def calculo(self):
self.entrada = self.kwargs["entrada"]
metodo = self.kwargs["metodo"]
self.Pout = Pressure(self.kwargs["Pout"])
razon = self.kwargs["razon"]
self.rendimientoCalculado = Dimensionless(self.kwargs["rendimiento"])
if self.kwargs["etapas"]:
self.etapas = self.kwargs["etapas"]
else:
self.etapas = 1.
self.power = Power(self.kwargs["trabajo"])
def f(Pout, rendimiento):
W_ideal = self.__Wideal(Pout)
power = W_ideal * self.entrada.caudalmasico.gs / rendimiento
return power
if metodo in [0, 3] or (metodo == 5 and self.Pout):
if self.etapas == 1:
razon = self.Pout.atm / self.entrada.P.atm
else:
razon = (self.Pout.atm / self.entrada.P.atm)**(1. /
self.etapas)
elif metodo in [1, 4] or (metodo == 5 and razon):
if self.etapas == 1:
self.Pout = Pressure(self.entrada.P * razon)
else:
self.Pout = Pressure(razon**self.etapas * self.entrada.P)
if metodo in [0, 1]:
Wideal = self.__Wideal(self.Pout.atm)
power = Wideal * self.entrada.caudalmasico.gs / self.rendimientoCalculado
self.power = Power(power * self.etapas)
elif metodo == 2:
funcion = lambda P: f(P, self.rendimientoCalculado) - self.power
self.Pout = Pressure(fsolve(funcion, self.entrada.P + 1))
if self.etapas == 1:
razon = self.Pout / self.entrada.P
else:
razon = (self.Pout / self.entrada.P)**(1. / self.etapas)
elif metodo in [3, 4]:
funcion = lambda rendimiento: f(self.Pout.atm, rendimiento
) - self.power
self.rendimientoCalculado = Dimensionless(fsolve(funcion, 0.5))
elif metodo == 5:
Wideal = self.__Wideal(self.Pout.atm)
caudalmasico = MassFlow(
self.power * self.rendimientoCalculado / Wideal, "gs")
self.Tout = self.__Tout(Wideal)
self.entrada = self.entrada.clone(caudalMasico=caudalmasico)
Wideal = self.__Wideal(self.Pout.atm)
self.Tout = Temperature(self.__Tout(Wideal))
self.salida = [self.entrada.clone(T=self.Tout, P=self.Pout)]
self.razonCalculada = Dimensionless(self.Pout / self.entrada.P)
self.deltaT = DeltaT(self.salida[0].T - self.entrada.T)
self.deltaP = DeltaP(self.salida[0].P - self.entrada.P)
self.cp_cv = self.entrada.Gas.cp_cv
self.Pin = self.entrada.P
self.Tin = self.entrada.T
def calculo(self):
Gas = self.kwargs["entradaGas"]
Liquido = self.kwargs["entradaLiquido"]
sigma = Liquido.sigma
rhoL = Liquido.Liquido.rho
muL = Liquido.Liquido.mu
self.Dt = Length(self.kwargs["diametro"])
self.Lt = Length(self.kwargs["Lt"])
if self.kwargs["k"]:
self.k = Dimensionless(self.kwargs["k"])
else:
self.k = Dimensionless(1000.)
if self.kwargs["f"]:
self.f = Dimensionless(self.kwargs["f"])
else:
self.f = Dimensionless(0.5)
self.At = Area(pi/4*self.Dt**2)
self.Vg = Speed(Gas.Q/self.At)
self.R = Liquido.Q/Gas.Q
self.dd = Length(58600/self.Vg*(sigma/rhoL)**0.5+597*(
muL/sigma**0.5/rhoL**0.5)**0.45*(1000*self.R)**1.5)
self.rendimiento_parcial = self._Efficiency()
self.rendimiento = self._GlobalEfficiency(self.rendimiento_parcial)
if self.statusDeltaP:
self.deltaP = self._deltaP()
else:
self.deltaP = DeltaP(0)
self.CalcularSalidas(Gas)
self.Pin = min(Gas.P, Liquido.P)
def calculo(self):
self.entrada = self.kwargs["entrada"]
self.rendimientoCalculado = Dimensionless(self.kwargs["rendimiento"])
if self.kwargs["Pout"]:
DeltaP = Pressure(self.kwargs["Pout"] - self.entrada.P)
elif self.kwargs["deltaP"]:
DeltaP = Pressure(self.kwargs["deltaP"])
elif self.kwargs["Carga"]:
DeltaP = Pressure(self.kwargs["Carga"] * self.entrada.Liquido.rho *
g)
else:
DeltaP = Pressure(0)
if self.kwargs["usarCurva"]:
if self.kwargs["diametro"] != self.kwargs["curvaCaracteristica"][
0] or self.kwargs["velocidad"] != self.kwargs[
"curvaCaracteristica"][1]:
self.curvaActual = self.calcularCurvaActual()
else:
self.curvaActual = self.kwargs["curvaCaracteristica"]
self.Ajustar_Curvas_Caracteristicas()
if not self.kwargs["usarCurva"]:
head = Length(DeltaP / g / self.entrada.Liquido.rho)
power = Power(head * g * self.entrada.Liquido.rho *
self.entrada.Q / self.rendimientoCalculado)
P_freno = Power(power * self.rendimientoCalculado)
elif not self.kwargs["incognita"]:
head = Length(polyval(self.CurvaHQ, self.entrada.Q))
self.DeltaP = Pressure(head * g * self.entrada.Liquido.rho)
power = Power(self.entrada.Q * DeltaP)
P_freno = Power(polyval(self.CurvaPotQ, self.entrada.Q))
self.rendimientoCalculado = Dimensionless(power / P_freno)
else:
head = Length(self.DeltaP / g / self.entrada.Liquido.rho)
caudalvolumetrico = roots(
[self.CurvaHQ[0], self.CurvaHQ[1], self.CurvaHQ[2] - head])[0]
power = Power(caudalvolumetrico * self.DeltaP)
self.entrada = Corriente(
self.entrada.T, self.entrada.P.atm,
caudalvolumetrico * self.entrada.Liquido.rho * 3600,
self.entrada.mezcla, self.entrada.solido)
P_freno = Power(polyval(self.CurvaPotQ, caudalvolumetrico))
self.rendimientoCalculado = Dimensionless(power / P_freno)
self.headCalculada = head
self.power = power
self.P_freno = P_freno
self.salida = [self.entrada.clone(P=self.entrada.P + DeltaP)]
self.Pin = self.entrada.P
self.PoutCalculada = self.salida[0].P
self.Q = self.entrada.Q.galUSmin
self.volflow = self.entrada.Q
def calculo(self):
entrada = self.kwargs["entrada"]
self.rendimientoCalculado = Dimensionless(self.kwargs["rendimiento"])
if self.kwargs["Pout"]:
DeltaP = Pressure(self.kwargs["Pout"] - entrada.P)
elif self.kwargs["deltaP"]:
DeltaP = Pressure(self.kwargs["deltaP"])
elif self.kwargs["Carga"]:
DeltaP = Pressure(self.kwargs["Carga"] * entrada.Liquido.rho * g)
else:
DeltaP = Pressure(0)
if self.kwargs["usarCurva"]:
b1 = self.kwargs["diametro"] != self.kwargs["curvaCaracteristica"][
0] # noqa
b2 = self.kwargs["velocidad"] != self.kwargs[
"curvaCaracteristica"][1] # noqa
if b1 or b2:
self.curvaActual = self.calcularCurvaActual()
else:
self.curvaActual = self.kwargs["curvaCaracteristica"]
self.Ajustar_Curvas_Caracteristicas()
if not self.kwargs["usarCurva"]:
head = Length(DeltaP / g / entrada.Liquido.rho)
power = Power(head * g * entrada.Liquido.rho * entrada.Q /
self.rendimientoCalculado)
P_freno = Power(power * self.rendimientoCalculado)
elif not self.kwargs["incognita"]:
head = Length(polyval(self.CurvaHQ, entrada.Q))
DeltaP = Pressure(head * g * entrada.Liquido.rho)
power = Power(entrada.Q * DeltaP)
P_freno = Power(polyval(self.CurvaPotQ, entrada.Q))
self.rendimientoCalculado = Dimensionless(power / P_freno)
else:
head = Length(self.DeltaP / g / entrada.Liquido.rho)
poli = [self.CurvaHQ[0], self.CurvaHQ[1], self.CurvaHQ[2] - head]
Q = roots(poli)[0]
power = Power(Q * self.DeltaP)
entrada = entrada.clone(split=Q / entrada.Q)
P_freno = Power(polyval(self.CurvaPotQ, Q))
self.rendimientoCalculado = Dimensionless(power / P_freno)
self.deltaP = DeltaP
self.headCalculada = head
self.power = power
self.P_freno = P_freno
self.salida = [entrada.clone(P=entrada.P + DeltaP)]
self.Pin = entrada.P
self.PoutCalculada = self.salida[0].P
self.volflow = entrada.Q
self.cp_cv = entrada.Liquido.cp_cv
def calculo(self):
self.entradaGas = self.kwargs["entradaGas"]
self.entradaLiquido = self.kwargs["entradaLiquido"]
self.Dt = Length(self.kwargs["diametro"])
self.Lt = Length(self.kwargs["Lt"])
if self.kwargs["k"]:
self.k = Dimensionless(self.kwargs["k"])
else:
self.k = Dimensionless(1000.)
if self.kwargs["f"]:
self.f = Dimensionless(self.kwargs["f"])
else:
self.f = Dimensionless(0.5)
self.At = Area(pi / 4 * self.Dt**2)
self.Vg = Speed(self.entradaGas.Q / self.At)
self.R = self.entradaLiquido.Q / self.entradaGas.Q
self.dd = Length(58600 *
(self.entradaLiquido.Liquido.sigma /
self.entradaLiquido.Liquido.rho)**0.5 / self.Vg**2 +
597 * (self.entradaLiquido.Liquido.mu /
self.entradaLiquido.Liquido.epsilon**0.5 /
self.entradaLiquido.Liquido.rho**0.5)**0.45 *
(1000 * self.R)**1.5)
self.efficiency_i = self._Efficiency()
self.efficiencyCalc = self._GlobalEfficiency(self.efficiency_i)
if self.statusDeltaP:
self.deltaP = self._deltaP()
else:
self.deltaP = DeltaP(0)
Solido_NoCapturado, Solido_Capturado = self.entradaGas.solido.Separar(
self.efficiency_i)
self.Pin = min(self.entradaGas.P, self.entradaLiquido.P)
self.Pout = Pressure(self.Pin - self.deltaP)
self.Min = self.entradaGas.solido.caudal
self.Dmin = self.entradaGas.solido.diametro_medio
self.Mr = Solido_NoCapturado.caudal
self.Dmr = Solido_NoCapturado.diametro_medio
self.Ms = Solido_Capturado.caudal
self.Dms = Solido_Capturado.diametro_medio
self.salida = []
self.salida.append(
self.entradaGas.clone(solido=Solido_NoCapturado,
P=self.Pin - self.deltaP))
self.salida.append(
self.entradaLiquido.clone(solido=Solido_Capturado,
P=self.Pin - self.deltaP))
def calculo(self):
self.entrada = self.kwargs["entrada"]
self.Pout = Pressure(self.kwargs["Pout"])
self.razon = Dimensionless(self.kwargs["razon"])
self.rendimientoCalculado = Dimensionless(self.kwargs["rendimiento"])
self.power = Power(-abs(self.kwargs["trabajo"]))
def f(Pout, rendimiento):
W_ideal = self.__Wideal(Pout)
power = W_ideal * self.entrada.caudalmasico.gs * rendimiento
return power
self.cp_cv = self.entrada.Gas.cp_cv
if self.kwargs["metodo"] in [0, 3] or (self.kwargs["metodo"] == 5
and self.Pout):
self.razon = Dimensionless(self.Pout / self.entrada.P)
elif self.kwargs["metodo"] in [1, 4] or (self.kwargs["metodo"] == 5
and self.razon):
self.Pout = Pressure(self.entrada.P * self.razon)
if self.kwargs["metodo"] in [0, 1]:
Wideal = self.__Wideal(self.Pout)
self.power = Power(Wideal * self.entrada.caudalmasico.gs *
self.rendimientoCalculado)
elif self.kwargs["metodo"] == 2:
funcion = lambda P: f(P, self.rendimientoCalculado) - self.power
self.Pout = Pressure(fsolve(funcion, self.entrada.P.atm + 1),
"atm")
self.razon = Dimensionless(self.Pout / self.entrada.P)
elif self.kwargs["metodo"] in [3, 4]:
funcion = lambda rendimiento: f(self.Pout.atm, rendimiento
) - self.power
self.rendimientoCalculado = fsolve(funcion, 0.5)
elif self.kwargs["metodo"] == 5:
Wideal = self.__Wideal(self.Pout)
caudalmasico = MassFlow(
self.power / self.rendimientoCalculado / Wideal, "gs")
self.Tout = self.__Tout(Wideal)
self.entrada = self.entrada.clone(caudalMasico=caudalmasico)
Wideal = self.__Wideal(self.Pout)
self.Tout = Temperature(self.__Tout(Wideal))
self.razonCalculada = Dimensionless(self.Pout / self.entrada.P)
self.salida = [self.entrada.clone(T=self.Tout, P=self.Pout)]
self.deltaT = DeltaT(self.salida[0].T - self.entrada.T)
self.deltaP = DeltaP(self.salida[0].P - self.entrada.P)
self.Pin = self.entrada.P
self.Tin = self.entrada.T
def f_papaevangelou(Re, eD):
"""
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
References
----------
.. [23] Papaevangelou, G., Evangelides, C., Tzimopoulos, C., A new explicit
relation for friction coefficient in the Darcy-Weisbach equation.
Proceedings of the Tenth Conference on Protection and Restoration of
the Environment 166,1-7pp, PRE10 July 6-09 2010 Corfu, Greece.
"""
f = (0.2479-9.47e-5*(7-log10(Re))**4)/log10(eD/3.615+7.366/Re**0.9142)**2
return Dimensionless(f)
def f_goudar(Re, eD):
"""
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, [-]
References
----------
.. [19] Goudar, C.T. Sonnad J.R. Comparison of the iterative approximations
of the Colebrook-White equation. Hydrocarb Process 87 (2008), 79-83
"""
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)
def f_buzzelli(Re, eD):
"""
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]
A = \frac{0.774\ln(Re)-1.41}{1+1.32\sqrt{\frac{\epsilon}{D}}}
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, [-]
References
----------
.. [20] Buzzelli, D. Calculating friction in one step. Machine Design, 80,
(2008) 54–55.
"""
# 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)
def f_manadilli(Re, eD):
"""
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
References
----------
.. [17] Manadilli, G. Replace implicit equations with signomial functions.
Chem Eng 104 (1997), 129-132.
"""
f = 1/(-2*log10(eD/3.7+95./Re**0.983-96.82/Re))**2
return Dimensionless(f)
def f_goudar2006(Re, eD):
"""
Calculates friction factor `f` with Goudar-Sonnad correlation (2006)
.. math::
\frac{1}{\sqrt{f}} = 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 of a pipe, [-]
Returns
-------
f : float
Friction factor, [-]
Notes
-----
Range of validity
4e3 <= Re <= 1e8
1e-6 <= eD <= 0.05
References
----------
.. [19] Goudar, C.T. Sonnad J.R. Comparison of the iterative approximations
of the Colebrook-White equation. Hydrocarb Process 87 (2008), 79-83
"""
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)
def f_moody(Re, eD):
"""
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.
References
----------
.. [4] Moody, L. F. (1947). An approximate formula for pipe friction
factors. Trans. ASME, 69(12), 1005–1006.
"""
f = 5.5e-3*(1+(2e4*eD+1e6/Re)**(1./3))
return Dimensionless(f)
def f_shacham(Re, eD):
"""
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
References
----------
.. [16] Shacham M. An explicit equation for friction factor in pipe. Ind
Eng Chem Fund 19 (1980), 228 - 229.
"""
f = 1/(-2*log10(eD/3.7-5.02/Re*log10(eD/3.7+14.5/Re)))**2
return Dimensionless(f)
def _GlobalEfficiency(self, rendimientos):
Gas = self.kwargs["entradaGas"]
rendimiento_global = 0
for i, fraccion in enumerate(Gas.solido.fracciones):
rendimiento_global += rendimientos[i]*fraccion
return Dimensionless(rendimiento_global)
def Nu(alfa, L, k):
r"""Calculates Nusselt number or `Nu`.
.. math::
Nu = \frac{\alpha L}{k}
Parameters
----------
k : float
Thermal conductivity, [W/m/K]
L : float
Characteristic length, [m]
alpha : float
Heat transfer coefficient, [W/m²/K]
Returns
-------
Nu : float
Nusselt number, [-]
Notes
-----
Nusselt number is a dimensionless heat transfer coeffcient.
Be careful with the characteristic lenght definition, it deppend of system
configuration (internal diameter in a flow channel).
Examples
--------
>>> print("%0.1f" % Nu(102.3, 0.03927, 0.03181))
126.3
"""
return Dimensionless(alfa * L / k)
def f_swamee(Re, eD):
"""
Calculates friction factor `f` with Swamee-Jain correlation (1976)
.. math::
\frac{1}{\sqrt{f_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
References
----------
.. [10] Swamee, P.K.; Jain, A.K. (1976). Explicit equations for pipe-flow
problems. Journal of the Hydraulics Division (ASCE) 102 (5): 657–664.
"""
f = 1/(-2*log10(eD/3.7+(6.97/Re)**0.9))**2
return Dimensionless(f)
def f_chen1979(Re, eD):
"""
Calculates friction factor `f` with Chen correlation (1979)
.. math::
$\frac{1}{\sqrt{f}}=-2\log\left(\frac{\nicefrac{\epsilon}{D}}{3.7065}-\frac{5.0452}{Re}\log\left(\frac{\left(\nicefrac{\epsilon}{D}\right)^{1.1098}}{2.8257}+\left(\frac{7.149}{Re}\right)^{0.8981}\right)\right)$
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
References
----------
.. [2] Chen, H-J, An Explicit Equation for Friction Factor in Pipe, Ind.
Eng. Chem. Fundam., Vol. 18, No. 3, 1979, p. 297..
"""
# 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)
def f_round(Re, eD):
"""
Calculates friction factor `f` with Round correlation (1980)
.. math::
\frac{1}{\sqrt{f}} = 1.8\log\left[\frac{Re}{0.135Re
\frac{\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
References
----------
.. [9] Round, G. F. (1980), An explicit approximation for the friction
factor-reynolds number relation for rough and smooth pipes. Can. J.
Chem. Eng., 58: 122–123.
"""
# Eq 8
f = 1/(1.8*log10(Re/(0.135*Re*eD+6.5)))**2
return Dimensionless(f)
def f_serghides(Re, eD):
"""
Calculates friction factor `f` with Serguides correlation (1984)
.. 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 of a pipe, [-]
Returns
-------
f : float
Friction factor, [-]
References
----------
.. [8] Serghides, T. K. (1984). Estimate friction factor accurately.
Chem. Eng., 91(5), 63–64.
"""
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)
def f_haaland(Re, eD):
"""
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
References
----------
.. [7] Haaland, S. E. (1983). Simple and explicit formulas for the
friction factor in turbulent flow. J. Fluids Eng., 105(1), 89–90.
"""
# Eq 8
f = 1/(-1.8*log10((eD/3.75)**1.11+6.9/Re))**2
return Dimensionless(f)
def f_avci(Re, eD):
"""
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, [-]
References
----------
.. [22] Avci, A.; Karagoz, I. A Novel Explicit Equation for Friction Factor
in Smooth and Rough Pipes; J. Fluids Eng 131(6), 061203 (2009)
"""
# Eq 17
f = 6.4/(log(Re)-log(1+0.01*Re*eD*(1+10*eD**0.5)))**2.4
return Dimensionless(f)
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)
def f_jain(Re, eD):
"""
Calculates friction factor `f` with Jain correlation (1976)
.. math::
\frac{1}{\sqrt{f_f}} = 1.14 - 2\log\left[ \frac{\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
References
----------
.. [11] Jain, Akalank K. Accurate Explicit Equation for Friction Factor.
Journal of the Hydraulics Division 102, no. 5 (May 1976): 674-77.
"""
f = 1/(1.14-2*log10(eD+(29.843/Re)**0.9))**2
return Dimensionless(f)
def f_chen(Re, eD):
"""
Calculates friction factor `f` with Chen correlation (1991)
.. math::
$\frac{1}{\sqrt{f}}=-4\log\left(\frac{\nicefrac{\epsilon}{D}}{3.7}-\frac{5.02}{Re}\log\left(\frac{\nicefrac{\epsilon}{D}}{3.7}+\left(\frac{6.7}{Re}\right)^{0.9}\right)\right)$
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].
References
----------
.. [3] Chen, H-J, An Exact Solution to the Colebrook Equation, Chem.
Eng., Vol. 94, No. 2, 1987, p. 196..
"""
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)
def f_barr(Re, eD):
"""
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, [-]
References
----------
.. [12] Barr D.I.H. (1981). Solutions of the Colebrook-White functions for
resistance to uniform turbulent flows. Proc Inst Civil Eng 71, 529-536.
"""
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)
def f_altshul(Re, eD):
"""
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, [-]
References
----------
.. [14] Tsal RJ (1989). Altshul-Tsal friction factor equation. Heating
Piping Air Conditioning 8, 30-45.
"""
f = 0.11*(eD+68/Re)**0.25
return Dimensionless(f)
def Fo(k, L, t):
r"""Calculates Fourier number `Fo`.
.. math::
Fo = \frac{kt}{l^2}
Parameters
----------
k : float
Thermal diffusivity [m²/s]
L : float
Characteristic length [m]
t : float
Time of cooling or heating [s]
Returns
-------
Fo : float
Fourier number, [-]
Notes
-----
Can be seen as a adimensional time.
It is commonly used in transient conduction problems.
Examples
--------
>>> print("%0.1f" % Fo(7e-6, 0.01, 60))
4.2
"""
return Dimensionless(k * t / L**2)
def f_eck(Re, eD):
"""
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, [-]
References
----------
.. [15] Eck B. Technische Stromungslehre. Springer, New York, 1973.
"""
f = 1/(-2*log10(eD/3.71+15/Re))**2
return Dimensionless(f)
def Ra(Pr, Gr):
r"""Calculates Rayleigh number or `Ra` using Prandtl number `Pr` and
Grashof number `Gr` for a fluid with the given
properties, temperature difference, and characteristic length used
to calculate `Gr` and `Pr`.
.. math::
Ra = PrGr
Parameters
----------
Pr : float
Prandtl number, [-]
Gr : float
Grashof number, [-]
Returns
-------
Ra : float
Rayleigh number, [-]
Notes
-----
Used in free convection problems only.
"""
return Dimensionless(Pr * Gr)
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)
