#!/usr/bin/python3
# -*- coding: utf-8 -*-
'''Pychemqt, Chemical Engineering Process simulator
Copyright (C) 2009-2025, Juan José Gómez Romera <jjgomera@gmail.com>
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
Module for implement friction factor related functionality
**Friction factor**
Global function with all functionality, :func:`f_friccion`
Friction factor for rough pipes, Colebrook-White intrinsic equation is solved
by iteration so so many method have been implement to get direct equations:
* :func:`f_colebrook`
* :func:`f_chen`
* :func:`f_Vatankhah`
* :func:`f_buzzelli`
* :func:`f_romeo`
* :func:`f_serghides`
* :func:`f_zigrang`
* :func:`f_Samadianfard`
* :func:`f_brkic`
* :func:`f_fang`
* :func:`f_ghanbari`
* :func:`f_haaland`
* :func:`f_round`
* :func:`f_swamee`
* :func:`f_jain`
* :func:`f_barr`
* :func:`f_shacham`
* :func:`f_tsal`
* :func:`f_manadilli`
* :func:`f_goudar`
* :func:`f_goudar2007`
* :func:`f_avci`
* :func:`f_papaevangelou`
* :func:`f_churchill`
* :func:`f_chen1979`
* :func:`f_moody`
* :func:`f_wood`
* :func:`f_eck`
* :func:`f_altshul`
'''
from math import exp, log, log10
from scipy.optimize import fsolve
from lib.unidades import Dimensionless
from lib.utilities import refDoc
__doi__ = {
1:
{"autor": "Colebrook, C.F., White, C.M.",
"title": "Experiments with Fluid Friction in Roughened Pipes",
"ref": "Proc. R. Soc. Lond. A 161 (1937) 367-381.",
"doi": "10.1098/rspa.1937.0150"},
2:
{"autor": "Chen, H.J.",
"title": "An Explicit Equation for Friction Factor in Pipe",
"ref": "Ind. Eng. Chem. Fundam. 18(3) (1979) 296-297",
"doi": "10.1021/i160071a019"},
3:
{"autor": "Chen, H.J.",
"title": "An Exact Solution to the Colebrook Equation",
"ref": "Chem. Eng. 94(2) (1987) 196-198",
"doi": ""},
4:
{"autor": "Moody, L. F.",
"title": "An approximate formula for pipe friction factors",
"ref": "Trans. ASME, 69(12) (1947) 1005-1006.",
"doi": ""},
5:
{"autor": "Churchill, S.W.",
"title": "Friction-factor equation spans all fluid-flow regimes",
"ref": "Chem. Eng. 84 (1977) 94-95",
"doi": ""},
6:
{"autor": "Wood D.J.",
"title": "An explicit friction factor relationship",
"ref": "Civil Eng. ASCE 60, 1966",
"doi": ""},
7:
{"autor": "Haaland, S.E.",
"title": "Simple and explicit formulas for the friction factor in"
"turbulent flow",
"ref": "J. Fluids Eng., 105(1) (1983) 89-90.",
"doi": "10.1115/1.3240948"},
8:
{"autor": "Serghides, T.K.",
"title": "Estimate friction factor accurately",
"ref": "Chem. Eng., 91(5) (1984) 63-64.",
"doi": ""},
9:
{"autor": "Round, G.F.",
"title": "An Explicit Approximation for the Friction Factor-Reynolds"
"Number Relation for Rough and Smooth Pipes",
"ref": "Can. J. Chem. Eng. 58 (1980) 122-123",
"doi": "10.1002/cjce.5450580119"},
10:
{"autor": "Swamee, P.K.; Jain, A.K.",
"title": "Explicit equations for pipe-flow problems",
"ref": "J. Hydraulics Division (ASCE) 102(5) (1976) 657-664.",
"doi": ""},
11:
{"autor": "Jain, A.K.",
"title": "Accurate Explicit Equation for Friction Factor",
"ref": "J. Hydraulics Division 102(5) (1976) 674-77",
"doi": ""},
12:
{"autor": "Barr, D.I.H.",
"title": "Solutions of the Colebrook-White functions for resistance "
"to uniform turbulent flows.",
"ref": "Proc Inst Civil Eng 71, 1981, 529-536.",
"doi": "10.1680/iicep.1981.1895"},
13:
{"autor": "Zigrang, D.J., Sylvester, N.D.",
"title": "Explicit approximations to the solution of Colebrook's"
"friction factor equation",
"ref": "AIChE J. 28(03) (1982) 514-515.",
"doi": "10.1002/aic.690280323"},
14:
{"autor": "Tsal, R.J.",
"title": "Altshul-Tsal friction factor equation",
"ref": "Heating Piping Air Conditioning 8 (1989), 30-45.",
"doi": ""},
15:
{"autor": "Eck, B.",
"title": "Technische Stromungslehre",
"ref": "Springer, New York, 1973.",
"doi": ""},
16:
{"autor": "Shacham. M.",
"title": "An explicit equation for friction factor in pipe",
"ref": "Ind. Eng. Chem. Fund. 19 (1981) 228-229.",
"doi": ""},
17:
{"autor": "Manadilli, G.",
"title": "Replace implicit equations with signomial functions.",
"ref": "Chem. Eng. 104 (1997) 129-132.",
"doi": ""},
18:
{"autor": "Romeo, E., Royo, C., Monzon, A.",
"title": "Improved explicit equation for estimation of the friction"
"factor in rough and smooth pipes.",
"ref": "Chem. Eng. J. 86(3) (2002) 369-374",
"doi": "10.1016/S1385-8947(01)00254-6"},
19:
{"autor": "Sonnad, J.R., Goudar, C.T.",
"title": "Explicit Reformulation of the Colebrook-White Equation for "
"Turbulent Flow Frcition Factor Calculation",
"ref": "Ind. Eng. Chem. Res. 46(8) (2007) 2593-2600",
"doi": "10.1021/ie0340241"},
20:
{"autor": "Buzzelli, D.",
"title": "Calculating friction in one step",
"ref": "Machine Design, 80 (2008), 54–55.",
"doi": ""},
21:
{"autor": "Vatankhah, A.R., Kouchakzadeh, S",
"title": "Full-range pipe-flow equations",
"ref": "Journal of Hydraulic Research 46(4) (2008) 559",
"doi": ""},
22:
{"autor": "Avci, A., Karagoz, I.",
"title": "A Novel Explicit Equation for Friction Factor in Smooth and"
"Rough Pipes",
"ref": "J. Fluids Eng 131(6) (2009) 061203",
"doi": "10.1115/1.3129132"},
23:
{"autor": "Papaevangelou, G., Evangelides, C., Tzimopoulos, C.,",
"title": "A new explicit relation for friction coefficient in the "
"Darcy-Weisbach equation",
"ref": "Proceedings of the Tenth Conference on Protection and "
"Restoration of the Environment 166,1-7pp, PRE10 July 6-09 "
"2010 Corfu, Greece.",
"doi": ""},
24:
{"autor": "Brkić, D.",
"title": "An Explicit Approximation of Colebrook’s equation for fluid"
"flow friction factor",
"ref": "Petroleum Science and Technology 29 (15): 1596–1602. ",
"doi": "10.1080/10916461003620453"},
25:
{"autor": "Fang, X,, Xu, Y., Zhou, Z.",
"title": "New correlations of single-phase friction factor for"
"turbulent pipe flow and evaluation of existing single-phase"
"friction factor correlations.",
"ref": "Nucl. Eng. Des. 241 (2011) 897-902",
"doi": "10.1016/j.nucengdes.2010.12.019"},
26:
{"autor": "Ghanbari, A., Farshad, F., Rieke, H.H.",
"title": "Newly developed friction factor correlation for pipe flow "
"and flow assurance",
"ref": "J Chem Eng Mat Sci 2 (2011), 83-86.",
"doi": ""},
27:
{"autor": "Goudar, C.T., Sonnad J.R.",
"title": "Comparison of the iterative approximations of the "
"Colebrook-White equation",
"ref": "Hydrocarb. Process. 87 (2008) 79-83",
"doi": ""},
28:
{"autor": "Samadianfard, S.",
"title": "Gene expression programming analysis of implicit "
"Colebrook-White equation in turbulent flow friction factor "
"calculation",
"ref": "J. Pet. Sci. Eng. 92-93 (2012) 48-55",
"doi": "10.1016/j.petrol.2012.06.005"},
29:
{"autor": "Darby, R., Chhabra, R.P.",
"title": "Chemical Engineering Fluid Mechanics, 3rd Edition",
"ref": "CRC Press, 2017",
"doi": ""},
30:
{"autor": "",
"title": "HTRI Design Manual",
"ref": "",
"doi": ""},
31:
{"autor": "Perkins, H.C., Woroe-Schmidt, P.",
"title": "Turbulent Heat and Momentum Transfer for Gases in a "
"Circular Tube at Wall to Bulk Temperature Ratios to Seven",
"ref": "Int. J. Heat Mass Transfer 8(7) (1965) 1011-1031",
"doi": "10.1016/0017-9310(65)90085-2"},
32:
{"autor": "Gnielinski, V.",
"title": "Berechnung des Druckverlustes in glatten konzentrischen "
"Ringspalten bei ausgebildeter laminarer und turbulenter "
"isothermer Strömung",
"ref": "Chemie Ingenieur Technik 79(1-2) (2007) 91-95",
"doi": "10.1002/cite.200600126"},
# 33:
# {"autor": "",
# "title": "",
# "ref": "",
# "doi": ""},
}
# Friction factor for pipes
# All this function return the darcy friction factor, fanning friction factor
# can be obtained divided darcy factor by 4.
[docs]
@refDoc(__doi__, [1])
def f_colebrook(Re, eD):
r"""Calculates friction factor `f` with Colebrook-White correlation (1939)
.. math::
\frac{1}{\sqrt{f}}=-2\log\left(\frac{\epsilon/D}{3.7}+
\frac{2.51}{Re\sqrt{f}}\right)
Parameters
----------
Re : float
Reynolds number, [-]
eD : float
Relative roughness of a pipe, [-]
Returns
-------
f : float
Friction factor, [-]
Notes
-----
This is the original, implicit expression, slowlest to solve
"""
fo = f_chen(Re, eD)
if eD:
f = fsolve(lambda x: 1/x**0.5+2.0*log10(eD/3.7+2.51/Re/x**0.5), fo)
else:
f = fsolve(lambda x: 1/x**0.5-2.0*log10(Re*x**0.5)+0.8, fo)
return Dimensionless(f[0])
[docs]
@refDoc(__doi__, [2])
def f_chen1979(Re, eD):
r"""Calculates friction factor `f` with Chen correlation (1979)
.. math::
\frac{1}{\sqrt{f}}=-2\log\left(\frac{\epsilon/D}{3.7065}
-\frac{5.0452}{Re}\log\left(\frac{\left(\epsilon/D\right)
^{1.1098}}{2.8257}+\left(\frac{7.149}{Re}\right)^{0.8981}\right)\right)
Parameters
----------
Re : float
Reynolds number, [-]
eD : float
Relative roughness of a pipe, [-]
Returns
-------
f : float
Friction factor, [-]
Notes
-----
Range of validity:
* 4e3 <= Re <= 4e8
* 1e-7 <= eD <= 0.05
"""
# Eq 7
A = eD**1.1098/2.8257+5.8506/Re**0.8981
f = 1/(-2*log10(eD/3.7065-5.0452/Re*log10(A)))**2
return Dimensionless(f)
[docs]
@refDoc(__doi__, [3])
def f_chen(Re, eD):
r"""Calculates friction factor `f` with Chen correlation (1987)
.. math::
\frac{1}{\sqrt{f}}=-4\log\left(\frac{\epsilon/D}{3.7}-
\frac{5.02}{Re}\log\left(\frac{\epsilon/D}{3.7}+
\left(\frac{6.7}{Re}\right)^{0.9}\right)\right)
Parameters
----------
Re : float
Reynolds number, [-]
eD : float
Relative roughness of a pipe, [-]
Returns
-------
f : float
Friction factor, [-]
Notes
-----
The most satisfactory explicit friction factor correlation by [2].
"""
A = eD/3.7+(6.7/Re)**0.9
f = 1/(-2*log10(eD/3.7-5.02/Re*log10(A)))**2
return Dimensionless(f)
[docs]
@refDoc(__doi__, [4])
def f_moody(Re, eD):
r"""Calculates friction factor `f` with Moody correlation (1947)
.. math::
f = 5.5 10^{-3}\left[1+\left(2 10^4\frac{\epsilon}{D} +
\frac{10^6}{Re}\right)^{1/3}\right]
Parameters
----------
Re : float
Reynolds number, [-]
eD : float
Relative roughness of a pipe, [-]
Returns
-------
f : float
Friction factor, [-]
Notes
-----
Range of validity:
* 4e3 <= Re <= 1e8
* 0<= eD < 0.01.
"""
f = 5.5e-3*(1+(2e4*eD+1e6/Re)**(1./3))
return Dimensionless(f)
[docs]
@refDoc(__doi__, [5])
def f_churchill(Re, eD):
r"""Calculates friction factor `f` with Churchill correlation (1977)
.. math::
f = 2\left[(\frac{8}{Re})^{12} + (A + B)^{-1.5}\right]^{1/12}
.. math::
A = \left\{2.457\ln\left[(\frac{7}{Re})^{0.9}
+ 0.27\frac{\epsilon}{D}\right]\right\}^{16}
.. math::
B = \left( \frac{37530}{Re}\right)^{16}
Parameters
----------
Re : float
Reynolds number, [-]
eD : float
Relative roughness of a pipe, [-]
Returns
-------
f : float
Friction factor, [-]
Notes
-----
Represent fanning friction factor over the entire range of Reynolds numbers
including intermediate region between laminar and turbulent flow.
"""
# Eq 18
A = (2.457*log(1/(0.27*eD+(7./Re)**0.9)))**16
B = (37530./Re)**16
f = 8.*((8./Re)**12+(A+B)**-1.5)**(1./12)
return Dimensionless(f)
[docs]
@refDoc(__doi__, [6])
def f_wood(Re, eD):
r"""Calculates friction factor `f` with Wood correlation (1966)
.. math::
f_d = 0.094\left(\epsilon/D\right)^{0.225} + 0.53\left(
\epsilon/D\right) + 88\left(\epsilon/D\right)^{0.4}Re^{-A_1}
.. math::
A_1 = 1.62\left(\epsilon/D\right)^{0.134}
Parameters
----------
Re : float
Reynolds number, [-]
eD : float
Relative roughness of a pipe, [-]
Returns
-------
f : float
Friction factor, [-]
Notes
-----
Range of validity:
* Re > 10000
* 1e-5 < eD < 0.04
"""
a = 0.094*eD**0.225+0.53*eD
b = 88*eD**0.44
c = -1.62*eD**0.134
f = a + b*Re**c
return Dimensionless(f)
[docs]
@refDoc(__doi__, [7])
def f_haaland(Re, eD):
r"""Calculates friction factor `f` with Haaland correlation (1983)
.. math::
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 of a pipe, [-]
Returns
-------
f : float
Friction factor, [-]
Notes
-----
Range of validity:
* 4e3 <= Re <= 1e8
* 1e-6 <= eD <= 0.05
"""
# Eq 8
f = 1/(-1.8*log10((eD/3.75)**1.11+6.9/Re))**2
return Dimensionless(f)
[docs]
@refDoc(__doi__, [8])
def f_serghides(Re, eD):
r"""Calculates friction factor `f` with Serguides correlation (1984)
.. math::
f=\left[A-\frac{(B-A)^2}{C-2B+A}\right]^{-2}
.. math::
A=-2\log_{10}\left[\frac{\epsilon/D}{3.7}+\frac{12}{Re}\right]
.. math::
B=-2\log_{10}\left[\frac{\epsilon/D}{3.7}+\frac{2.51A}{Re}\right]
.. math::
C=-2\log_{10}\left[\frac{\epsilon/D}{3.7}+\frac{2.51B}{Re}\right]
Parameters
----------
Re : float
Reynolds number, [-]
eD : float
Relative roughness of a pipe, [-]
Returns
-------
f : float
Friction factor, [-]
"""
A = -2*log10(eD/3.7+12/Re)
B = -2*log10(eD/3.7+2.51*A/Re)
C = -2*log10(eD/3.7+2.51*B/Re)
f = (A-(B-A)**2/(C-2*B+A))**-2
return Dimensionless(f)
[docs]
@refDoc(__doi__, [9])
def f_round(Re, eD):
r"""Calculates friction factor `f` with Round correlation (1980)
.. math::
\frac{1}{\sqrt{f}} = 1.8\log\left[\frac{Re}{0.135Re
\epsilon/D+6.5}\right]
Parameters
----------
Re : float
Reynolds number, [-]
eD : float
Relative roughness of a pipe, [-]
Returns
-------
f : float
Friction factor, [-]
Notes
-----
Range of validity:
* 4e3 <= Re <= 4e8
* eD <= 0.05
"""
# Eq 8
f = 1/(1.8*log10(Re/(0.135*Re*eD+6.5)))**2
return Dimensionless(f)
[docs]
@refDoc(__doi__, [10])
def f_swamee(Re, eD):
r"""Calculates friction factor `f` with Swamee-Jain correlation (1976)
.. math::
\frac{1}{\sqrt{f}} = -2\log\left[\left(\frac{6.97}{Re}\right)^{0.9}
+ (\frac{\epsilon}{3.7D})\right]
Parameters
----------
Re : float
Reynolds number, [-]
eD : float
Relative roughness of a pipe, [-]
Returns
-------
f : float
Friction factor, [-]
Notes
-----
Range of validity:
* 5e3 <= Re <= 1e8
* 1e-6 <= eD <= 5e-2
"""
f = 1/(-2*log10(eD/3.7+(6.97/Re)**0.9))**2
return Dimensionless(f)
[docs]
@refDoc(__doi__, [11])
def f_jain(Re, eD):
r"""Calculates friction factor `f` with Jain correlation (1976)
.. math::
\frac{1}{\sqrt{f}} = 1.14 - 2\log\left[\epsilon/D +
\left(\frac{29.843}{Re}\right)^{0.9}\right]
Parameters
----------
Re : float
Reynolds number, [-]
eD : float
Relative roughness of a pipe, [-]
Returns
-------
f : float
Friction factor, [-]
Notes
-----
Range of validity:
* 5e3 <= Re <= 1e7
* 4e-5 <= eD <= 0.05
"""
f = 1/(1.14-2*log10(eD+(29.843/Re)**0.9))**2
return Dimensionless(f)
[docs]
@refDoc(__doi__, [12])
def f_barr(Re, eD):
r"""Calculates friction factor `f` with Barr correlation (1981)
.. math::
\frac{1}{\sqrt{f}} = -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 of a pipe, [-]
Returns
-------
f : float
Friction factor, [-]
"""
# Eq 6
f = 1/(2*log10(eD/3.7+4.518*log10(Re/7)/Re/(1+Re**0.52/29*eD**0.7)))**2
return Dimensionless(f)
[docs]
@refDoc(__doi__, [13])
def f_zigrang(Re, eD):
r"""Calculates friction factor `f` with Zigrang-Sylvester correlation (1982)
.. math::
\frac{1}{\sqrt{f}} = -2\log\left[\frac{\epsilon}{3.7D}
- \frac{5.02}{Re}\log A\right]
.. math::
A = \frac{\epsilon}{3.7D} + \frac{13}{Re}
Parameters
----------
Re : float
Reynolds number, [-]
eD : float
Relative roughness of a pipe, [-]
Returns
-------
f : float
Friction factor, [-]
Notes
-----
Range of validity:
* 4e3 <= Re <= 1e8
* 4e-5 <= eD <= 5e-2
"""
# Eq 12
A = log10(eD/3.7-5.02/Re*log10(eD/3.7+13./Re))
f = 1/(-2*log10(eD/3.7-5.02*A/Re))**2
return Dimensionless(f)
[docs]
@refDoc(__doi__, [14])
def f_altshul(Re, eD):
r"""Calculates friction factor `f` with Altshul correlation (1975)
.. math::
f = 0.11\left( \frac{68}{Re} + \frac{\epsilon}{D}\right)^{0.25}
Parameters
----------
Re : float
Reynolds number, [-]
eD : float
Relative roughness of a pipe, [-]
Returns
-------
f : float
Friction factor, [-]
"""
f = 0.11*(eD+68/Re)**0.25
return Dimensionless(f)
[docs]
@refDoc(__doi__, [14])
def f_tsal(Re, eD):
r"""Calculates friction factor `f` with Tsal correlation (1989)
.. math::
A = 0.11(\frac{68}{Re} + \frac{\epsilon}{D})^{0.25}
if A >= 0.018 then f = A
if A < 0.018 then f = 0.0028 + 0.85 A
Parameters
----------
Re : float
Reynolds number, [-]
eD : float
Relative roughness of a pipe, [-]
Returns
-------
f : float
Friction factor, [-]
Notes
-----
Range of validity:
* 4e3 <= Re <= 1e8
* eD <= 0.05
"""
f = 0.11*(68/Re+eD)**0.25
if f < 0.018:
f = 0.0028+0.85*f
return f
[docs]
@refDoc(__doi__, [15])
def f_eck(Re, eD):
r"""Calculates friction factor `f` with Eck correlation (1973)
.. 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 of a pipe, [-]
Returns
-------
f : float
Friction factor, [-]
"""
f = 1/(-2*log10(eD/3.71+15/Re))**2
return Dimensionless(f)
[docs]
@refDoc(__doi__, [16])
def f_shacham(Re, eD):
r"""Calculates friction factor `f` with Shacham correlation (1980)
.. math::
\frac{1}{\sqrt{f}} = -2\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 of a pipe, [-]
Returns
-------
f : float
Friction factor, [-]
Notes
-----
Range of validity:
* 4e3 <= Re <= 4e8
"""
f = 1/(-2*log10(eD/3.7-5.02/Re*log10(eD/3.7+14.5/Re)))**2
return Dimensionless(f)
[docs]
@refDoc(__doi__, [17])
def f_manadilli(Re, eD):
r"""Calculates friction factor `f` with Manadilli correlation (1997)
.. math::
\frac{1}{\sqrt{f}} = -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 of a pipe, [-]
Returns
-------
f : float
Friction factor, [-]
Notes
-----
Range of validity:
* 5.245e3 <= Re <= 1e8
* eD <= 0.05
"""
f = 1/(-2*log10(eD/3.7+95./Re**0.983-96.82/Re))**2
return Dimensionless(f)
[docs]
@refDoc(__doi__, [18])
def f_romeo(Re, eD):
r"""Calculates friction factor `f` with Monzon-Romeo-Royo correlation (2002)
.. 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 of a pipe, [-]
Returns
-------
f : float
Friction factor, [-]
Notes
-----
Range of validity:
* 3e3 <= Re <= 1.5e8
* eD <= 0.05
"""
A = log10((eD/7.7918)**0.9924+(5.3326/(208.815+Re))**0.9345)
B = log10(eD/3.827-4.567/Re*A)
f = 1/(-2*log10(eD/3.7065-5.0272*B/Re))**2
return Dimensionless(f)
[docs]
@refDoc(__doi__, [19])
def f_goudar2007(Re, eD):
r"""Calculates friction factor `f` with Goudar-Sonnad correlation (2007)
.. math::
\frac{1}{\sqrt{f}} = 0.8686\ln\left(\frac{0.4587Re}{S^{S/(S+1)}}\right)
.. math::
S = 0.1240\times\frac{\epsilon}{D}\times Re + \ln(0.4587Re)
Parameters
----------
Re : float
Reynolds number, [-]
eD : float
Relative roughness of a pipe, [-]
Returns
-------
f : float
Friction factor, [-]
Notes
-----
Range of validity:
* 4e3 <= Re <= 1e8
* 1e-6 <= eD <= 0.05
"""
C = 0.124*Re*eD+log(0.4587*Re)
f = 1/(0.8686*log(0.4587*Re/(C-0.31)**(C/(C+1))))**2
return Dimensionless(f)
[docs]
@refDoc(__doi__, [27])
def f_goudar(Re, eD):
r"""Calculates friction factor `f` with Goudar-Sonnad correlation (2008)
Parameters
----------
Re : float
Reynolds number, [-]
eD : float
Relative roughness of a pipe, [-]
Returns
-------
f : float
Friction factor, [-]
"""
a = 2/log(10)
b = eD/3.7
d = log(10)*Re/5.2
s = b*d+log(d)
q = s**(s/(s+1))
g = b*d+log(d/q)
z = log(q/g)
Dla = g/(g+1)*z
Dcfa = Dla*(1+z/2/((g+1)**2+z/3*(2*g-1)))
f = (a*(log(d/q)+Dcfa))**-2
return Dimensionless(f)
[docs]
@refDoc(__doi__, [20])
def f_buzzelli(Re, eD):
r"""Calculates friction factor `f` with Buzzelli correlation (2008)
.. math::
\frac{1}{\sqrt{f}} = A - \left[\frac{A +2\log(\frac{B}{Re})}
{1 + \frac{2.18}{B}}\right]
.. math::
A = \frac{0.774\ln(Re)-1.41}{1+1.32\sqrt{\frac{\epsilon}{D}}}
.. math::
B = \frac{\epsilon}{3.7D}Re+2.51\times B_1
Parameters
----------
Re : float
Reynolds number, [-]
eD : float
Relative roughness of a pipe, [-]
Returns
-------
f : float
Friction factor, [-]
"""
# Eq 2
A = (0.744*log(Re)-1.41)/(1+1.32*eD**0.5)
B = eD/3.7*Re+2.51*A
f = 1/(A-((A+2*log10(B/Re))/(1+2.18/B)))**2
return Dimensionless(f)
[docs]
@refDoc(__doi__, [21])
def f_Vatankhah(Re, eD):
r"""Calculates friction factor `f` with Vatankhah-Kouchakzadeh corr (2008)
Parameters
----------
Re : float
Reynolds number, [-]
eD : float
Relative roughness of a pipe, [-]
Returns
-------
f : float
Friction factor, [-]
"""
S = 0.124*Re*eD+log(0.4587*Re)
f = 1/(0.8686*log(0.4587*Re/(S-0.31)**(S/(S+0.9633))))**2
return Dimensionless(f)
[docs]
@refDoc(__doi__, [22])
def f_avci(Re, eD):
r"""Calculates friction factor `f` with Avci-Karagoz correlation (2009)
.. math::
f = \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 of a pipe, [-]
Returns
-------
f : float
Friction factor, [-]
"""
# Eq 17
f = 6.4/(log(Re)-log(1+0.01*Re*eD*(1+10*eD**0.5)))**2.4
return Dimensionless(f)
[docs]
@refDoc(__doi__, [23])
def f_papaevangelou(Re, eD):
r"""Calculates friction factor `f` with Papaevangelou correlation (2009)
.. math::
f = \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 of a pipe, [-]
Returns
-------
f : float
Friction factor, [-]
Notes
-----
Range of validity:
* 1e4 <= Re <= 1e7
* 1e-5 <= eD <= 1e-3
"""
# Eq 12
f = (0.2479-9.47e-5*(7-log10(Re))**4)/log10(eD/3.615+7.366/Re**0.9142)**2
return Dimensionless(f)
[docs]
@refDoc(__doi__, [24])
def f_brkic(Re, eD, alternate=False):
r"""Calculates friction factor `f` with Brkić correlation (2010)
.. math::
f = [-2\log(10^{-0.4343\beta} + \frac{\epsilon}{3.71D})]^{-2}
.. math::
\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 of a pipe, [-]
alternate : boolean
Choose the alternate correlation from the paper
Returns
-------
f : float
Friction factor, [-]
"""
S = log(Re/1.816/log(1.1*Re/log(1+1.1*Re))) # Eq 8
# Eq 7
if alternate:
f = 1/(-2*log10(2.18*S/Re+eD/3.71))**2
else:
f = 1/(-2*log10(10**(-0.4343*S)+eD/3.71))**2
return Dimensionless(f)
[docs]
@refDoc(__doi__, [25])
def f_fang(Re, eD):
r"""Calculates friction factor `f` with Fang-Xua-Zhou correlation (2011)
.. math::
f = 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 of a pipe, [-]
Returns
-------
f : float
Friction factor, [-]
Notes
-----
Range of validity:
* 3e3 <= Re <= 1e8
* eD <= 0.05
"""
# Eq 13
f = 1.613/(log(0.234*eD**1.1007-60.525/Re**1.1105+56.291/Re**1.0712))**2
return Dimensionless(f)
[docs]
@refDoc(__doi__, [26])
def f_ghanbari(Re, eD):
r"""Calculates friction factor `f` with Ghanbari correlation (2011)
Second correlation
.. math::
f = \left(-1.52\log\left(\left(\frac{\epsilon/D}{7.21}\right)^{1.042}
+ \left(\frac{2.731}{Re}\right)^{0.9152}\right)\right)^{-2.169}
Parameters
----------
Re : float
Reynolds number, [-]
eD : float
Relative roughness of a pipe, [-]
Returns
-------
f : float
Friction factor, [-]
"""
# Eq 10
return (-1.52*log10((eD/7.21)**1.042+(2.731/Re)**0.9152))**-2.169
[docs]
@refDoc(__doi__, [28])
def f_Samadianfard(Re, eD):
r"""Calculates friction factor `f` with Samadianfard correlation (2012)
.. math::
f = \frac{Re^{\epsilon/D}-0.6315093}{Re^{1/3}+Re·\epsilon/D}
+ 0.0275308\left(\frac{6.929841}{Re}+\epsilon/D\right)^{1/9}
+ \frac{10^{\epsilon/D}}{\epsilon/D+4.781616} \left(\epsilon/D
+\frac{9.99701}{Re}\right)
Parameters
----------
Re : float
Reynolds number, [-]
eD : float
Relative roughness of a pipe, [-]
Returns
-------
f : float
Friction factor, [-]
"""
# Eq 29
f = (Re**eD-0.6315093)/(Re**(1/3)+Re*eD) + \
0.0275308*(6.929841/Re+eD)**(1/9) + \
10**eD/(eD+4.481616)*(eD**0.5+9.99701/Re)
return f
f_list = (f_colebrook, f_chen, f_Vatankhah, f_buzzelli, f_romeo, f_serghides,
f_zigrang, f_Samadianfard, f_brkic, f_fang, f_ghanbari, f_haaland,
f_round, f_swamee, f_jain, f_barr, f_shacham, f_tsal, f_manadilli,
f_goudar, f_goudar2007, f_avci, f_papaevangelou, f_churchill,
f_chen1979, f_moody, f_wood, f_eck, f_altshul)
[docs]
def f_blasius(Re):
"""
Friction factor by Blasius, for bare tubes
Input parameters:
Re: Reynolds number
"""
return 0.079/Re**0.25
[docs]
@refDoc(__doi__, [32])
def f_annulli_Gnielinski(Re, Di, Do):
"""Friction factor for annulli section in bare tubes using the Gnielinski
correlation (2007)
Input parameters:
Re: Reynolds number, based in hydraulic number
"""
a = Di/Do # Eq 4
phi = ((1+a**2)*log(a) + (1-a**2))/((1-a)**2*log(a)) # Eq 7
Reh = phi*Re # Eq 9
if Reh < 2000:
# Laminar flow
f = 64/Re # Eq 10
else:
# Turbulent flow
f = 1/(1.8*log(Reh)-1.5)**2 # Eq 13
return f
[docs]
@refDoc(__doi__, [29])
def f_friccion(Re, eD=0, method=0, geometry=0, **kw):
"""
Generalized method for calculate friction factor for laminar or turbulent
flux in several geometries
Parameters
----------
Re : float
Reynolds number, [-]
eD : float
Relative roughness of a pipe, [-]
method: int
Index of method to use (default 0 for use Colebrook original function):
* 0 - Colebrook (default)
* 1 - Chen (1987)
* 2 - Vatankhah-Kouchakzadeh (2008)
* 3 - Buzzelli (2008)
* 4 - Romeo (2002)
* 5 - Serghides (1984)
* 6 - Zigrang-Sylvester (1982)
* 7 - Samadianfard (2012)
* 8 - Brkić (2011)
* 9 - Fang-Xu-Zhou (2011)
* 10 - Ghanbari (2011)
* 11 - Haaland (1983)
* 12 - Round (1980)
* 13 - Swamee-Jain (1976)
* 14 - Jain (1976)
* 15 - Barr (1981)
* 16 - Shacham (1980)
* 17 - Tsal (1989)`
* 18 - Manadilli (1997)
* 19 - Goudar (2008)
* 20 - Goudar (2007)
* 21 - Avci (2009)
* 22 - Papaevangelou (2010)
* 23 - Churchill (1977)
* 24 - Chen (1979)
* 25 - Moody (1947)
* 26 - Wood (1966)
* 27 - Eck (1973)
* 28 - Altshul (1975)
geometry: int
Index for duct geometry (Table 7.1, Pag 184 in [29]_)
* 0 - Circular section (default)
* 1 - Square
* 2 - Isosceles triangle
* 3 - Rectangle
* 4 - Ellipse
* 5 - Right triangle
* 6 - Anulli
args: float
Other parameter necessary for noncircular geometries
* Isosceles triangle: Angle, [º]
* Rectangle: Ratio width/height, [-]
* Ellipse: Both diameters of ellipse, [m]
* Right triangle: Angle, [º]
* Anulli: Internal and external diameter, [m]
"""
if geometry == 6:
f = f_annulli_Gnielinski(Re, **kw)
elif Re < 2100:
if geometry == 0:
# Circle
f = 16./Re
elif geometry == 1:
# Square
f = 14.2/Re
elif geometry == 2:
# Isosceles triangle
pass
elif geometry == 3:
# Rectangle
D = kw["D"]
d = kw["d"]
f = 16/(2/3+11/24*d/D*(2-d/D))/Re
elif geometry == 4:
# Ellipse
D = kw["D"]
d = kw["d"]
c = (D-d)/(D+d)
Dh = 4*d*D*(64-16*c**2)/((d+D)*(64-3*c**4))
f = 2*Dh**2*(D**2+d**2)/D**2/d**2/Re
elif geometry == 5:
pass
# elif geometry == 6:
# # Annulli
# # Eq 7.9, 7.10, pag 183
# Di, Do = args
# alpha = (Do-Di)**2/(Do**2+Di**2-(Do**2-Di**2)/log(Do/Di))
# f= 16*alpha/Re
else:
f = f_list[method](Re, eD)
return Dimensionless(f)
[docs]
@refDoc(__doi__, [1])
def eD(Re, f):
"""Calculates relative roughness
Parameters
----------
Re : float
Reynolds number, [-]
f : float
Friction factor, [-]
Returns
-------
eD : float
Relative roughness of a pipe, [-]
"""
eD = (10**(-0.5/f**0.5)-2.51/Re/f**0.5)*3.7
return eD
[docs]
@refDoc(__doi__, [30])
def f_liquid_noisothermal(Re, mu, muW, Gr=None, Pr=None, heating=True):
"""Calculate nonisothermal correction factor to friction factor for liquid
flow
Parameters
----------
Re : float
Reynolds number, [-]
mu : float
Bulk flow temperature viscosity, [Pa·s]
muW : float
Wall flow temperature viscosity, [Pa·s]
Gr : float
Grashof number, [-]
Pr : float
Prandtl number, [-]
heating : boolean
Set heating of cooling process
Returns
-------
fp : float
Nonisothermal correction factor to friction factor in liquid flow, [-]
Examples
--------
B2.1.1.3.1 turbulent flow
>>> print("%0.3f" % f_liquid_noisothermal(24491, 0.208, 0.111))
0.915
B2.1.1.3.2 transition flow
>>> Pr = 0.649*0.83/0.062
>>> beta = -2/(47.6+40.8)*(47.6-40.8)/(82-355)
>>> Gr = 0.0211**3*653**2*9.81*beta*(355-82)/0.000343**2
>>> print("%0.2f" % f_liquid_noisothermal(1656, 0.343, 2.02, Pr=Pr, Gr=Gr, heating=False))
2.64
"""
# Ref in HTRI design manual B2.1.1.2
if Re > 1e4:
# Turbulent flow
# Eq B2.1-12
phiM = (muW/mu)**0.14
psiN = 1
else:
if Re < 1500:
# Laminar flow
# Eq B2.1-14
M = 1
A = 0
else:
# Transition flow
M = 1 + exp(-6.4e6/Re**2)
A = 1e-11*Re**3
if heating:
Ctp = -1
else:
Ctp = 1
B1 = log10(muW/mu)**Ctp
B = 0.28*Ctp*B1**(0.5*M)/M
phiM = 10**B
Enc = (Gr*Pr*(mu/muW))**0.33
psiN = 1 + exp(-214/Enc)
# Eq B2.1-11
return phiM * psiN
[docs]
@refDoc(__doi__, [30, 31])
def f_gas_noisothermal_turbulent(Re, mu, muw, T, Tw, eD=0):
"""Calculate nonisothermal correction factor to friction factor for gas
flow in turbulent regimen
Parameters
----------
Re : float
Reynolds number, [-]
mu : float
Bulk flow temperature viscosity, [Pa·s]
muw : float
Wall flow temperature viscosity, [Pa·s]
T : float
Bulk temperature, [K]
Tw : float
Wall temperature, [K]
eD : float
Relative roughness of a pipe, [-]
Returns
-------
f : float
Non isothermal gas friction factor, [-]
"""
Reeff = Re*(mu/muw)*(T/Tw)
fiso = f_colebrook(Reeff, eD)
# Eq B2.1-24 removing term ab as show in 31_, Eq 7
return fiso*(2/((Tw/T)**0.5+1))**2
if __name__ == "__main__":
for f in f_list:
line = f.__doc__.split("\n")[0]
year = line.split(" ")[-1]
name = line.split(" ")[-3]
doc = name + " " + year
print(f(1e7, 0.0002), doc)
