, Turbulence and Combustion 90, no. 1 (January 1, 2013): 1-27. doi:10.1007/s10494-012-9419-7 '''
r'''Calculates Darcy friction factor using the method in Wood (1966) [2]_ as shown in [1]_.
.. math:: f_d = 0.094(\frac{\epsilon}{D})^{0.225} + 0.53(\frac{\epsilon}{D}) + 88(\frac{\epsilon}{D})^{0.4}Re^{-A_1}
A_1 = 1.62(\frac{\epsilon}{D})^{0.134}
Parameters ---------- Re : float Reynolds number, [-] eD : float Relative roughness, [-]
Returns ------- fd : float Darcy friction factor [-]
Notes ----- Range is 4E3 <= Re <= 5E7; 1E-5 <= eD <= 4E-2.
Examples -------- >>> Wood_1966(1E5, 1E-4) 0.021587570560090762
References ---------- .. [1] Winning, H. and T. Coole. "Explicit Friction Factor Accuracy and Computational Efficiency for Turbulent Flow in Pipes." Flow, Turbulence and Combustion 90, no. 1 (January 1, 2013): 1-27. doi:10.1007/s10494-012-9419-7 .. [2] Wood, D.J.: An Explicit Friction Factor Relationship, vol. 60. Civil Engineering American Society of Civil Engineers (1966) '''
r'''Calculates Darcy friction factor using the method in Churchill (1973) [2]_ as shown in [1]_
.. math:: \frac{1}{\sqrt{f_d}} = -2\log\left[\frac{\epsilon}{3.7D} + (\frac{7}{Re})^{0.9}\right]
Parameters ---------- Re : float Reynolds number, [-] eD : float Relative roughness, [-]
Returns ------- fd : float Darcy friction factor [-]
Notes ----- No range of validity specified for this equation.
Examples -------- >>> Churchill_1973(1E5, 1E-4) 0.01846708694482294
References ---------- .. [1] Winning, H. and T. Coole. "Explicit Friction Factor Accuracy and Computational Efficiency for Turbulent Flow in Pipes." Flow, Turbulence and Combustion 90, no. 1 (January 1, 2013): 1-27. doi:10.1007/s10494-012-9419-7 .. [2] Churchill, Stuart W. "Empirical Expressions for the Shear Stress in Turbulent Flow in Commercial Pipe." AIChE Journal 19, no. 2 (March 1, 1973): 375-76. doi:10.1002/aic.690190228. '''
r'''Calculates Darcy friction factor using the method in Eck (1973) [2]_ as shown in [1]_.
.. math:: \frac{1}{\sqrt{f_d}} = -2\log\left[\frac{\epsilon}{3.715D} + \frac{15}{Re}\right]
Parameters ---------- Re : float Reynolds number, [-] eD : float Relative roughness, [-]
Returns ------- fd : float Darcy friction factor [-]
Notes ----- No range of validity specified for this equation.
Examples -------- >>> Eck_1973(1E5, 1E-4) 0.01775666973488564
References ---------- .. [1] Winning, H. and T. Coole. "Explicit Friction Factor Accuracy and Computational Efficiency for Turbulent Flow in Pipes." Flow, Turbulence and Combustion 90, no. 1 (January 1, 2013): 1-27. doi:10.1007/s10494-012-9419-7 .. [2] Eck, B.: Technische Stromungslehre. Springer, New York (1973) '''
r'''Calculates Darcy friction factor using the method in Jain (1976) [2]_ as shown in [1]_.
.. math:: \frac{1}{\sqrt{f_f}} = 2.28 - 4\log\left[ \frac{\epsilon}{D} + \left(\frac{29.843}{Re}\right)^{0.9}\right]
Parameters ---------- Re : float Reynolds number, [-] eD : float Relative roughness, [-]
Returns ------- fd : float Darcy friction factor [-]
Notes ----- Range is 5E3 <= Re <= 1E7; 4E-5 <= eD <= 5E-2.
Examples -------- >>> Jain_1976(1E5, 1E-4) 0.018436560312693327
References ---------- .. [1] Winning, H. and T. Coole. "Explicit Friction Factor Accuracy and Computational Efficiency for Turbulent Flow in Pipes." Flow, Turbulence and Combustion 90, no. 1 (January 1, 2013): 1-27. doi:10.1007/s10494-012-9419-7 .. [2] Jain, Akalank K."Accurate Explicit Equation for Friction Factor." Journal of the Hydraulics Division 102, no. 5 (May 1976): 674-77. '''
r'''Calculates Darcy friction factor using the method in Swamee and Jain (1976) [2]_ as shown in [1]_.
.. math:: \frac{1}{\sqrt{f_f}} = -4\log\left[\left(\frac{6.97}{Re}\right)^{0.9} + (\frac{\epsilon}{3.7D})\right]
Parameters ---------- Re : float Reynolds number, [-] eD : float Relative roughness, [-]
Returns ------- fd : float Darcy friction factor [-]
Notes ----- Range is 5E3 <= Re <= 1E8; 1E-6 <= eD <= 5E-2.
Examples -------- >>> Swamee_Jain_1976(1E5, 1E-4) 0.018452424431901808
References ---------- .. [1] Winning, H. and T. Coole. "Explicit Friction Factor Accuracy and Computational Efficiency for Turbulent Flow in Pipes." Flow, Turbulence and Combustion 90, no. 1 (January 1, 2013): 1-27. doi:10.1007/s10494-012-9419-7 .. [2] Swamee, Prabhata K., and Akalank K. Jain."Explicit Equations for Pipe-Flow Problems." Journal of the Hydraulics Division 102, no. 5 (May 1976): 657-664. '''
r'''Calculates Darcy friction factor using the method in Churchill and (1977) [2]_ as shown in [1]_.
.. math:: f_f = 2\left[(\frac{8}{Re})^{12} + (A_2 + A_3)^{-1.5}\right]^{1/12}
A_2 = \left\{2.457\ln\left[(\frac{7}{Re})^{0.9} + 0.27\frac{\epsilon}{D}\right]\right\}^{16}
A_3 = \left( \frac{37530}{Re}\right)^{16}
Parameters ---------- Re : float Reynolds number, [-] eD : float Relative roughness, [-]
Returns ------- fd : float Darcy friction factor [-]
Notes ----- No range of validity specified for this equation.
Examples -------- >>> Churchill_1977(1E5, 1E-4) 0.018462624566280075
References ---------- .. [1] Winning, H. and T. Coole. "Explicit Friction Factor Accuracy and Computational Efficiency for Turbulent Flow in Pipes." Flow, Turbulence and Combustion 90, no. 1 (January 1, 2013): 1-27. doi:10.1007/s10494-012-9419-7 .. [2] Churchill, S.W.: Friction factor equation spans all fluid flow regimes. Chem. Eng. J. 91, 91-92 (1977) '''
r'''Calculates Darcy friction factor using the method in Chen (1979) [2]_ as shown in [1]_.
.. math:: \frac{1}{\sqrt{f_f}} = -4\log\left[\frac{\epsilon}{3.7065D} -\frac{5.0452}{Re}\log A_4\right]
A_4 = \frac{(\epsilon/D)^{1.1098}}{2.8257} + \left(\frac{7.149}{Re}\right)^{0.8981}
Parameters ---------- Re : float Reynolds number, [-] eD : float Relative roughness, [-]
Returns ------- fd : float Darcy friction factor [-]
Notes ----- Range is 4E3 <= Re <= 4E8; 1E-7 <= eD <= 5E-2.
Examples -------- >>> Chen_1979(1E5, 1E-4) 0.018552817507472126
References ---------- .. [1] Winning, H. and T. Coole. "Explicit Friction Factor Accuracy and Computational Efficiency for Turbulent Flow in Pipes." Flow, Turbulence and Combustion 90, no. 1 (January 1, 2013): 1-27. doi:10.1007/s10494-012-9419-7 .. [2] Chen, Ning Hsing. "An Explicit Equation for Friction Factor in Pipe." Industrial & Engineering Chemistry Fundamentals 18, no. 3 (August 1, 1979): 296-97. doi:10.1021/i160071a019. '''
r'''Calculates Darcy friction factor using the method in Round (1980) [2]_ as shown in [1]_.
.. math:: \frac{1}{\sqrt{f_f}} = -3.6\log\left[\frac{Re}{0.135Re \frac{\epsilon}{D}+6.5}\right]
Parameters ---------- Re : float Reynolds number, [-] eD : float Relative roughness, [-]
Returns ------- fd : float Darcy friction factor [-]
Notes ----- Range is 4E3 <= Re <= 4E8; 0 <= eD <= 5E-2.
Examples -------- >>> Round_1980(1E5, 1E-4) 0.01831475391244354
References ---------- .. [1] Winning, H. and T. Coole. "Explicit Friction Factor Accuracy and Computational Efficiency for Turbulent Flow in Pipes." Flow, Turbulence and Combustion 90, no. 1 (January 1, 2013): 1-27. doi:10.1007/s10494-012-9419-7 .. [2] Round, G. F."An Explicit Approximation for the Friction Factor-Reynolds Number Relation for Rough and Smooth Pipes." The Canadian Journal of Chemical Engineering 58, no. 1 (February 1, 1980): 122-23. doi:10.1002/cjce.5450580119. '''
r'''Calculates Darcy friction factor using the method in Shacham (1980) [2]_ as shown in [1]_.
.. math:: \frac{1}{\sqrt{f_f}} = -4\log\left[\frac{\epsilon}{3.7D} - \frac{5.02}{Re} \log\left(\frac{\epsilon}{3.7D} + \frac{14.5}{Re}\right)\right]
Parameters ---------- Re : float Reynolds number, [-] eD : float Relative roughness, [-]
Returns ------- fd : float Darcy friction factor [-]
Notes ----- Range is 4E3 <= Re <= 4E8
Examples -------- >>> Shacham_1980(1E5, 1E-4) 0.01860641215097828
References ---------- .. [1] Winning, H. and T. Coole. "Explicit Friction Factor Accuracy and Computational Efficiency for Turbulent Flow in Pipes." Flow, Turbulence and Combustion 90, no. 1 (January 1, 2013): 1-27. doi:10.1007/s10494-012-9419-7 .. [2] Shacham, M. "Comments on: 'An Explicit Equation for Friction Factor in Pipe.'" Industrial & Engineering Chemistry Fundamentals 19, no. 2 (May 1, 1980): 228-228. doi:10.1021/i160074a019. '''
r'''Calculates Darcy friction factor using the method in Barr (1981) [2]_ as shown in [1]_.
.. math:: \frac{1}{\sqrt{f_d}} = -2\log\left\{\frac{\epsilon}{3.7D} + \frac{4.518\log(\frac{Re}{7})}{Re\left[1+\frac{Re^{0.52}}{29} \left(\frac{\epsilon}{D}\right)^{0.7}\right]}\right\}
Parameters ---------- Re : float Reynolds number, [-] eD : float Relative roughness, [-]
Returns ------- fd : float Darcy friction factor [-]
Notes ----- No range of validity specified for this equation.
Examples -------- >>> Barr_1981(1E5, 1E-4) 0.01849836032779929
References ---------- .. [1] Winning, H. and T. Coole. "Explicit Friction Factor Accuracy and Computational Efficiency for Turbulent Flow in Pipes." Flow, Turbulence and Combustion 90, no. 1 (January 1, 2013): 1-27. doi:10.1007/s10494-012-9419-7 .. [2] Barr, Dih, and Colebrook White."Technical Note. Solutions Of The Colebrook-White Function For Resistance To Uniform Turbulent Flow." ICE Proceedings 71, no. 2 (January 6, 1981): 529-35. doi:10.1680/iicep.1981.1895. '''
r'''Calculates Darcy friction factor using the method in Zigrang and Sylvester (1982) [2]_ as shown in [1]_.
.. math:: \frac{1}{\sqrt{f_f}} = -4\log\left[\frac{\epsilon}{3.7D} - \frac{5.02}{Re}\log A_5\right]
A_5 = \frac{\epsilon}{3.7D} + \frac{13}{Re}
Parameters ---------- Re : float Reynolds number, [-] eD : float Relative roughness, [-]
Returns ------- fd : float Darcy friction factor [-]
Notes ----- Range is 4E3 <= Re <= 1E8; 4E-5 <= eD <= 5E-2.
Examples -------- >>> Zigrang_Sylvester_1(1E5, 1E-4) 0.018646892425980794
References ---------- .. [1] Winning, H. and T. Coole. "Explicit Friction Factor Accuracy and Computational Efficiency for Turbulent Flow in Pipes." Flow, Turbulence and Combustion 90, no. 1 (January 1, 2013): 1-27. doi:10.1007/s10494-012-9419-7 .. [2] Zigrang, D. J., and N. D. Sylvester."Explicit Approximations to the Solution of Colebrook's Friction Factor Equation." AIChE Journal 28, no. 3 (May 1, 1982): 514-15. doi:10.1002/aic.690280323. '''
r'''Calculates Darcy friction factor using the second method in Zigrang and Sylvester (1982) [2]_ as shown in [1]_.
.. math:: \frac{1}{\sqrt{f_f}} = -4\log\left[\frac{\epsilon}{3.7D} - \frac{5.02}{Re}\log A_6\right]
A_6 = \frac{\epsilon}{3.7D} - \frac{5.02}{Re}\log A_5
A_5 = \frac{\epsilon}{3.7D} + \frac{13}{Re}
Parameters ---------- Re : float Reynolds number, [-] eD : float Relative roughness, [-]
Returns ------- fd : float Darcy friction factor [-]
Notes ----- Range is 4E3 <= Re <= 1E8; 4E-5 <= eD <= 5E-2
Examples -------- >>> Zigrang_Sylvester_2(1E5, 1E-4) 0.01850021312358548
References ---------- .. [1] Winning, H. and T. Coole. "Explicit Friction Factor Accuracy and Computational Efficiency for Turbulent Flow in Pipes." Flow, Turbulence and Combustion 90, no. 1 (January 1, 2013): 1-27. doi:10.1007/s10494-012-9419-7 .. [2] Zigrang, D. J., and N. D. Sylvester."Explicit Approximations to the Solution of Colebrook's Friction Factor Equation." AIChE Journal 28, no. 3 (May 1, 1982): 514-15. doi:10.1002/aic.690280323. '''
r'''Calculates Darcy friction factor using the method in Haaland (1983) [2]_ as shown in [1]_.
.. math:: f_f = \left(-1.8\log_{10}\left[\left(\frac{\epsilon/D}{3.7} \right)^{1.11} + \frac{6.9}{Re}\right]\right)^{-2}
Parameters ---------- Re : float Reynolds number, [-] eD : float Relative roughness, [-]
Returns ------- fd : float Darcy friction factor [-]
Notes ----- Range is 4E3 <= Re <= 1E8; 1E-6 <= eD <= 5E-2
Examples -------- >>> Haaland(1E5, 1E-4) 0.018265053014793857
References ---------- .. [1] Winning, H. and T. Coole. "Explicit Friction Factor Accuracy and Computational Efficiency for Turbulent Flow in Pipes." Flow, Turbulence and Combustion 90, no. 1 (January 1, 2013): 1-27. doi:10.1007/s10494-012-9419-7 .. [2] Haaland, S. E."Simple and Explicit Formulas for the Friction Factor in Turbulent Pipe Flow." Journal of Fluids Engineering 105, no. 1 (March 1, 1983): 89-90. doi:10.1115/1.3240948. '''
r'''Calculates Darcy friction factor using the method in Serghides (1984) [2]_ as shown in [1]_.
.. math:: f=\left[A-\frac{(B-A)^2}{C-2B+A}\right]^{-2}
A=-2\log_{10}\left[\frac{\epsilon/D}{3.7}+\frac{12}{Re}\right]
B=-2\log_{10}\left[\frac{\epsilon/D}{3.7}+\frac{2.51A}{Re}\right]
C=-2\log_{10}\left[\frac{\epsilon/D}{3.7}+\frac{2.51B}{Re}\right]
Parameters ---------- Re : float Reynolds number, [-] eD : float Relative roughness, [-]
Returns ------- fd : float Darcy friction factor [-]
Notes ----- No range of validity specified for this equation.
Examples -------- >>> Serghides_1(1E5, 1E-4) 0.01851358983180063
References ---------- .. [1] Winning, H. and T. Coole. "Explicit Friction Factor Accuracy and Computational Efficiency for Turbulent Flow in Pipes." Flow, Turbulence and Combustion 90, no. 1 (January 1, 2013): 1-27. doi:10.1007/s10494-012-9419-7 .. [2] Serghides T.K (1984)."Estimate friction factor accurately" Chemical Engineering, Vol. 91(5), pp. 63-64. '''
r'''Calculates Darcy friction factor using the method in Serghides (1984) [2]_ as shown in [1]_.
.. math:: f_d = \left[ 4.781 - \frac{(A - 4.781)^2} {B-2A+4.781}\right]^{-2}
A=-2\log_{10}\left[\frac{\epsilon/D}{3.7}+\frac{12}{Re}\right]
B=-2\log_{10}\left[\frac{\epsilon/D}{3.7}+\frac{2.51A}{Re}\right]
Parameters ---------- Re : float Reynolds number, [-] eD : float Relative roughness, [-]
Returns ------- fd : float Darcy friction factor [-]
Notes ----- No range of validity specified for this equation.
Examples -------- >>> Serghides_2(1E5, 1E-4) 0.018486377560664482
References ---------- .. [1] Winning, H. and T. Coole. "Explicit Friction Factor Accuracy and Computational Efficiency for Turbulent Flow in Pipes." Flow, Turbulence and Combustion 90, no. 1 (January 1, 2013): 1-27. doi:10.1007/s10494-012-9419-7 .. [2] Serghides T.K (1984)."Estimate friction factor accurately" Chemical Engineering, Vol. 91(5), pp. 63-64. '''
r'''Calculates Darcy friction factor using the method in Tsal (1989) [2]_ as shown in [1]_.
.. math:: A = 0.11(\frac{68}{Re} + \frac{\epsilon}{D})^{0.25}
if A >= 0.018 then fd = A
if A < 0.018 then fd = 0.0028 + 0.85 A
Parameters ---------- Re : float Reynolds number, [-] eD : float Relative roughness, [-]
Returns ------- fd : float Darcy friction factor [-]
Notes ----- Range is 4E3 <= Re <= 1E8; 0 <= eD <= 5E-2
Examples -------- >>> Tsal_1989(1E5, 1E-4) 0.018382997825686878
References ---------- .. [1] Winning, H. and T. Coole. "Explicit Friction Factor Accuracy and Computational Efficiency for Turbulent Flow in Pipes." Flow, Turbulence and Combustion 90, no. 1 (January 1, 2013): 1-27. doi:10.1007/s10494-012-9419-7 .. [2] Tsal, R.J.: Altshul-Tsal friction factor equation. Heat-Piping-Air Cond. 8, 30-45 (1989) ''' else:
r'''Calculates Darcy friction factor using the method in Manadilli (1997) [2]_ as shown in [1]_.
.. math:: \frac{1}{\sqrt{f_d}} = -2\log\left[\frac{\epsilon}{3.7D} + \frac{95}{Re^{0.983}} - \frac{96.82}{Re}\right]
Parameters ---------- Re : float Reynolds number, [-] eD : float Relative roughness, [-]
Returns ------- fd : float Darcy friction factor [-]
Notes ----- Range is 5.245E3 <= Re <= 1E8; 0 <= eD <= 5E-2
Examples -------- >>> Manadilli_1997(1E5, 1E-4) 0.01856964649724108
References ---------- .. [1] Winning, H. and T. Coole. "Explicit Friction Factor Accuracy and Computational Efficiency for Turbulent Flow in Pipes." Flow, Turbulence and Combustion 90, no. 1 (January 1, 2013): 1-27. doi:10.1007/s10494-012-9419-7 .. [2] Manadilli, G.: Replace implicit equations with signomial functions. Chem. Eng. 104, 129 (1997) '''
r'''Calculates Darcy friction factor using the method in Romeo (2002) [2]_ as shown in [1]_.
.. math:: \frac{1}{\sqrt{f_d}} = -2\log\left\{\frac{\epsilon}{3.7065D}\times \frac{5.0272}{Re}\times\log\left[\frac{\epsilon}{3.827D} - \frac{4.567}{Re}\times\log\left(\frac{\epsilon}{7.7918D}^{0.9924} + \left(\frac{5.3326}{208.815+Re}\right)^{0.9345}\right)\right]\right\}
Parameters ---------- Re : float Reynolds number, [-] eD : float Relative roughness, [-]
Returns ------- fd : float Darcy friction factor [-]
Notes ----- Range is 3E3 <= Re <= 1.5E8; 0 <= eD <= 5E-2
Examples -------- >>> Romeo_2002(1E5, 1E-4) 0.018530291219676177
References ---------- .. [1] Winning, H. and T. Coole. "Explicit Friction Factor Accuracy and Computational Efficiency for Turbulent Flow in Pipes." Flow, Turbulence and Combustion 90, no. 1 (January 1, 2013): 1-27. doi:10.1007/s10494-012-9419-7 .. [2] Romeo, Eva, Carlos Royo, and Antonio Monzon."Improved Explicit Equations for Estimation of the Friction Factor in Rough and Smooth Pipes." Chemical Engineering Journal 86, no. 3 (April 28, 2002): 369-74. doi:10.1016/S1385-8947(01)00254-6. '''
r'''Calculates Darcy friction factor using the method in Sonnad and Goudar (2006) [2]_ as shown in [1]_.
.. math:: \frac{1}{\sqrt{f_d}} = 0.8686\ln\left(\frac{0.4587Re}{S^{S/(S+1)}}\right)
S = 0.1240\times\frac{\epsilon}{D}\times Re + \ln(0.4587Re)
Parameters ---------- Re : float Reynolds number, [-] eD : float Relative roughness, [-]
Returns ------- fd : float Darcy friction factor [-]
Notes ----- Range is 4E3 <= Re <= 1E8; 1E-6 <= eD <= 5E-2
Examples -------- >>> Sonnad_Goudar_2006(1E5, 1E-4) 0.0185971269898162
References ---------- .. [1] Winning, H. and T. Coole. "Explicit Friction Factor Accuracy and Computational Efficiency for Turbulent Flow in Pipes." Flow, Turbulence and Combustion 90, no. 1 (January 1, 2013): 1-27. doi:10.1007/s10494-012-9419-7 .. [2] Travis, Quentin B., and Larry W. Mays."Relationship between Hazen-William and Colebrook-White Roughness Values." Journal of Hydraulic Engineering 133, no. 11 (November 2007): 1270-73. doi:10.1061/(ASCE)0733-9429(2007)133:11(1270). '''
r'''Calculates Darcy friction factor using the method in Rao and Kumar (2007) [2]_ as shown in [1]_.
.. math:: \frac{1}{\sqrt{f_d}} = 2\log\left(\frac{(2\frac{\epsilon}{D})^{-1}} {\left(\frac{0.444 + 0.135Re}{Re}\right)\beta}\right)
\beta = 1 - 0.55\exp(-0.33\ln\left[\frac{Re}{6.5}\right]^2)
Parameters ---------- Re : float Reynolds number, [-] eD : float Relative roughness, [-]
Returns ------- fd : float Darcy friction factor [-]
Notes ----- No range of validity specified for this equation. This equation is fit to original experimental friction factor data. Accordingly, this equation should not be used unless appropriate consideration is given.
Examples -------- >>> Rao_Kumar_2007(1E5, 1E-4) 0.01197759334600925
References ---------- .. [1] Winning, H. and T. Coole. "Explicit Friction Factor Accuracy and Computational Efficiency for Turbulent Flow in Pipes." Flow, Turbulence and Combustion 90, no. 1 (January 1, 2013): 1-27. doi:10.1007/s10494-012-9419-7 .. [2] Rao, A.R., Kumar, B.: Friction factor for turbulent pipe flow. Division of Mechanical Sciences, Civil Engineering Indian Institute of Science Bangalore, India ID Code 9587 (2007) '''
r'''Calculates Darcy friction factor using the method in Buzzelli (2008) [2]_ as shown in [1]_.
.. math:: \frac{1}{\sqrt{f_d}} = B_1 - \left[\frac{B_1 +2\log(\frac{B_2}{Re})} {1 + \frac{2.18}{B_2}}\right]
B_1 = \frac{0.774\ln(Re)-1.41}{1+1.32\sqrt{\frac{\epsilon}{D}}}
B_2 = \frac{\epsilon}{3.7D}Re+2.51\times B_1
Parameters ---------- Re : float Reynolds number, [-] eD : float Relative roughness, [-]
Returns ------- fd : float Darcy friction factor [-]
Notes ----- No range of validity specified for this equation.
Examples -------- >>> Buzzelli_2008(1E5, 1E-4) 0.018513948401365277
References ---------- .. [1] Winning, H. and T. Coole. "Explicit Friction Factor Accuracy and Computational Efficiency for Turbulent Flow in Pipes." Flow, Turbulence and Combustion 90, no. 1 (January 1, 2013): 1-27. doi:10.1007/s10494-012-9419-7 .. [2] Buzzelli, D.: Calculating friction in one step. Mach. Des. 80, 54-55 (2008) '''
r'''Calculates Darcy friction factor using the method in Avci and Karagoz (2009) [2]_ as shown in [1]_.
.. math:: f_D = \frac{6.4} {\left\{\ln(Re) - \ln\left[ 1 + 0.01Re\frac{\epsilon}{D}\left(1 + 10(\frac{\epsilon}{D})^{0.5} \right)\right]\right\}^{2.4}}
Parameters ---------- Re : float Reynolds number, [-] eD : float Relative roughness, [-]
Returns ------- fd : float Darcy friction factor [-]
Notes ----- No range of validity specified for this equation.
Examples -------- >>> Avci_Karagoz_2009(1E5, 1E-4) 0.01857058061066499
References ---------- .. [1] Winning, H. and T. Coole. "Explicit Friction Factor Accuracy and Computational Efficiency for Turbulent Flow in Pipes." Flow, Turbulence and Combustion 90, no. 1 (January 1, 2013): 1-27. doi:10.1007/s10494-012-9419-7 .. [2] Avci, Atakan, and Irfan Karagoz."A Novel Explicit Equation for Friction Factor in Smooth and Rough Pipes." Journal of Fluids Engineering 131, no. 6 (2009): 061203. doi:10.1115/1.3129132. '''
r'''Calculates Darcy friction factor using the method in Papaevangelo (2010) [2]_ as shown in [1]_.
.. math:: f_D = \frac{0.2479 - 0.0000947(7-\log Re)^4}{\left[\log\left (\frac{\epsilon}{3.615D} + \frac{7.366}{Re^{0.9142}}\right)\right]^2}
Parameters ---------- Re : float Reynolds number, [-] eD : float Relative roughness, [-]
Returns ------- fd : float Darcy friction factor [-]
Notes ----- Range is 1E4 <= Re <= 1E7; 1E-5 <= eD <= 1E-3
Examples -------- >>> Papaevangelo_2010(1E5, 1E-4) 0.015685600818488177
References ---------- .. [1] Winning, H. and T. Coole. "Explicit Friction Factor Accuracy and Computational Efficiency for Turbulent Flow in Pipes." Flow, Turbulence and Combustion 90, no. 1 (January 1, 2013): 1-27. doi:10.1007/s10494-012-9419-7 .. [2] Papaevangelou, G., Evangelides, C., Tzimopoulos, C.: A New Explicit Relation for the Friction Factor Coefficient in the Darcy-Weisbach Equation, pp. 166-172. Protection and Restoration of the Environment Corfu, Greece: University of Ioannina Greece and Stevens Institute of Technology New Jersey (2010) '''
r'''Calculates Darcy friction factor using the method in Brkic (2011) [2]_ as shown in [1]_.
.. math:: f_d = [-2\log(10^{-0.4343\beta} + \frac{\epsilon}{3.71D})]^{-2}
\beta = \ln \frac{Re}{1.816\ln\left(\frac{1.1Re}{\ln(1+1.1Re)}\right)}
Parameters ---------- Re : float Reynolds number, [-] eD : float Relative roughness, [-]
Returns ------- fd : float Darcy friction factor [-]
Notes ----- No range of validity specified for this equation.
Examples -------- >>> Brkic_2011_1(1E5, 1E-4) 0.01812455874141297
References ---------- .. [1] Winning, H. and T. Coole. "Explicit Friction Factor Accuracy and Computational Efficiency for Turbulent Flow in Pipes." Flow, Turbulence and Combustion 90, no. 1 (January 1, 2013): 1-27. doi:10.1007/s10494-012-9419-7 .. [2] Brkic, Dejan."Review of Explicit Approximations to the Colebrook Relation for Flow Friction." Journal of Petroleum Science and Engineering 77, no. 1 (April 2011): 34-48. doi:10.1016/j.petrol.2011.02.006. '''
r'''Calculates Darcy friction factor using the method in Brkic (2011) [2]_ as shown in [1]_.
.. math:: f_d = [-2\log(\frac{2.18\beta}{Re}+ \frac{\epsilon}{3.71D})]^{-2}
\beta = \ln \frac{Re}{1.816\ln\left(\frac{1.1Re}{\ln(1+1.1Re)}\right)}
Parameters ---------- Re : float Reynolds number, [-] eD : float Relative roughness, [-]
Returns ------- fd : float Darcy friction factor [-]
Notes ----- No range of validity specified for this equation.
Examples -------- >>> Brkic_2011_2(1E5, 1E-4) 0.018619745410688716
References ---------- .. [1] Winning, H. and T. Coole. "Explicit Friction Factor Accuracy and Computational Efficiency for Turbulent Flow in Pipes." Flow, Turbulence and Combustion 90, no. 1 (January 1, 2013): 1-27. doi:10.1007/s10494-012-9419-7 .. [2] Brkic, Dejan."Review of Explicit Approximations to the Colebrook Relation for Flow Friction." Journal of Petroleum Science and Engineering 77, no. 1 (April 2011): 34-48. doi:10.1016/j.petrol.2011.02.006. '''
r'''Calculates Darcy friction factor using the method in Fang (2011) [2]_ as shown in [1]_.
.. math:: f_D = 1.613\left\{\ln\left[0.234\frac{\epsilon}{D}^{1.1007} - \frac{60.525}{Re^{1.1105}} + \frac{56.291}{Re^{1.0712}}\right]\right\}^{-2}
Parameters ---------- Re : float Reynolds number, [-] eD : float Relative roughness, [-]
Returns ------- fd : float Darcy friction factor [-]
Notes ----- Range is 3E3 <= Re <= 1E8; 0 <= eD <= 5E-2
Examples -------- >>> Fang_2011(1E5, 1E-4) 0.018481390682985432
References ---------- .. [1] Winning, H. and T. Coole. "Explicit Friction Factor Accuracy and Computational Efficiency for Turbulent Flow in Pipes." Flow, Turbulence and Combustion 90, no. 1 (January 1, 2013): 1-27. doi:10.1007/s10494-012-9419-7 .. [2] Fang, Xiande, Yu Xu, and Zhanru Zhou."New Correlations of Single-Phase Friction Factor for Turbulent Pipe Flow and Evaluation of Existing Single-Phase Friction Factor Correlations." Nuclear Engineering and Design, The International Conference on Structural Mechanics in Reactor Technology (SMiRT19) Special Section, 241, no. 3 (March 2011): 897-902. doi:10.1016/j.nucengdes.2010.12.019. '''
r'''Calculates Darcy friction factor for rough pipes at infinite Reynolds number from the von Karman equation (as given in [1]_ and [2]_:
.. math:: \frac{1}{\sqrt{f_d}} = -2 \log_{10} \left(\frac{\epsilon/D}{3.7}\right)
Parameters ---------- eD : float Relative roughness, [-]
Returns ------- fd : float Darcy friction factor [-]
Notes ----- This case does not actually occur; Reynolds number is always finite. It is normally applied as a "limiting" value when a pipe's roughness is so high it has a friction factor curve effectively independent of Reynods number.
Examples -------- >>> von_Karman(1E-4) 0.01197365149564789
References ---------- .. [1] Rennels, Donald C., and Hobart M. Hudson. Pipe Flow: A Practical and Comprehensive Guide. 1st edition. Hoboken, N.J: Wiley, 2012. .. [2] McGovern, Jim. "Technical Note: Friction Factor Diagrams for Pipe Flow." Paper, October 3, 2011. http://arrow.dit.ie/engschmecart/28. '''
r'''Calculates Darcy friction factor for smooth pipes as a function of Reynolds number from the Prandtl-von Karman Nikuradse equation as given in [1]_ and [2]_:
.. math:: \frac{1}{\sqrt{f}} = -2\log_{10}\left(\frac{2.51}{Re\sqrt{f}}\right)
Parameters ---------- Re : float Reynolds number, [-]
Returns ------- fd : float Darcy friction factor [-]
Notes ----- This equation is often stated as follows; the correct constant is not 0.8, but 2log10(2.51) or approximately 0.7993474:
.. math:: \frac{1}{\sqrt{f}}\approx 2\log_{10}(\text{Re}\sqrt{f})-0.8
This function is calculable for all Reynolds numbers between 1E151 and 1E-151. It is solved with the LambertW function from SciPy. The solution is:
.. math:: f_d = \frac{\frac{1}{4}\log_{10}^2}{\left(\text{lambertW}\left(\frac{ \log(10)Re}{2(2.51)}\right)\right)^2}
Examples -------- >>> Prandtl_von_Karman_Nikuradse(1E7) 0.0081026694308749137
References ---------- .. [1] Rennels, Donald C., and Hobart M. Hudson. Pipe Flow: A Practical and Comprehensive Guide. 1st edition. Hoboken, N.J: Wiley, 2012. .. [2] McGovern, Jim. "Technical Note: Friction Factor Diagrams for Pipe Flow." Paper, October 3, 2011. http://arrow.dit.ie/engschmecart/28. ''' # Good 1E150 to 1E-150
### Main functions
r'''Calculates friction factor. Uses a specified method, or automatically picks one from the dictionary of available methods. 29 approximations are available as well as the direct solution, described in the table below. The default is to use the exact solution. Can also be accesed under the name `fd`.
For Re < 2320, the laminar solution is always returned, regardless of selected method.
Examples -------- >>> friction_factor(Re=1E5, eD=1E-4) 0.01851386607747165
Parameters ---------- Re : float Reynolds number, [-] eD : float, optional Relative roughness of the wall, []
Returns ------- f : float Friction factor, [-] methods : list, only returned if AvailableMethods == True List of methods which claim to be valid for the range of `Re` and `eD` given
Other Parameters ---------------- Method : string, optional A string of the function name to use Darcy : bool, optional If False, will return fanning friction factor, 1/4 of the Darcy value AvailableMethods : bool, optional If True, function will consider which methods claim to be valid for the range of `Re` and `eD` given
See Also -------- Colebrook Clamond
Notes ----- +-------------------+------+------+----------+----------------------+----------------------+--------------------------+ |Nice name |Re min|Re max|Re Default|:math:`\epsilon/D` Min|:math:`\epsilon/D` Max|:math:`\epsilon/D` Default| +===================+======+======+==========+======================+======================+==========================+ |Clamond |0 |None |None |0 |None |None | +-------------------+------+------+----------+----------------------+----------------------+--------------------------+ |Rao Kumar 2007 |None |None |None |None |None |None | +-------------------+------+------+----------+----------------------+----------------------+--------------------------+ |Eck 1973 |None |None |None |None |None |None | +-------------------+------+------+----------+----------------------+----------------------+--------------------------+ |Jain 1976 |5000 |1.0E+7|None |4.0E-5 |0.05 |None | +-------------------+------+------+----------+----------------------+----------------------+--------------------------+ |Avci Karagoz 2009 |None |None |None |None |None |None | +-------------------+------+------+----------+----------------------+----------------------+--------------------------+ |Swamee Jain 1976 |5000 |1.0E+8|None |1.0E-6 |0.05 |None | +-------------------+------+------+----------+----------------------+----------------------+--------------------------+ |Churchill 1977 |None |None |None |None |None |None | +-------------------+------+------+----------+----------------------+----------------------+--------------------------+ |Brkic 2011 1 |None |None |None |None |None |None | +-------------------+------+------+----------+----------------------+----------------------+--------------------------+ |Chen 1979 |4000 |4.0E+8|None |1.0E-7 |0.05 |None | +-------------------+------+------+----------+----------------------+----------------------+--------------------------+ |Round 1980 |4000 |4.0E+8|None |0 |0.05 |None | +-------------------+------+------+----------+----------------------+----------------------+--------------------------+ |Papaevangelo 2010 |10000 |1.0E+7|None |1.0E-5 |0.001 |None | +-------------------+------+------+----------+----------------------+----------------------+--------------------------+ |Fang 2011 |3000 |1.0E+8|None |0 |0.05 |None | +-------------------+------+------+----------+----------------------+----------------------+--------------------------+ |Shacham 1980 |4000 |4.0E+8|None |None |None |None | +-------------------+------+------+----------+----------------------+----------------------+--------------------------+ |Barr 1981 |None |None |None |None |None |None | +-------------------+------+------+----------+----------------------+----------------------+--------------------------+ |Churchill 1973 |None |None |None |None |None |None | +-------------------+------+------+----------+----------------------+----------------------+--------------------------+ |Moody |4000 |1.0E+8|None |0 |1 |None | +-------------------+------+------+----------+----------------------+----------------------+--------------------------+ |Zigrang Sylvester 1|4000 |1.0E+8|None |4.0E-5 |0.05 |None | +-------------------+------+------+----------+----------------------+----------------------+--------------------------+ |Zigrang Sylvester 2|4000 |1.0E+8|None |4.0E-5 |0.05 |None | +-------------------+------+------+----------+----------------------+----------------------+--------------------------+ |Buzzelli 2008 |None |None |None |None |None |None | +-------------------+------+------+----------+----------------------+----------------------+--------------------------+ |Haaland |4000 |1.0E+8|None |1.0E-6 |0.05 |None | +-------------------+------+------+----------+----------------------+----------------------+--------------------------+ |Serghides 1 |None |None |None |None |None |None | +-------------------+------+------+----------+----------------------+----------------------+--------------------------+ |Serghides 2 |None |None |None |None |None |None | +-------------------+------+------+----------+----------------------+----------------------+--------------------------+ |Tsal 1989 |4000 |1.0E+8|None |0 |0.05 |None | +-------------------+------+------+----------+----------------------+----------------------+--------------------------+ |Alshul 1952 |None |None |None |None |None |None | +-------------------+------+------+----------+----------------------+----------------------+--------------------------+ |Wood 1966 |4000 |5.0E+7|None |1.0E-5 |0.04 |None | +-------------------+------+------+----------+----------------------+----------------------+--------------------------+ |Manadilli 1997 |5245 |1.0E+8|None |0 |0.05 |None | +-------------------+------+------+----------+----------------------+----------------------+--------------------------+ |Brkic 2011 2 |None |None |None |None |None |None | +-------------------+------+------+----------+----------------------+----------------------+--------------------------+ |Romeo 2002 |3000 |1.5E+8|None |0 |0.05 |None | +-------------------+------+------+----------+----------------------+----------------------+--------------------------+ |Sonnad Goudar 2006 |4000 |1.0E+8|None |1.0E-6 |0.05 |None | +-------------------+------+------+----------+----------------------+----------------------+--------------------------+ ''' (not fmethods[i]['Arguments']['eD']['Min'] or fmethods[i]['Arguments']['eD']['Min'] <= eD) and (not fmethods[i]['Arguments']['eD']['Max'] or eD <= fmethods[i]['Arguments']['eD']['Max']) and (not fmethods[i]['Arguments']['Re']['Min'] or Re > fmethods[i]['Arguments']['Re']['Min']) and (not fmethods[i]['Arguments']['Re']['Max'] or Re <= fmethods[i]['Arguments']['Re']['Max'])] else:
r'''Calculates Darcy friction factor for a fluid flowing inside a curved pipe such as a helical coil under laminar conditions, using the method of White [1]_ as shown in [2]_.
.. math:: f_{curved} = f_{\text{straight,laminar}} \left[1 - \left(1-\left( \frac{11.6}{De}\right)^{0.45}\right)^{\frac{1}{0.45}}\right]^{-1}
Parameters ---------- Re : float Reynolds number with `D=Di`, [-] Di : float Inner diameter of the coil, [m] Dc : float Diameter of the helix/coil measured from the center of the tube on one side to the center of the tube on the other side, [m]
Returns ------- fd : float Darcy friction factor for a curved pipe [-]
Notes ----- The range of validity of this equation is :math:`11.6< De < 2000`, :math:`3.878\times 10^{-4}<D_i/D_c < 0.066`.
The form of the equation means it yields nonsense results for De < 11.6; at De < 11.6, the equation is modified to return the straight pipe value.
Examples -------- >>> helical_laminar_fd_White(250, .02, .1) 0.4063281817830202
References ---------- .. [1] White, C. M. "Streamline Flow through Curved Pipes." Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 123, no. 792 (April 6, 1929): 645-63. doi:10.1098/rspa.1929.0089. .. [2] El-Genk, Mohamed S., and Timothy M. Schriener. "A Review and Correlations for Convection Heat Transfer and Pressure Losses in Toroidal and Helically Coiled Tubes." Heat Transfer Engineering 0, no. 0 (June 7, 2016): 1-28. doi:10.1080/01457632.2016.1194693. '''
r'''Calculates Darcy friction factor for a fluid flowing inside a curved pipe such as a helical coil under laminar conditions, using the method of Mori and Nakayama [1]_ as shown in [2]_ and [3]_.
.. math:: f_{curved} = f_{\text{straight,laminar}} \left(\frac{0.108\sqrt{De}} {1-3.253De^{-0.5}}\right)
Parameters ---------- Re : float Reynolds number with `D=Di`, [-] Di : float Inner diameter of the coil, [m] Dc : float Diameter of the helix/coil measured from the center of the tube on one side to the center of the tube on the other side, [m]
Returns ------- fd : float Darcy friction factor for a curved pipe [-]
Notes ----- The range of validity of this equation is :math:`100 < De < 2000`.
The form of the equation means it yields nonsense results for De < 42.328; under that, the equation is modified to return the value at De=42.328, which is a multiplier of 1.405296 on the straight pipe friction factor.
Examples -------- >>> helical_laminar_fd_Mori_Nakayama(250, .02, .1) 0.4222458285779544
References ---------- .. [1] Mori, Yasuo, and Wataru Nakayama. "Study on Forced Convective Heat Transfer in Curved Pipes : 1st Report, Laminar Region." Transactions of the Japan Society of Mechanical Engineers 30, no. 216 (1964): 977-88. doi:10.1299/kikai1938.30.977. .. [2] El-Genk, Mohamed S., and Timothy M. Schriener. "A Review and Correlations for Convection Heat Transfer and Pressure Losses in Toroidal and Helically Coiled Tubes." Heat Transfer Engineering 0, no. 0 (June 7, 2016): 1-28. doi:10.1080/01457632.2016.1194693. .. [3] Pimenta, T. A., and J. B. L. M. Campos. "Friction Losses of Newtonian and Non-Newtonian Fluids Flowing in Laminar Regime in a Helical Coil." Experimental Thermal and Fluid Science 36 (January 2012): 194-204. doi:10.1016/j.expthermflusci.2011.09.013. '''
r'''Calculates Darcy friction factor for a fluid flowing inside a curved pipe such as a helical coil under laminar conditions, using the method of Schmidt [1]_ as shown in [2]_ and [3]_.
.. math:: f_{curved} = f_{\text{straight,laminar}} \left[1 + 0.14\left(\frac{D_i} {D_c}\right)^{0.97}Re^{\left[1 - 0.644\left(\frac{D_i}{D_c} \right)^{0.312}\right]}\right]
Parameters ---------- Re : float Reynolds number with `D=Di`, [-] Di : float Inner diameter of the coil, [m] Dc : float Diameter of the helix/coil measured from the center of the tube on one side to the center of the tube on the other side, [m]
Returns ------- fd : float Darcy friction factor for a curved pipe [-]
Notes ----- The range of validity of this equation is specified only for Re, :math:`100 < Re < Re_{critical}`.
The form of the equation is such that as the curvature becomes negligible, straight tube result is obtained.
Examples -------- >>> helical_laminar_fd_Schmidt(250, .02, .1) 0.47460725672835236
References ---------- .. [1] Schmidt, Eckehard F. "Wärmeübergang Und Druckverlust in Rohrschlangen." Chemie Ingenieur Technik 39, no. 13 (July 10, 1967): 781-89. doi:10.1002/cite.330391302. .. [2] El-Genk, Mohamed S., and Timothy M. Schriener. "A Review and Correlations for Convection Heat Transfer and Pressure Losses in Toroidal and Helically Coiled Tubes." Heat Transfer Engineering 0, no. 0 (June 7, 2016): 1-28. doi:10.1080/01457632.2016.1194693. .. [3] Pimenta, T. A., and J. B. L. M. Campos. "Friction Losses of Newtonian and Non-Newtonian Fluids Flowing in Laminar Regime in a Helical Coil." Experimental Thermal and Fluid Science 36 (January 2012): 194-204. doi:10.1016/j.expthermflusci.2011.09.013. '''
r'''Calculates Darcy friction factor for a fluid flowing inside a curved pipe such as a helical coil under turbulent conditions, using the method of Schmidt [1]_, also shown in [2]_.
For :math:`Re_{crit} < Re < 2.2\times 10^{4}`:
.. math:: f_{curv} = f_{\text{str,turb}} \left[1 + \frac{2.88\times10^{4}}{Re} \left(\frac{D_i}{D_c}\right)^{0.62}\right]
For :math:`2.2\times 10^{4} < Re < 1.5\times10^{5}`:
.. math:: f_{curv} = f_{\text{str,turb}} \left[1 + 0.0823\left(1 + \frac{D_i} {D_c}\right)\left(\frac{D_i}{D_c}\right)^{0.53} Re^{0.25}\right]
Parameters ---------- Re : float Reynolds number with `D=Di`, [-] Di : float Inner diameter of the coil, [m] Dc : float Diameter of the helix/coil measured from the center of the tube on one side to the center of the tube on the other side, [m] roughness : float, optional Roughness of pipe wall [m]
Returns ------- fd : float Darcy friction factor for a curved pipe [-]
Notes ----- Valid from the transition to turbulent flow up to :math:`Re=1.5\times10^{5}`. At very low curvatures, converges on the straight pipe result.
Examples -------- >>> helical_turbulent_fd_Schmidt(1E4, 0.01, .02) 0.08875550767040916
References ---------- .. [1] Schmidt, Eckehard F. "Wärmeübergang Und Druckverlust in Rohrschlangen." Chemie Ingenieur Technik 39, no. 13 (July 10, 1967): 781-89. doi:10.1002/cite.330391302. .. [2] El-Genk, Mohamed S., and Timothy M. Schriener. "A Review and Correlations for Convection Heat Transfer and Pressure Losses in Toroidal and Helically Coiled Tubes." Heat Transfer Engineering 0, no. 0 (June 7, 2016): 1-28. doi:10.1080/01457632.2016.1194693. ''' else:
r'''Calculates Darcy friction factor for a fluid flowing inside a curved pipe such as a helical coil under turbulent conditions, using the method of Mori and Nakayama [1]_, also shown in [2]_ and [3]_.
.. math:: f_{curv} = 0.3\left(\frac{D_i}{D_c}\right)^{0.5} \left[Re\left(\frac{D_i}{D_c}\right)^2\right]^{-0.2}\left[1 + 0.112\left[Re\left(\frac{D_i}{D_c}\right)^2\right]^{-0.2}\right]
Parameters ---------- Re : float Reynolds number with `D=Di`, [-] Di : float Inner diameter of the coil, [m] Dc : float Diameter of the helix/coil measured from the center of the tube on one side to the center of the tube on the other side, [m]
Returns ------- fd : float Darcy friction factor for a curved pipe [-]
Notes ----- Valid from the transition to turbulent flow up to :math:`Re=6.5\times10^{5}\sqrt{D_i/D_c}`. Does not use a straight pipe correlation, and so will not converge on the straight pipe result at very low curvature.
Examples -------- >>> helical_turbulent_fd_Mori_Nakayama(1E4, 0.01, .2) 0.037311802071379796
References ---------- .. [1] Mori, Yasuo, and Wataru Nakayama. "Study of Forced Convective Heat Transfer in Curved Pipes (2nd Report, Turbulent Region)." International Journal of Heat and Mass Transfer 10, no. 1 (January 1, 1967): 37-59. doi:10.1016/0017-9310(67)90182-2. .. [2] El-Genk, Mohamed S., and Timothy M. Schriener. "A Review and Correlations for Convection Heat Transfer and Pressure Losses in Toroidal and Helically Coiled Tubes." Heat Transfer Engineering 0, no. 0 (June 7, 2016): 1-28. doi:10.1080/01457632.2016.1194693. .. [3] Ali, Shaukat. "Pressure Drop Correlations for Flow through Regular Helical Coil Tubes." Fluid Dynamics Research 28, no. 4 (April 2001): 295-310. doi:10.1016/S0169-5983(00)00034-4. '''
r'''Calculates Darcy friction factor for a fluid flowing inside a curved pipe such as a helical coil under turbulent conditions, using the method of Prasad [1]_, also shown in [2]_.
.. math:: f_{curv} = f_{\text{str,turb}}\left[1 + 0.18\left[Re\left(\frac{D_i} {D_c}\right)^2\right]^{0.25}\right]
Parameters ---------- Re : float Reynolds number with `D=Di`, [-] Di : float Inner diameter of the coil, [m] Dc : float Diameter of the helix/coil measured from the center of the tube on one side to the center of the tube on the other side, [m] roughness : float, optional Roughness of pipe wall [m]
Returns ------- fd : float Darcy friction factor for a curved pipe [-]
Notes ----- No range of validity was specified, but the experiments used were with coil/tube diameter ratios of 17.24 and 34.9, hot water in the tube, and :math:`1780 < Re < 59500`. At very low curvatures, converges on the straight pipe result.
Examples -------- >>> helical_turbulent_fd_Prasad(1E4, 0.01, .2) 0.043313098093994626
References ---------- .. [1] Prasad, B. V. S. S. S., D. H. Das, and A. K. Prabhakar. "Pressure Drop, Heat Transfer and Performance of a Helically Coiled Tubular Exchanger." Heat Recovery Systems and CHP 9, no. 3 (January 1, 1989): 249-56. doi:10.1016/0890-4332(89)90008-2. .. [2] El-Genk, Mohamed S., and Timothy M. Schriener. "A Review and Correlations for Convection Heat Transfer and Pressure Losses in Toroidal and Helically Coiled Tubes." Heat Transfer Engineering 0, no. 0 (June 7, 2016): 1-28. doi:10.1080/01457632.2016.1194693. '''
r'''Calculates Darcy friction factor for a fluid flowing inside a curved pipe such as a helical coil under turbulent conditions, using the method of Czop [1]_, also shown in [2]_.
.. math:: f_{curv} = 0.096De^{-0.1517}
Parameters ---------- Re : float Reynolds number with `D=Di`, [-] Di : float Inner diameter of the coil, [m] Dc : float Diameter of the helix/coil measured from the center of the tube on one side to the center of the tube on the other side, [m]
Returns ------- fd : float Darcy friction factor for a curved pipe [-]
Notes ----- Valid for :math:`2\times10^4 < Re < 1.5\times10^{5}`. Does not use a straight pipe correlation, and so will not converge on the straight pipe result at very low curvature.
Examples -------- >>> helical_turbulent_fd_Czop(1E4, 0.01, .2) 0.02979575250574106
References ---------- .. [1] Czop, V., D. Barbier, and S. Dong. "Pressure Drop, Void Fraction and Shear Stress Measurements in an Adiabatic Two-Phase Flow in a Coiled Tube." Nuclear Engineering and Design 149, no. 1 (September 1, 1994): 323-33. doi:10.1016/0029-5493(94)90298-4. .. [2] El-Genk, Mohamed S., and Timothy M. Schriener. "A Review and Correlations for Convection Heat Transfer and Pressure Losses in Toroidal and Helically Coiled Tubes." Heat Transfer Engineering 0, no. 0 (June 7, 2016): 1-28. doi:10.1080/01457632.2016.1194693. '''
r'''Calculates Darcy friction factor for a fluid flowing inside a curved pipe such as a helical coil under turbulent conditions, using the method of Guo [1]_, also shown in [2]_.
.. math:: f_{curv} = 0.638Re^{-0.15}\left(\frac{D_i}{D_c}\right)^{0.51}
Parameters ---------- Re : float Reynolds number with `D=Di`, [-] Di : float Inner diameter of the coil, [m] Dc : float Diameter of the helix/coil measured from the center of the tube on one side to the center of the tube on the other side, [m]
Returns ------- fd : float Darcy friction factor for a curved pipe [-]
Notes ----- Valid for :math:`2\times10^4 < Re < 1.5\times10^{5}`. Does not use a straight pipe correlation, and so will not converge on the straight pipe result at very low curvature.
Examples -------- >>> helical_turbulent_fd_Guo(2E5, 0.01, .2) 0.022189161013253147
References ---------- .. [1] Guo, Liejin, Ziping Feng, and Xuejun Chen. "An Experimental Investigation of the Frictional Pressure Drop of Steam–water Two-Phase Flow in Helical Coils." International Journal of Heat and Mass Transfer 44, no. 14 (July 2001): 2601-10. doi:10.1016/S0017-9310(00)00312-4. .. [2] El-Genk, Mohamed S., and Timothy M. Schriener. "A Review and Correlations for Convection Heat Transfer and Pressure Losses in Toroidal and Helically Coiled Tubes." Heat Transfer Engineering 0, no. 0 (June 7, 2016): 1-28. doi:10.1080/01457632.2016.1194693. '''
r'''Calculates Darcy friction factor for a fluid flowing inside a curved pipe such as a helical coil under turbulent conditions, using the method of Ju et al. [1]_, also shown in [2]_.
.. math:: f_{curv} = f_{\text{str,turb}}\left[1 +0.11Re^{0.23}\left(\frac{D_i} {D_c}\right)^{0.14}\right]
Parameters ---------- Re : float Reynolds number with `D=Di`, [-] Di : float Inner diameter of the coil, [m] Dc : float Diameter of the helix/coil measured from the center of the tube on one side to the center of the tube on the other side, [m] roughness : float, optional Roughness of pipe wall [m]
Returns ------- fd : float Darcy friction factor for a curved pipe [-]
Notes ----- Claimed to be valid for all turbulent conditions with :math:`De>11.6`. At very low curvatures, converges on the straight pipe result.
Examples -------- >>> helical_turbulent_fd_Ju(1E4, 0.01, .2) 0.04945959480770937
References ---------- .. [1] Ju, Huaiming, Zhiyong Huang, Yuanhui Xu, Bing Duan, and Yu Yu. "Hydraulic Performance of Small Bending Radius Helical Coil-Pipe." Journal of Nuclear Science and Technology 38, no. 10 (October 1, 2001): 826-31. doi:10.1080/18811248.2001.9715102. .. [2] El-Genk, Mohamed S., and Timothy M. Schriener. "A Review and Correlations for Convection Heat Transfer and Pressure Losses in Toroidal and Helically Coiled Tubes." Heat Transfer Engineering 0, no. 0 (June 7, 2016): 1-28. doi:10.1080/01457632.2016.1194693. '''
r'''Calculates Darcy friction factor for a fluid flowing inside a curved pipe such as a helical coil under turbulent conditions, using the method of Mandal and Nigam [1]_, also shown in [2]_.
.. math:: f_{curv} = f_{\text{str,turb}} [1 + 0.03{De}^{0.27}]
Parameters ---------- Re : float Reynolds number with `D=Di`, [-] Di : float Inner diameter of the coil, [m] Dc : float Diameter of the helix/coil measured from the center of the tube on one side to the center of the tube on the other side, [m] roughness : float, optional Roughness of pipe wall [m]
Returns ------- fd : float Darcy friction factor for a curved pipe [-]
Notes ----- Claimed to be valid for all turbulent conditions with :math:`2500 < De < 15000`. At very low curvatures, converges on the straight pipe result.
Examples -------- >>> helical_turbulent_fd_Mandal_Nigam(1E4, 0.01, .2) 0.03831658117115902
References ---------- .. [1] Mandal, Monisha Mridha, and K. D. P. Nigam. "Experimental Study on Pressure Drop and Heat Transfer of Turbulent Flow in Tube in Tube Helical Heat Exchanger." Industrial & Engineering Chemistry Research 48, no. 20 (October 21, 2009): 9318-24. doi:10.1021/ie9002393. .. [2] El-Genk, Mohamed S., and Timothy M. Schriener. "A Review and Correlations for Convection Heat Transfer and Pressure Losses in Toroidal and Helically Coiled Tubes." Heat Transfer Engineering 0, no. 0 (June 7, 2016): 1-28. doi:10.1080/01457632.2016.1194693. '''
r'''Calculates the transition Reynolds number for flow inside a curved or helical coil between laminar and turbulent flow, using the method of [1]_.
.. math:: Re_{crit} = 1900\left[1 + 8 \sqrt{\frac{D_i}{D_c}}\right]
Parameters ---------- Di : float Inner diameter of the coil, [m] Dc : float Diameter of the helix/coil measured from the center of the tube on one side to the center of the tube on the other side, [m]
Returns ------- Re_crit : float Transition Reynolds number between laminar and turbulent [-]
Notes ----- At very low curvatures, converges to Re = 1900.
Examples -------- >>> helical_transition_Re_Seth_Stahel(1, 7.) 7645.0599897402535
References ---------- .. [1] Seth, K. K., and E. P. Stahel. "HEAT TRANSFER FROM HELICAL COILS IMMERSED IN AGITATED VESSELS." Industrial & Engineering Chemistry 61, no. 6 (June 1, 1969): 39-49. doi:10.1021/ie50714a007. '''
r'''Calculates the transition Reynolds number for flow inside a curved or helical coil between laminar and turbulent flow, using the method of [1]_, as shown in [2]_ and in [3]_.
.. math:: Re_{crit} = 20000 \left(\frac{D_i}{D_c}\right)^{0.32}
Parameters ---------- Di : float Inner diameter of the coil, [m] Dc : float Diameter of the helix/coil measured from the center of the tube on one side to the center of the tube on the other side, [m]
Returns ------- Re_crit : float Transition Reynolds number between laminar and turbulent [-]
Notes ----- At very low curvatures, converges to Re = 0. Recommended for :math:`0.00116 < d_i/D_c < 0.067`
Examples -------- >>> helical_transition_Re_Ito(1, 7.) 10729.972844697186
References ---------- .. [1] H. Ito. "Friction factors for turbulent flow in curved pipes." Journal Basic Engineering, Transactions of the ASME, 81 (1959): 123-134. .. [2] El-Genk, Mohamed S., and Timothy M. Schriener. "A Review and Correlations for Convection Heat Transfer and Pressure Losses in Toroidal and Helically Coiled Tubes." Heat Transfer Engineering 0, no. 0 (June 7, 2016): 1-28. doi:10.1080/01457632.2016.1194693. .. [3] Mori, Yasuo, and Wataru Nakayama. "Study on Forced Convective Heat Transfer in Curved Pipes." International Journal of Heat and Mass Transfer 10, no. 5 (May 1, 1967): 681-95. doi:10.1016/0017-9310(67)90113-5. '''
r'''Calculates the transition Reynolds number for flow inside a curved or helical coil between laminar and turbulent flow, using the method of [1]_, as shown in [2]_.
.. math:: Re_{crit} = 12730 \left(\frac{D_i}{D_c}\right)^{0.2}
Parameters ---------- Di : float Inner diameter of the coil, [m] Dc : float Diameter of the helix/coil measured from the center of the tube on one side to the center of the tube on the other side, [m]
Returns ------- Re_crit : float Transition Reynolds number between laminar and turbulent [-]
Notes ----- At very low curvatures, converges to Re = 0. Recommended for :math:`0.0005 < d_i/D_c < 0.103`
Examples -------- >>> helical_transition_Re_Kubair_Kuloor(1, 7.) 8625.986927588123
References ---------- .. [1] Kubair, Venugopala, and N. R. Kuloor. "Heat Transfer to Newtonian Fluids in Coiled Pipes in Laminar Flow." International Journal of Heat and Mass Transfer 9, no. 1 (January 1, 1966): 63-75. doi:10.1016/0017-9310(66)90057-3. .. [2] El-Genk, Mohamed S., and Timothy M. Schriener. "A Review and Correlations for Convection Heat Transfer and Pressure Losses in Toroidal and Helically Coiled Tubes." Heat Transfer Engineering 0, no. 0 (June 7, 2016): 1-28. doi:10.1080/01457632.2016.1194693. '''
r'''Calculates the transition Reynolds number for flow inside a curved or helical coil between laminar and turbulent flow, using the method of [1]_, also shown in [2]_.
.. math:: Re_{crit} = 2300 + 1.05\times 10^4 \left(\frac{D_i}{D_c}\right)^{0.3}
Parameters ---------- Di : float Inner diameter of the coil, [m] Dc : float Diameter of the helix/coil measured from the center of the tube on one side to the center of the tube on the other side, [m]
Returns ------- Re_crit : float Transition Reynolds number between laminar and turbulent [-]
Notes ----- At very low curvatures, converges to Re = 2300. Recommended for :math:`0.0417 < d_i/D_c < 0.1667`
Examples -------- >>> helical_transition_Re_Kutateladze_Borishanskii(1, 7.) 7121.143774574058
References ---------- .. [1] Kutateladze, S. S, and V. M Borishanskiĭ. A Concise Encyclopedia of Heat Transfer. Oxford; New York: Pergamon Press, 1966. .. [2] El-Genk, Mohamed S., and Timothy M. Schriener. "A Review and Correlations for Convection Heat Transfer and Pressure Losses in Toroidal and Helically Coiled Tubes." Heat Transfer Engineering 0, no. 0 (June 7, 2016): 1-28. doi:10.1080/01457632.2016.1194693. '''
r'''Calculates the transition Reynolds number for flow inside a curved or helical coil between laminar and turbulent flow, using the method of [1]_, also shown in [2]_ and [3]_. Correlation recommended in [3]_.
.. math:: Re_{crit} = 2300\left[1 + 8.6\left(\frac{D_i}{D_c}\right)^{0.45}\right]
Parameters ---------- Di : float Inner diameter of the coil, [m] Dc : float Diameter of the helix/coil measured from the center of the tube on one side to the center of the tube on the other side, [m]
Returns ------- Re_crit : float Transition Reynolds number between laminar and turbulent [-]
Notes ----- At very low curvatures, converges to Re = 2300. Recommended for :math:`d_i/D_c < 0.14`
Examples -------- >>> helical_transition_Re_Schmidt(1, 7.) 10540.094061770815
References ---------- .. [1] Schmidt, Eckehard F. "Wärmeübergang Und Druckverlust in Rohrschlangen." Chemie Ingenieur Technik 39, no. 13 (July 10, 1967): 781-89. doi:10.1002/cite.330391302. .. [2] El-Genk, Mohamed S., and Timothy M. Schriener. "A Review and Correlations for Convection Heat Transfer and Pressure Losses in Toroidal and Helically Coiled Tubes." Heat Transfer Engineering 0, no. 0 (June 7, 2016): 1-28. doi:10.1080/01457632.2016.1194693. .. [3] Schlunder, Ernst U, and International Center for Heat and Mass Transfer. Heat Exchanger Design Handbook. Washington: Hemisphere Pub. Corp., 1983. '''
r'''Calculates the transition Reynolds number for flow inside a curved or helical coil between laminar and turbulent flow, using the method of [1]_, also shown in [2]_ and [3]_. Correlation recommended in [3]_.
.. math:: Re_{crit} = 2100\left[1 + 12\left(\frac{D_i}{D_c}\right)^{0.5}\right]
Parameters ---------- Di : float Inner diameter of the coil, [m] Dc : float Diameter of the helix/coil measured from the center of the tube on one side to the center of the tube on the other side, [m]
Returns ------- Re_crit : float Transition Reynolds number between laminar and turbulent [-]
Notes ----- At very low curvatures, converges to Re = 2100. Recommended for :math:`0.004 < d_i/D_c < 0.1`.
Examples -------- >>> helical_transition_Re_Srinivasan(1, 7.) 11624.704719832524
References ---------- .. [1] Srinivasan, P. S., Nandapurkar, S. S., and Holland, F. A., "Pressure Drop and Heat Transfer in Coils", Chemical Engineering, 218, CE131-119, (1968). .. [2] El-Genk, Mohamed S., and Timothy M. Schriener. "A Review and Correlations for Convection Heat Transfer and Pressure Losses in Toroidal and Helically Coiled Tubes." Heat Transfer Engineering 0, no. 0 (June 7, 2016): 1-28. doi:10.1080/01457632.2016.1194693. .. [3] Rohsenow, Warren and James Hartnett and Young Cho. Handbook of Heat Transfer, 3E. New York: McGraw-Hill, 1998. '''
'Mori Nakayama laminar': helical_laminar_fd_Mori_Nakayama, 'Schmidt laminar': helical_laminar_fd_Schmidt}
# Format: 'key': (correlation, supports_roughness) 'Mori Nakayama turbulent': (helical_turbulent_fd_Mori_Nakayama, False), 'Prasad': (helical_turbulent_fd_Prasad, True), 'Czop': (helical_turbulent_fd_Czop, False), 'Guo': (helical_turbulent_fd_Guo, False), 'Ju': (helical_turbulent_fd_Ju, True), 'Mandel Nigam': (helical_turbulent_fd_Mandal_Nigam, True)}
'Ito': helical_transition_Re_Ito, 'Kubair Kuloor': helical_transition_Re_Kubair_Kuloor, 'Kutateladze Borishanskii': helical_transition_Re_Kutateladze_Borishanskii, 'Schmidt': helical_transition_Re_Schmidt, 'Srinivasan': helical_transition_Re_Srinivasan}
Rec_method='Schmidt', laminar_method='Schmidt laminar', turbulent_method='Schmidt turbulent', Darcy=True, AvailableMethods=False): r'''Calculates friction factor fluid flowing in a curved pipe or helical coil, supporting both laminar and turbulent regimes. Selects the appropriate regime by default, and has default correlation choices. Optionally, a specific correlation can be specified with the `Method` keyword.
The default correlations are those recommended in [1]_, and are believed to be the best publically available.
Examples -------- >>> friction_factor_curved(Re=1E5, Di=0.02, Dc=0.5) 0.022961996738387523
Parameters ---------- Re : float Reynolds number with `D=Di`, [-] Di : float Inner diameter of the coil, [m] Dc : float Diameter of the helix/coil measured from the center of the tube on one side to the center of the tube on the other side, [m] roughness : float, optional Roughness of pipe wall [m]
Returns ------- f : float Friction factor, [-] methods : list, only returned if AvailableMethods == True List of methods in the regime the specified `Re` is in at the given `Di` and `Dc`.
Other Parameters ---------------- Method : string, optional A string of the function name to use, overriding the default turbulent/ laminar selection. Rec_method : str, optional Critical Reynolds number transition criteria; one of ['Seth Stahel', 'Ito', 'Kubair Kuloor', 'Kutateladze Borishanskii', 'Schmidt', 'Srinivasan']; the default is 'Schmidt'. laminar_method : str, optional Friction factor correlation for the laminar regime; one of ['White', 'Mori Nakayama laminar', 'Schmidt laminar']; the default is 'Schmidt laminar'. turbulent_method : str, optional Friction factor correlation for the turbulent regime; one of ['Guo', 'Ju', 'Schmidt turbulent', 'Prasad', 'Mandel Nigam', 'Mori Nakayama turbulent', 'Czop']; the default is 'Schmidt turbulent'. Darcy : bool, optional If False, will return fanning friction factor, 1/4 of the Darcy value AvailableMethods : bool, optional If True, function will consider which methods claim to be valid for the range of `Re` and `eD` given
See Also -------- fluids.geometry.HelicalCoil helical_turbulent_fd_Schmidt helical_turbulent_fd_Mandal_Nigam helical_turbulent_fd_Ju helical_turbulent_fd_Guo helical_turbulent_fd_Czop helical_turbulent_fd_Prasad helical_turbulent_fd_Mori_Nakayama helical_laminar_fd_Schmidt helical_laminar_fd_Mori_Nakayama helical_laminar_fd_White helical_transition_Re_Schmidt helical_transition_Re_Srinivasan helical_transition_Re_Kutateladze_Borishanskii helical_transition_Re_Kubair_Kuloor helical_transition_Re_Ito helical_transition_Re_Seth_Stahel
Notes ----- The range of acccuracy of these correlations is much than that in a straight pipe.
References ---------- .. [1] Schlunder, Ernst U, and International Center for Heat and Mass Transfer. Heat Exchanger Design Handbook. Washington: Hemisphere Pub. Corp., 1983. ''' else:
else:
else: else:
# Data from the Handbook of Hydraulic Resistance, 4E, in format (min, max, avg) # roughness in m; may have one, two, or three of the values.
'Cleaned, following years of use': (None, 4.0E-5, None), 'Bituminized': (None, 4.0E-5, None), 'Heating systems piping; either superheated steam pipes, or just water pipes of systems with deaerators and chemical treatment': (None, None, 1.0E-4), 'Following one year as a gas pipeline': (None, None, 1.2E-4), 'Following multiple year as a gas pipeline': (4.0E-5, 2.0E-4, None), 'Casings in gas wells, different conditions, several years of use': (6.0E-5, 2.2E-4, None), 'Heating systems, saturated steam ducts or water pipes (with minor water leakage < 0.5%, and balance water deaerated)': (None, None, 2.0E-4), 'Water heating system pipelines, any source': (None, None, 2.0E-4), 'Oil pipelines, intermediate operating conditions ': (None, None, 2.0E-4), 'Corroded, moderately ': (None, None, 4.0E-4), 'Scale, small depositions only ': (None, None, 4.0E-4), 'Condensate pipes in open systems or periodically operated steam pipelines': (None, None, 5.0E-4), 'Compressed air piping': (None, None, 8.0E-4), 'Following multiple years of operation, generally corroded or with small amounts of scale': (1.5E-4, 1.0E-3, None), 'Water heating piping without deaeration but with chemical treatment of water; leakage up to 3%; or condensate piping operated periodically': (None, None, 1.0E-3), 'Used water piping': (1.2E-3, 1.5E-3, None), 'Poor condition': (5.0E-3, None, None)}
'New and covered with bitumen': (None, None, 5.0E-5), 'Used and covered with partially dissolved bitumen; corroded': (None, None, 1.0E-4), 'Used, suffering general corrosion': (None, None, 1.5E-4), 'Surface looks like new, 10 mm lacquer inside, even joints': (3.0E-4, 4.0E-4, None), 'Used Gas mains': (None, None, 5.0E-4), 'Double or simple transverse riveted joints; with or without lacquer; without corrosion': (6.0E-4, 7.0E-4, None), 'Lacquered inside but rusted': (9.5E-4, 1.0E-3, None), 'Gas mains, many years of use, with layered deposits': (None, None, 1.1E-3), 'Non-corroded and with double transverse riveted joints': (1.2E-3, 1.5E-3, None), 'Small deposits': (None, None, 1.5E-3), 'Heavily corroded and with double transverse riveted joints': (None, None, 2.0E-3), 'Appreciable deposits': (2.0E-3, 4.0E-3, None), 'Gas mains, many years of use, deposits of resin/naphthalene': (None, None, 2.4E-3), 'Poor condition': (5.0E-3, None, None)}
'Riveted laterally and longitudinally with one line; lacquered on the inside': (3.0E-4, 4.0E-4, None), 'Riveted laterally and longitudinally with two lines; with or without lacquer on the inside and without corrosion': (6.0E-4, 7.0E-4, None), 'Riveted laterally with one line and longitudinally with two lines; thickly lacquered or torred on the inside': (1.2E-3, 1.4E-3, None), 'Riveted longitudinally with six lines, after extensive use': (None, None, 2.0E-3), 'Riveted laterally with four line and longitudinally with six lines; overlapping joints inside': (None, None, 4.0E-3), 'Extremely poor surface; overlapping and uneven joints': (5.0E-3, None, None)}
'Not Oiled': (2.0E-5, 4.0E-5, None)}
'Ordinary galvanization': (1.0E-4, 1.5E-4, None)}
'Used previously for water': (None, None, 1.8E-4)}
'New': (2.5E-4, 1.0E-3, None)}
'Coated with asphalt': (1.2E-4, 3.0E-4, None), 'Used water pipelines': (None, None, 1.4E-3), 'Used and corroded': (1.0E-3, 1.5E-3, None), 'Deposits visible': (1.0E-3, 1.5E-3, None), 'Substantial deposits': (2.0E-3, 4.0E-3, None), 'Cleaned after extensive use': (3.0E-4, 1.5E-3, None), 'Severely corroded': (None, 3.0E-3, None)}
'New, clean, seamless (without joints), well fitted': (1.5E-5, 4.0E-5, None), 'New, clean, welded lengthwise and well fitted': (1.2E-5, 3.0E-5, None), 'New, clean, welded lengthwise and well fitted, with transverse welded joints': (8.0E-5, 1.7E-4, None), 'New, clean, coated, bituminized when manufactured': (1.4E-5, 1.8E-5, None), 'New, clean, coated, bituminized when manufactured, with transverse welded joints': (2.0E-4, 6.0E-4, None), 'New, clean, coated, galvanized': (1.0E-4, 2.0E-4, None), 'New, clean, coated, roughly galvanized': (4.0E-4, 7.0E-4, None), 'New, clean, coated, bituminized, curved': (1.0E-4, 1.4E-3, None), 'Used, clean, slight corrosion': (1.0E-4, 3.0E-4, None), 'Used, clean, moderate corrosion or slight deposits': (3.0E-4, 7.0E-4, None), 'Used, clean, severe corrosion': (8.0E-4, 1.5E-3, None), 'Used, clean, previously cleaned of either deposits or rust': (1.5E-4, 2.0E-4, None)}
'Used, all welded, <2 years use, no deposits': (1.2E-4, 2.4E-4, None), 'Used, all welded, <20 years use, no deposits': (6.0E-4, 5.0E-3, None), 'Used, iron-bacterial corrosion': (3.0E-3, 4.0E-3, None), 'Used, heavy corrosion, or with incrustation (deposit 1.5 - 9 mm deep)': (3.0E-3, 5.0E-3, None), 'Used, heavy corrosion, or with incrustation (deposit 3 - 25 mm deep)': (6.0E-3, 6.5E-3, None), 'Used, inside coating, bituminized, < 2 years use': (1.0E-4, 3.5E-4, None)}
seamless_other_metals, 'Seamless steel tubes': seamless_steel, 'Welded steel tubes': welded_steel, 'Riveted steel tubes': riveted_steel, 'Roofing steel sheets': roofing_metal, 'Galzanized steel tubes': galvanized_steel_tube, 'Galzanized sheet steel': galvanized_steel_sheet, 'Steel tubes': steel, 'Cast-iron tubes': cast_iron, 'Steel water conduits in generating stations': water_conduit_steel, 'Used steel water conduits in generating stations': water_conduit_steel_used}
'New and finished with plater; excellent manufacture (joints aligned, prime coated and smoothed)': (5.0E-5, 1.5E-4, None), 'Used and corroded; with a wavy surface and wood framework': (1.0E-3, 4.0E-3, None), 'Old, poor fitting and manufacture; with an overgrown surface and deposits of sand and gravel': (1.0E-3, 4.0E-3, None), 'Very old; damaged surface, very overgrown': (5.0E-3, None, None), 'Water conduit, finished with smoothed plaster': (5.0E-3, None, None), 'New, very well manufactured, hand smoothed, prime-coated joints': (1.0E-4, 2.0E-4, None), 'Hand-smoothed cement finish and smoothed joints': (1.5E-4, 3.5E-4, None), 'Used, no deposits, moderately smooth, steel or wooden casing, joints prime coated but not smoothed': (3.0E-4, 6.0E-4, None), 'Used, prefabricated monoliths, cement plaster (wood floated), rough joints': (5.0E-4, 1.0E-3, None), 'Conduits for water, sprayed surface of concrete': (5.0E-4, 1.0E-3, None), 'Smoothed air-placed, either sprayed concrete or concrete on more concrete': (None, None, 5.0E-4), 'Brushed air-placed, either sprayed concrete or concrete on more concrete': (None, None, 2.3E-3), 'Non-smoothed air-placed, either sprayed concrete or concrete on more concrete': (3.0E-3, 6.0E-3, None), 'Smoothed air-placed, either sprayed concrete or concrete on more concrete': (6.0E-3, 1.7E-2, None)}
'Nonprocessed': (2.5E-3, None, None)}
'Average': (6.0E-4, None, None)}
'Non processed': (1.0E-3, 2.0E-3, None), 'Joints, non smoothed': (1.9E-3, 6.4E-3, None)}
'Plaster, cement, smoothed joints and protrusions, and a casing': (5.0E-5, 2.2E-4, None), 'Steel trowled': (None, None, 5.0E-4)}
'Salt-glazed ceramic': (None, None, 1.4E-3), 'Slag-concrete': (None, None, 1.5E-3), 'Slag and alabaster-filling': (1.0E-3, 1.5E-3, None)}
'Reinforced concrete tubes': concrete_reinforced_tubes, 'Asbestos cement tubes': asbestos_cement, 'Cement tubes': cement_tubes, 'Cement-mortar plaster channels': cement_mortar_channels, 'Other': cement_other}
'Boards, well dressed': (None, None, 3.0E-4), 'Boards, undressed but fitted': (None, None, 7.0E-4), 'Boards, undressed': (None, None, 1.0E-3), 'Staved': (None, None, 6.0E-4)}
(None, None, 1.2E-4), 'Birch plywood, longitudal grain, good quality': (3.0E-5, 5.0E-5, None)}
'Plywood tubes': plywood_tube, 'Glass tubes': glass_tube}
'Blast-hewed, substantial jointing': (1.3E-1, 5.0E-1, None), 'Roughly cut or very uneven surface': (5.0E-1, 1.5E+0, None)}
'Rocks, granite, diameter 3-9 m': (2.0E-1, 7.0E-1, None), 'Shale, diameter, diameter 9-12 m': (2.5E-1, 6.5E-1, None), 'Shale, quartz, quartzile, diameter 7-10 m': (2.0E-1, 6.0E-1, None), 'Shale, sedimentary, diameter 4-7 m': (None, None, 4.0E-1), 'Shale, nephrite bearing, diameter 3-8 m': (None, None, 2.0E-1)}
'Unlined tunnels': unlined_tunnels}
# Roughness, in m 'Steel': .00000152, 'Asphalted cast iron': .000122, 'Galvanized iron': .000152, 'Cast iron': .000259, 'Wood stave': .000183, 'Rough wood stave': .000914, 'Concrete': .000305, 'Rough concrete': .00305, 'Riveted steel': .000914, 'Rough riveted steel': .00914}
# Create a more friendly data structure
'''Holds a dict of tuples in format (min, max, average) roughness values in meters from the source Idelʹchik, I. E, and A. S Ginevskiĭ. Handbook of Hydraulic Resistance. Redding, CT: Begell House, 2007. '''
# For searching only
# Format : ID: (avg_roughness, coef A (inches), coef B (inches)) 'Carbon steel, honed bare': (12.5E-6, 0.0005, -1.0101), 'Cr13, electropolished bare': (30E-6, 0.0012, -1.0086), 'Cement lining': (33E-6, 0.0014, -1.0105), 'Carbon steel, bare': (36E-6, 0.0014, -1.0112), 'Fiberglass lining': (38E-6, 0.0016, -1.0086), 'Cr13, bare': (55E-6, 0.0021, -1.0055) }
r'''Calculates of retrieves the roughness of a pipe based on the work of [1]_. This function will return an average value for pipes of a given material, or if diameter is provided, will calculate one specifically for the pipe inner diameter according to the following expression with constants `A` and `B`:
.. math:: \epsilon = A\cdot D^{B+1}
Please not that `A` has units of inches, and `B` requires `D` to be in inches as well.
The list of supported materials is as follows:
* 'Plastic coated' * 'Carbon steel, honed bare' * 'Cr13, electropolished bare' * 'Cement lining' * 'Carbon steel, bare' * 'Fiberglass lining' * 'Cr13, bare'
If `coeffs` and `D` are given, the custom coefficients for the equation as given by the user will be used and `ID` is not required.
Parameters ---------- ID : str, optional Name of pipe material from above list D : float, optional Actual inner diameter of pipe, [m] coeffs : tuple, optional (A, B) Coefficients to use directly, instead of looking them up [inch^-B, -]
Returns ------- epsilon : float Roughness of pipe [m]
Notes ----- The diameter-dependent form provides lower roughness values for larger diameters.
The measurements were based on DIN 4768/1 (1987), using both a "Dektak ST Surface Profiler" and a "Hommel Tester T1000". Both instruments were found to be in agreement. A series of flow tests, in which pressure drop directly measured, were performed as well, with nitrogen gas as an operating fluid. The accuracy of the data from these tests is claimed to be within 1%.
Using those results, the authors back-calculated what relative roughness values would be ncessary to produce the observed pressure drops. The average difference between this back-calculated roughness and the measured roughness was 6.75%.
For microchannels, this model will predict roughness much larger than the actual channel diameter.
Examples -------- >>> roughness_Farshad('Cr13, bare', 0.05) 5.3141677781137006e-05
References ---------- .. [1] Farshad, Fred F., and Herman H. Rieke. "Surface Roughness Design Values for Modern Pipes." SPE Drilling & Completion 21, no. 3 (September 1, 2006): 212-215. doi:10.2118/89040-PA. ''' # Case 1, coeffs given; only run if ID is not given. # Case 2, lookup parameters else:
r'''Searches through either a dict of clean pipe materials or used pipe materials and conditions and returns the ID of the nearest material. Search is performed with either the standard library's difflib or with the fuzzywuzzy module if available.
Parameters ---------- name : str Search term for matching pipe materials clean : bool, optional If True, search only clean pipe database; if False, search only the dirty database; if None, search both
Returns ------- ID : str String for lookup of roughness of a pipe, in either `roughness_clean_dict` or `HHR_roughness` depending on if clean is True
Examples -------- >>> nearest_material_roughness('condensate pipes', clean=False) 'Seamless steel tubes, Condensate pipes in open systems or periodically operated steam pipelines'
References ---------- .. [1] Idelʹchik, I. E, and A. S Ginevskiĭ. Handbook of Hydraulic Resistance. Redding, CT: Begell House, 2007. '''
r'''Searches through either a dict of clean pipe materials or used pipe materials and conditions and returns the ID of the nearest material. Search is performed with either the standard library's difflib or with the fuzzywuzzy module if available.
Parameters ---------- ID : str Search terms for matching pipe materials D : float, optional Diameter of desired pipe; used only if ID is in [2]_ optimism : bool, optional For values in [1]_, a minimum, maximum, and average value is normally given; if True, returns the minimum roughness; if False, the maximum roughness; and if None, returns the average roughness. Most entries do not have all three values, so fallback logic to return the closest entry is used.
Returns ------- roughness : float Retrieved or calculated roughness, [m]
Examples -------- >>> material_roughness('condensate pipes') 0.0005
References ---------- .. [1] Idelʹchik, I. E, and A. S Ginevskiĭ. Handbook of Hydraulic Resistance. Redding, CT: Begell House, 2007. .. [2] Farshad, Fred F., and Herman H. Rieke. "Surface Roughness Design Values for Modern Pipes." SPE Drilling & Completion 21, no. 3 (September 1, 2006): 212-215. doi:10.2118/89040-PA. ''' else: else: D=D, optimism=optimism)
r'''Calculates either transmission factor from Darcy friction factor, or Darcy friction factor from the transmission factor. Raises an exception if neither input is given.
Transmission factor is a term used in compressible gas flow in pipelines.
.. math:: F = \frac{2}{\sqrt{f_d}}
f_d = \frac{4}{F^2}
Parameters ---------- fd : float, optional Darcy friction factor, [-] F : float, optional Transmission factor, [-]
Returns ------- fd or F : float Darcy friction factor or transmission factor [-]
Examples -------- >>> transmission_factor(fd=0.0185) 14.704292441876154
References ---------- .. [1] Menon, E. Shashi. Gas Pipeline Hydraulics. 1st edition. Boca Raton, FL: CRC Press, 2005. ''' else:
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