iapws-1.0.2/ 0000755 0001750 0001750 00000000000 12146106671 013773 5 ustar amckinstry amckinstry iapws-1.0.2/setup.py 0000644 0001750 0001750 00000000650 12146106660 015504 0 ustar amckinstry amckinstry from distutils.core import setup
setup(
name = 'iapws',
version = '1.0.2',
py_modules = ['iapws'],
author = 'jjgomera',
author_email = 'jjgomera@gmail.com',
url = '',
description = 'Python implementation of international-standard IAPWS-IF97 steam tables ',
license = "gpl v3")
iapws-1.0.2/license 0000644 0001750 0001750 00000104513 12146106660 015342 0 ustar amckinstry amckinstry GNU GENERAL PUBLIC LICENSE
Version 3, 29 June 2007
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END OF TERMS AND CONDITIONS
How to Apply These Terms to Your New Programs
If you develop a new program, and you want it to be of the greatest
possible use to the public, the best way to achieve this is to make it
free software which everyone can redistribute and change under these terms.
To do so, attach the following notices to the program. It is safest
to attach them to the start of each source file to most effectively
state the exclusion of warranty; and each file should have at least
the "copyright" line and a pointer to where the full notice is found.
Copyright (C)
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 .
Also add information on how to contact you by electronic and paper mail.
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Copyright (C)
This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
This is free software, and you are welcome to redistribute it
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The hypothetical commands `show w' and `show c' should show the appropriate
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if any, to sign a "copyright disclaimer" for the program, if necessary.
For more information on this, and how to apply and follow the GNU GPL, see
.
The GNU General Public License does not permit incorporating your program
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may consider it more useful to permit linking proprietary applications with
the library. If this is what you want to do, use the GNU Lesser General
Public License instead of this License. But first, please read
.
iapws-1.0.2/iapws.py 0000644 0001750 0001750 00000336025 12146106660 015477 0 ustar amckinstry amckinstry #!/usr/bin/python
# -*- coding: utf-8 -*-
##########################################################################
### Implementación de la IAPWS-IF97 Steam Tables ###
##########################################################################
from math import sqrt, log, exp, tan, atan, acos
from scipy.optimize import fsolve
#Boundary Region1-Region2
def _h13_s(s):
"""Define the boundary between Region 1 and 3, h=f(s)
>>> "%.6f" % _h13_s(3.7)
'1632.525047'
>>> "%.6f" % _h13_s(3.5)
'1566.104611'
"""
sigma=s/3.8
I=[0, 1, 1, 3, 5, 6]
J=[0, -2, 2, -12, -4, -3]
n=[0.913965547600543, -0.430944856041991e-4, 0.603235694765419e2, 0.117518273082168e-17, 0.220000904781292, -0.690815545851641e2]
suma=0
for i in range(6):
suma+=n[i]*(sigma-0.884)**I[i]*(sigma-0.864)**J[i]
return 1700*suma
#Boundary Region2-Region3
def _P23_T(T):
"""Define the boundary between Region 2 and 3, P=f(T)
>>> "%.8f" % _P23_T(623.15)
'16.52916425'
"""
n=[0, 0.34805185628969e3, -0.11671859879975e1, 0.10192970039326e-2,0.57254459862746e3, 0.1391883977870e2]
return n[1]+n[2]*T+n[3]*T**2
def _t_P(P):
"""Define the boundary between Region 2 and 3, T=f(P)
>>> "%.2f" % _t_P(16.52916425)
'623.15'
"""
n=[0, 0.34805185628969e3, -0.11671859879975e1, 0.10192970039326e-2,0.57254459862746e3, 0.1391883977870e2]
return n[4]+((P-n[5])/n[3])**0.5
def _t_hs(h, s):
"""Define the boundary between Region 2 and 3, T=f(h,s)
>>> "%.7f" % _t_hs(2600, 5.1)
'713.5259364'
>>> "%.7f" % _t_hs(2800, 5.2)
'817.6202120'
"""
nu=h/3000
sigma=s/5.3
I=[-12, -10, -8, -4, -3, -2, -2, -2, -2, 0, 1, 1, 1, 3, 3, 5, 6, 6, 8, 8, 8, 12, 12, 14, 14]
J=[10, 8, 3, 4, 3, -6, 2, 3, 4, 0, -3, -2, 10, -2, -1, -5, -6, -3, -8, -2, -1, -12, -1, -12, 1]
n=[0.629096260829810e-3, -0.823453502583165e-3, 0.515446951519474e-7, -0.117565945784945e1, 0.348519684726192e1, -0.507837382408313e-11, -0.284637670005479e1, -0.236092263939673e1, 0.601492324973779e1, 0.148039650824546e1, 0.360075182221907e-3, -0.126700045009952e-1, -0.122184332521413e7, 0.149276502463272, 0.698733471798484, -0.252207040114321e-1, 0.147151930985213e-1, -0.108618917681849e1, -0.936875039816322e-3, 0.819877897570217e2, -0.182041861521835e3, 0.261907376402688e-5, -0.291626417025961e5, 0.140660774926165e-4, 0.783237062349385e7]
suma=0
for i in range(25):
suma+=n[i]*(nu-0.727)**I[i]*(sigma-0.864)**J[i]
return 900*suma
#Saturated line
def _PSat_T(T):
"""Define the saturated line, P=f(T)
>>> "%.8f" % _PSat_T(500)
'2.63889776'
"""
if T<273.15:
T=273.15
elif T>Tc:
T=Tc
n=[0, 0.11670521452767E+04, -0.72421316703206E+06, -0.17073846940092E+02, 0.12020824702470E+05, -0.32325550322333E+07, 0.14915108613530E+02, -0.48232657361591E+04, 0.40511340542057E+06, -0.23855557567849E+00, 0.65017534844798E+03]
tita=T+n[9]/(T-n[10])
A=tita**2+n[1]*tita+n[2]
B=n[3]*tita**2+n[4]*tita+n[5]
C=n[6]*tita**2+n[7]*tita+n[8]
return (2*C/(-B+(B**2-4*A*C)**0.5))**4
def _TSat_P(P):
"""Define the saturated line, T=f(P)
>>> "%.6f" % _TSat_P(10)
'584.149488'
"""
if P<611.212677/1e6:
P=611.212677/1e6
elif P>22.064:
P=22.064
n=[0, 0.11670521452767E+04, -0.72421316703206E+06, -0.17073846940092E+02, 0.12020824702470E+05, -0.32325550322333E+07, 0.14915108613530E+02, -0.48232657361591E+04, 0.40511340542057E+06, -0.23855557567849E+00, 0.65017534844798E+03]
beta=P**0.25
E=beta**2+n[3]*beta+n[6]
F=n[1]*beta**2+n[4]*beta+n[7]
G=n[2]*beta**2+n[5]*beta+n[8]
D=2*G/(-F-(F**2-4*E*G)**0.5)
return (n[10]+D-((n[10]+D)**2-4*(n[9]+n[10]*D))**0.5)/2
def _PSat_h(h):
"""Define the saturated line, P=f(h)
>>> "%.8f" % _PSat_h(1700)
'17.24175718'
>>> "%.8f" % _PSat_h(2400)
'20.18090839'
"""
hmin_Ps3=_Region1(623.15, _PSat_T(623.15))["h"]
hmax_Ps3=_Region2(623.15, _PSat_T(623.15))["h"]
if hhmax_Ps3:
h=hmax_Ps3
nu=h/2600
I=[0, 1, 1, 1, 1, 5, 7, 8, 14, 20, 22, 24, 28, 36]
J=[0, 1, 3, 4, 36, 3, 0, 24, 16, 16, 3, 18, 8, 24]
n=[0.600073641753024, -0.936203654849857e1, 0.246590798594147e2, -0.107014222858224e3, -0.915821315805768e14, -0.862332011700662e4, -0.235837344740032e2, 0.252304969384128e18, -0.389718771997719e19, -0.333775713645296e23, 0.356499469636328e11, -0.148547544720641e27, 0.330611514838798e19, 0.813641294467829e38]
suma=0
for i in range(14):
suma+=n[i]*(nu-1.02)**I[i]*(nu-0.608)**J[i]
return 22*suma
def _PSat_s(s):
"""Define the saturated line, P=f(s)
>>> "%.8f" % _PSat_s(3.8)
'16.87755057'
>>> "%.8f" % _PSat_s(5.2)
'16.68968482'
"""
sigma=s/5.2
I=[0, 1, 1, 4, 12, 12, 16, 24, 28, 32]
J=[0, 1, 32, 7, 4, 14, 36, 10, 0, 18]
n=[0.639767553612785, -0.129727445396014e2, -0.224595125848403e16, 0.177466741801846e7, 0.717079349571538e10, -0.378829107169011e18, -0.955586736431328e35, 0.187269814676188e24, 0.119254746466473e12, 0.110649277244882e37]
suma=0
for i in range(10):
suma+=n[i]*(sigma-1.03)**I[i]*(sigma-0.699)**J[i]
return 22*suma
def _h1_s(s):
"""Define the saturated line boundary between Region 1 and 4, h=f(s)
>>> "%.7f" % _h1_s(1)
'308.5509647'
>>> "%.6f" % _h1_s(3)
'1198.359754'
"""
sigma=s/3.8
I=[0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 7, 8, 12, 12, 14, 14, 16, 20, 20, 22, 24, 28, 32, 32]
J=[14, 36, 3, 16, 0, 5, 4, 36, 4, 16, 24, 18, 24, 1, 4, 2, 4, 1, 22, 10, 12, 28, 8, 3, 0, 6, 8]
n=[0.332171191705237, 0.611217706323496e-3, -0.882092478906822e1, -0.455628192543250, -0.263483840850452e-4, -0.223949661148062e2, -0.428398660164013e1, -0.616679338856916, -0.146823031104040e2, 0.284523138727299e3, -0.113398503195444e3, 0.115671380760859e4, 0.395551267359325e3, -0.154891257229285e1, 0.194486637751291e2, -0.357915139457043e1, -0.335369414148819e1, -0.664426796332460, 0.323321885383934e5, 0.331766744667084e4, -0.223501257931087e5, 0.573953875852936e7, 0.173226193407919e3, -0.363968822121321e-1, 0.834596332878346e-6, 0.503611916682674e1, 0.655444787064505e2]
suma=0
for i in range(27):
suma+=n[i]*(sigma-1.09)**I[i]*(sigma+0.366e-4)**J[i]
return 1700*suma
def _h3a_s(s):
"""Define the saturated line boundary between Region 4 and 3a, h=f(s)
>>> "%.6f" % _h3a_s(3.8)
'1685.025565'
>>> "%.6f" % _h3a_s(4.2)
'1949.352563'
"""
sigma=s/3.8
I=[0, 0, 0, 0, 2, 3, 4, 4, 5, 5, 6, 7, 7, 7, 10, 10, 10, 32, 32]
J=[1, 4, 10, 16, 1, 36, 3, 16, 20, 36, 4, 2, 28, 32, 14, 32, 36, 0, 6]
n=[0.822673364673336, 0.181977213534479, -0.112000260313624e-1, -0.746778287048033e-3, -0.179046263257381, 0.424220110836657e-1, -0.341355823438768, -0.209881740853565e1, -0.822477343323596e1, -0.499684082076008e1, 0.191413958471069, 0.581062241093136e-1, -0.165505498701029e4, 0.158870443421201e4, -0.850623535172818e2, -0.317714386511207e5, -0.945890406632871e5, -0.139273847088690e-5, 0.631052532240980]
suma=0
for i in range(19):
suma+=n[i]*(sigma-1.09)**I[i]*(sigma+0.366e-4)**J[i]
return 1700*suma
def _h2ab_s(s):
"""Define the saturated line boundary between Region 4 and 2a-2b, h=f(s)
>>> "%.6f" % _h2ab_s(7)
'2723.729985'
>>> "%.6f" % _h2ab_s(9)
'2511.861477'
"""
sigma1=s/5.21
sigma2=s/9.2
I=[1, 1, 2, 2, 4, 4, 7, 8, 8, 10, 12, 12, 18, 20, 24, 28, 28, 28, 28, 28, 32, 32, 32, 32, 32, 36, 36, 36, 36, 36]
J=[8, 24, 4, 32, 1, 2, 7, 5, 12, 1, 0, 7, 10, 12, 32, 8, 12, 20, 22, 24, 2, 7, 12, 14, 24, 10, 12, 20, 22, 28]
n=[-0.524581170928788e3, -0.926947218142218e7, -0.237385107491666e3, 0.210770155812776e11, -0.239494562010986e2, 0.221802480294197e3, -0.510472533393438e7, 0.124981396109147e7, 0.200008436996201e10, -0.815158509791035e3, -0.157612685637523e3, -0.114200422332791e11, 0.662364680776872e16, -0.227622818296144e19, -0.171048081348406e32, 0.660788766938091e16, 0.166320055886021e23, -0.218003784381501e30, -0.787276140295618e30, 0.151062329700346e32, 0.795732170300541e7, 0.131957647355347e16, -0.325097068299140e24, -0.418600611419248e26, 0.297478906557467e35, -0.953588761745473e20, 0.166957699620939e25, -0.175407764869978e33, 0.347581490626396e35, -0.710971318427851e39]
suma=0
for i in range(30):
suma+=n[i]*(1/sigma1-0.513)**I[i]*(sigma2-0.524)**J[i]
return 2800*exp(suma)
def _h2c3b_s(s):
"""Define the saturated line boundary between Region 4 and 2c-3b, h=f(s)
>>> "%.6f" % _h2c3b_s(5.5)
'2687.693850'
>>> "%.6f" % _h2c3b_s(4.5)
'2144.360448'
"""
sigma=s/5.9
I=[0, 0, 0, 1, 1, 5, 6, 7, 8, 8, 12, 16, 22, 22, 24, 36]
J=[0, 3, 4, 0, 12, 36, 12, 16, 2, 20, 32, 36, 2, 32, 7, 20]
n=[0.104351280732769e1, -0.227807912708513e1, 0.180535256723202e1, 0.420440834792042, -0.105721244834660e6, 0.436911607493884e25, -0.328032702839753e12, -0.678686760804270e16, 0.743957464645363e4, -0.356896445355761e20, 0.167590585186801e32, -0.355028625419105e38, 0.396611982166538e12, -0.414716268484468e41, 0.359080103867382e19, -0.116994334851995e41]
suma=0
for i in range(16):
suma+=n[i]*(sigma-1.02)**I[i]*(sigma-0.726)**J[i]
return 2800*suma**4
#Region 1
def _Region1(T, P):
"""Basic equation for region 1
>>> "%.11f" % _Region1(300,3)["v"]
'0.00100215168'
>>> "%.6f" % _Region1(300,3)["h"]
'115.331273'
>>> "%.6f" % (_Region1(300,3)["h"]-3000*_Region1(300,3)["v"], )
'112.324818'
>>> "%.9f" % _Region1(300,80)["s"]
'0.368563852'
>>> "%.8f" % _Region1(300,80)["cp"]
'4.01008987'
>>> "%.8f" % _Region1(300,80)["cv"]
'3.91736606'
>>> "%.5f" % _Region1(500,3)["w"]
'1240.71337'
>>> "%.11f" % _Region1(500,3)["alfav"]
'0.00164118128'
>>> "%.11f" % _Region1(500,3)["kt"]
'0.00112892188'
"""
n=[0.14632971213167, -0.84548187169114, -0.37563603672040e1, 0.33855169168385e1, -0.95791963387872, 0.15772038513228, -0.16616417199501e-1, 0.81214629983568e-3, 0.28319080123804e-3, -0.60706301565874e-3, -0.18990068218419e-1, -0.32529748770505e-1, -0.21841717175414e-1, -0.52838357969930e-4, -0.47184321073267e-3, -0.30001780793026e-3, 0.47661393906987e-4, -0.44141845330846e-5, -0.72694996297594e-15, -0.31679644845054e-4, -0.28270797985312e-5, -0.85205128120103e-9, -0.22425281908000e-5, -0.65171222895601e-6, -0.14341729937924e-12, -0.40516996860117e-6, -0.12734301741641e-8, -0.17424871230634e-9, -0.68762131295531e-18, 0.14478307828521e-19, 0.26335781662795e-22, -0.11947622640071e-22, 0.18228094581404e-23, -0.93537087292458e-25]
I=[0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 8, 8, 21, 23, 29, 30, 31, 32]
J=[-2, -1, 0, 1, 2, 3, 4, 5, -9, -7, -1, 0, 1, 3, -3, 0, 1, 3, 17, -4, 0, 6, -5, -2, 10, -8, -11, -6, -29, -31, -38, -39, -40, -41]
Tr=1386/T
Pr=P/16.53
g=gp=gpp=gt=gtt=gpt=0
for i in range(34):
g+=n[i]*(7.1-Pr)**I[i]*(Tr-1.222)**J[i]
gp-=n[i]*I[i]*(7.1-Pr)**(I[i]-1)*(Tr-1.222)**J[i]
gpp+=n[i]*I[i]*(I[i]-1)*(7.1-Pr)**(I[i]-2)*(Tr-1.222)**J[i]
gt+= n[i] * (7.1-Pr)**I[i] * J[i] * (Tr-1.222)**(J[i]-1)
gtt+=n[i]*(7.1-Pr)**I[i]*J[i]*(J[i]-1)*(Tr-1.222)**(J[i]-2)
gpt-=n[i]*I[i]*(7.1-Pr)**(I[i]-1)*J[i]*(Tr-1.222)**(J[i]-1)
propiedades={}
propiedades["T"]=T
propiedades["P"]=P
propiedades["v"]=Pr*gp*R*T/P/1000
propiedades["h"]=Tr*gt*R*T
propiedades["s"]=R*(Tr*gt-g)
propiedades["cp"]=-R*Tr**2*gtt
propiedades["cv"]=R*(-Tr**2*gtt+(gp-Tr*gpt)**2/gpp)
propiedades["w"]=sqrt(R*T*1000*gp**2/((gp-Tr*gpt)**2/(Tr**2*gtt)-gpp))
propiedades["alfav"]=(1-Tr*gpt/gp)/T
propiedades["kt"]=-Pr*gpp/gp/P
propiedades["region"]=1
propiedades["x"]=0
return propiedades
def _Backward1_T_Ph(P, h):
"""Backward equation for region 1, T=f(P,h)
>>> "%.6f" % _Backward1_T_Ph(3,500)
'391.798509'
>>> "%.6f" % _Backward1_T_Ph(80,1500)
'611.041229'
"""
I=[0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 5, 6]
J=[0, 1, 2, 6, 22, 32, 0, 1, 2, 3, 4, 10, 32, 10, 32, 10, 32, 32, 32, 32]
n=[-0.23872489924521e3, 0.40421188637945e3, 0.11349746881718e3, -0.58457616048039e1, -0.15285482413140e-3, -0.10866707695377e-5, -0.13391744872602e2, 0.43211039183559e2, -0.54010067170506e2, 0.30535892203916e2, -0.65964749423638e1, 0.93965400878363e-2, 0.11573647505340e-6, -0.25858641282073e-4, -0.40644363084799e-8, 0.66456186191635e-7, 0.80670734103027e-10, -0.93477771213947e-12, 0.58265442020601e-14, -0.15020185953503e-16]
Pr=P/1
nu=h/2500
T=0
for i in range(20):
T+=n[i]*Pr**I[i]*(nu+1)**J[i]
return T
def _Backward1_T_Ps(P, s):
"""Backward equation for region 1, T=f(P,s)
>>> "%.6f" % _Backward1_T_Ps(3,0.5)
'307.842258'
>>> "%.6f" % _Backward1_T_Ps(80,3)
'565.899909'
"""
I=[0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 4]
J=[0, 1, 2, 3, 11, 31, 0, 1, 2, 3, 12, 31, 0, 1, 2, 9, 31, 10, 32, 32]
n=[0.17478268058307e3, 0.34806930892873e2, 0.65292584978455e1, 0.33039981775489, -0.19281382923196e-6, -0.24909197244573e-22, -0.26107636489332, 0.22592965981586, -0.64256463395226e-1, 0.78876289270526e-2, 0.35672110607366e-9, 0.17332496994895e-23, 0.56608900654837e-3, -0.32635483139717e-3, 0.44778286690632e-4, -0.51322156908507e-9, -0.42522657042207e-25, 0.26400441360689e-12, 0.78124600459723e-28, -0.30732199903668e-30]
Pr=P/1
sigma=s/1
T=0
for i in range(20):
T+=n[i]*Pr**I[i]*(sigma+2)**J[i]
return T
def _Backward1_P_hs(h, s):
"""Backward equation for region 1, P=f(h,s)
>>> "%.13f" % _Backward1_P_hs(0.001,0)
'0.0009800980612'
>>> "%.8f" % _Backward1_P_hs(90,0)
'91.92954727'
>>> "%.8f" % _Backward1_P_hs(1500,3.4)
'58.68294423'
"""
I=[0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 4, 4, 5]
J=[0, 1, 2, 4, 5, 6, 8, 14, 0, 1, 4, 6, 0, 1, 10, 4, 1, 4, 0]
n=[-0.691997014660582, -0.183612548787560e2, -0.928332409297335e1, 0.659639569909906e2, -0.162060388912024e2, 0.450620017338667e3, 0.854680678224170e3, 0.607523214001162e4, 0.326487682621856e2, -0.269408844582931e2, -0.319947848334300e3, -0.928354307043320e3, 0.303634537455249e2, -0.650540422444146e2, -0.430991316516130e4, -0.747512324096068e3, 0.730000345529245e3, 0.114284032569021e4, -0.436407041874559e3]
nu=h/3400
sigma=s/7.6
P=0
for i in range(19):
P+=n[i]*(nu+0.05)**I[i]*(sigma+0.05)**J[i]
return 100*P
#Region 2
def _Region2(T, P):
"""Basic equation for region 2
>>> "%.11f" % _Region2(700,30)["v"]
'0.00542946619'
>>> "%.5f" % _Region2(700,30)["h"]
'2631.49474'
>>> "%.5f" % (_Region2(700,30)["h"]-30000*_Region2(700,30)["v"], )
'2468.61076'
>>> "%.7f" % _Region2(700,0.0035)["s"]
'10.1749996'
>>> "%.8f" % _Region2(700,0.0035)["cp"]
'2.08141274'
>>> "%.8f" % _Region2(700,0.0035)["cv"]
'1.61978333'
>>> "%.6f" % _Region2(300,0.0035)["w"]
'427.920172'
>>> "%.11f" % _Region2(300,0.0035)["alfav"]
'0.00337578289'
>>> "%.6f" % _Region2(300,0.0035)["kt"]
'286.239651'
"""
Tr=540/T
Pr=P/1
Jo=[0, 1, -5, -4, -3, -2, -1, 2, 3]
no=[-0.96927686500217E+01, 0.10086655968018E+02, -0.56087911283020E-02, 0.71452738081455E-01, -0.40710498223928E+00, 0.14240819171444E+01, -0.43839511319450E+01, -0.28408632460772E+00, 0.21268463753307E-01]
go=log(Pr)
gop=Pr**-1
gopp=-Pr**-2
got=gott=gopt=0
for i in range(9):
go+=no[i]*Tr**Jo[i]
got+=no[i]*Jo[i]*Tr**(Jo[i]-1)
gott+=no[i]*Jo[i]*(Jo[i]-1)*Tr**(Jo[i]-2)
Ir=[1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 5, 6, 6, 6, 7, 7, 7, 8, 8, 9, 10, 10, 10, 16, 16, 18, 20, 20, 20, 21, 22, 23, 24, 24, 24]
Jr=[0, 1, 2, 3, 6, 1, 2, 4, 7, 36, 0, 1, 3, 6, 35, 1, 2, 3, 7, 3, 16, 35, 0, 11, 25, 8, 36, 13, 4, 10, 14, 29, 50, 57, 20, 35, 48, 21, 53, 39, 26, 40, 58]
nr=[-0.0017731742473212999, -0.017834862292357999, -0.045996013696365003, -0.057581259083432, -0.050325278727930002, -3.3032641670203e-05, -0.00018948987516315, -0.0039392777243355001, -0.043797295650572998, -2.6674547914087001e-05, 2.0481737692308999e-08, 4.3870667284435001e-07, -3.2277677238570002e-05, -0.0015033924542148, -0.040668253562648998, -7.8847309559367001e-10, 1.2790717852285001e-08, 4.8225372718507002e-07, 2.2922076337661001e-06, -1.6714766451061001e-11, -0.0021171472321354998, -23.895741934103999, -5.9059564324270004e-18, -1.2621808899101e-06, -0.038946842435739003, 1.1256211360459e-11, -8.2311340897998004, 1.9809712802088e-08, 1.0406965210174e-19, -1.0234747095929e-13, -1.0018179379511e-09, -8.0882908646984998e-11, 0.10693031879409, -0.33662250574170999, 8.9185845355420999e-25, 3.0629316876231997e-13, -4.2002467698208001e-06, -5.9056029685639003e-26, 3.7826947613457002e-06, -1.2768608934681e-15, 7.3087610595061e-29, 5.5414715350778001e-17, -9.4369707241209998e-07]
gr=grp=grpp=grt=grtt=grpt=0
for i in range(43):
gr+=nr[i]*Pr**Ir[i]*(Tr-0.5)**Jr[i]
grp+=nr[i]*Ir[i]*Pr**(Ir[i]-1)*(Tr-0.5)**Jr[i]
grpp+=nr[i]*Ir[i]*(Ir[i]-1)*Pr**(Ir[i]-2)*(Tr-0.5)**Jr[i]
grt+=nr[i]*Pr**Ir[i]*Jr[i]*(Tr-0.5)**(Jr[i]-1)
grtt+=nr[i]*Pr**Ir[i]*Jr[i]*(Jr[i]-1)*(Tr-0.5)**(Jr[i]-2)
grpt+=nr[i]*Ir[i]*Pr**(Ir[i]-1)*Jr[i]*(Tr-0.5)**(Jr[i]-1)
propiedades={}
propiedades["T"]=T
propiedades["P"]=P
propiedades["v"]=Pr*(gop+grp)*R*T/P/1000
propiedades["h"]=Tr*(got+grt)*R*T
propiedades["s"]=R*(Tr*(got+grt)-(go+gr))
propiedades["cp"]=-R*Tr**2*(gott+grtt)
propiedades["cv"]=R*(-Tr**2*(gott+grtt)-(1+Pr*grp-Tr*Pr*grpt)**2/(1-Pr**2*grpp))
propiedades["w"]=(R*T*1000*(1+2*Pr*grp+Pr**2*grp**2)/(1-Pr**2*grpp+(1+Pr*grp-Tr*Pr*grpt)**2/Tr**2/(gott+grtt)))**0.5
propiedades["alfav"]=(1+Pr*grp-Tr*Pr*grpt)/(1+Pr*grp)/T
propiedades["kt"]=(1-Pr**2*grpp)/(1+Pr*grp)/P
propiedades["region"]=2
propiedades["x"]=1
return propiedades
def _P_2bc(h):
"""Define the boundary between Region 2b and 2c, P=f(h)
>>> "%.3f" % _P_2bc(3516.004323)
'100.000'
"""
return 905.84278514723-0.67955786399241*h+1.2809002730136e-4*h**2
def _hbc_P(P):
"""Define the boundary between Region 2b and 2c, h=f(P)
>>> "%.6f" % _hbc_P(100)
'3516.004323'
"""
return 0.26526571908428e4+((P-0.45257578905948e1)/1.2809002730136e-4)**0.5
def _hab_s(s):
"""Define the boundary between Region 2a and 2b, h=f(s)
>>> "%.6f" % _hab_s(7)
'3376.437884'
"""
smin=_Region2(_TSat_P(4), 4)["s"]
smax=_Region2(1073.15, 4)["s"]
if ssmax:
h=5000
else:
h=-0.349898083432139e4+0.257560716905876e4*s-0.421073558227969e3*s**2+0.276349063799944e2*s**3
return h
def _Backward2a_T_Ph(P, h):
"""Backward equation for region 2a, T=f(P,h)
>>> "%.6f" % _Backward2a_T_Ph(0.001,3000)
'534.433241'
>>> "%.5f" % _Backward2a_T_Ph(3,4000)
'1010.77577'
"""
I=[0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 7]
J=[0, 1, 2, 3, 7, 20, 0, 1, 2, 3, 7, 9, 11, 18, 44, 0, 2, 7, 36, 38, 40, 42, 44, 24, 44, 12, 32, 44, 32, 36, 42, 34, 44, 28]
n=[0.10898952318288e4, 0.84951654495535e3, -0.10781748091826e3, 0.33153654801263e2, -0.74232016790248e1, 0.11765048724356e2, 0.18445749355790e1, -0.41792700549624e1, 0.62478196935812e1, -0.17344563108114e2, -0.20058176862096e3, 0.27196065473796e3, -0.45511318285818e3, 0.30919688604755e4, 0.25226640357872e6, -0.61707422868339e-2, -0.31078046629583, 0.11670873077107e2, 0.12812798404046e9, -0.98554909623276e9, 0.28224546973002e10, -0.35948971410703e10, 0.17227349913197e10, -0.13551334240775e5, 0.12848734664650e8, 0.13865724283226e1, 0.23598832556514e6, -0.13105236545054e8, 0.73999835474766e4, -0.55196697030060e6, 0.37154085996233e7, 0.19127729239660e5, -0.41535164835634e6, -0.62459855192507e2]
Pr=P/1
nu=h/2000
T=0
for i in range(34):
T+=n[i]*Pr**I[i]*(nu-2.1)**J[i]
return T
def _Backward2b_T_Ph(P, h):
"""Backward equation for region 2b, T=f(P,h)
>>> "%.5f" % _Backward2b_T_Ph(5,4000)
'1015.31583'
>>> "%.6f" % _Backward2b_T_Ph(25,3500)
'875.279054'
"""
I=[0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 6, 7, 7, 9, 9]
J=[0, 1, 2, 12, 18, 24, 28, 40, 0, 2, 6, 12, 18, 24, 28, 40, 2, 8, 18, 40, 1, 2, 12, 24, 2, 12, 18, 24, 28, 40, 18, 24, 40, 28, 2, 28, 1, 40]
n=[0.14895041079516e4, 0.74307798314034e3, -0.97708318797837e2, 0.24742464705674e1, -0.63281320016026, 0.11385952129658e1, -0.47811863648625, 0.85208123431544e-2, 0.93747147377932, 0.33593118604916e1, 0.33809355601454e1, 0.16844539671904, 0.73875745236695, -0.47128737436186, 0.15020273139707, -0.21764114219750e-2, -0.21810755324761e-1, -0.10829784403677, -0.46333324635812e-1, 0.71280351959551e-4, 0.11032831789999e-3, 0.18955248387902e-3, 0.30891541160537e-2, 0.13555504554949e-2, 0.28640237477456e-6, -0.10779857357512e-4, -0.76462712454814e-4, 0.14052392818316e-4, -0.31083814331434e-4, -0.10302738212103e-5, 0.28217281635040e-6, 0.12704902271945e-5, 0.73803353468292e-7, -0.11030139238909e-7, -0.81456365207833e-13, -0.25180545682962e-10, -0.17565233969407e-17, 0.86934156344163e-14]
Pr=P/1
nu=h/2000
T=0
for i in range(38):
T+=n[i]*(Pr-2)**I[i]*(nu-2.6)**J[i]
return T
def _Backward2c_T_Ph(P, h):
"""Backward equation for region 2c, T=f(P,h)
>>> "%.6f" % _Backward2c_T_Ph(40,2700)
'743.056411'
>>> "%.6f" % _Backward2c_T_Ph(60,3200)
'882.756860'
"""
I=[-7, -7, -6, -6, -5, -5, -2, -2, -1, -1, 0, 0, 1, 1, 2, 6, 6, 6, 6, 6, 6, 6, 6]
J=[0, 4, 0, 2, 0, 2, 0, 1, 0, 2, 0, 1, 4, 8, 4, 0, 1, 4, 10, 12, 16, 20, 22]
n=[-0.32368398555242e13, 0.73263350902181e13, 0.35825089945447e12, -0.58340131851590e12, -0.10783068217470e11, 0.20825544563171e11, 0.61074783564516e6, 0.85977722535580e6, -0.25745723604170e5, 0.31081088422714e5, 0.12082315865936e4, 0.48219755109255e3, 0.37966001272486e1, -0.10842984880077e2, -0.45364172676660e-1, 0.14559115658698e-12, 0.11261597407230e-11, -0.17804982240686e-10, 0.12324579690832e-6, -0.11606921130984e-5, 0.27846367088554e-4, -0.59270038474176e-3, 0.12918582991878e-2]
Pr=P/1
nu=h/2000
T=0
for i in range(23):
T+=n[i]*(Pr+25)**I[i]*(nu-1.8)**J[i]
return T
def _Backward2_T_Ph(P, h):
"""Backward equation for region 2, T=f(P,h)"""
Tsat=_TSat_P(P)
if P<=4:
T=_Backward2a_T_Ph(P, h)
elif 4=hf:
T=_Backward2b_T_Ph(P, h)
else:
T=_Backward2c_T_Ph(P, h)
return max(Tsat, T)
def _Backward2a_T_Ps(P, s):
"""Backward equation for region 2a, T=f(P,s)
>>> "%.6f" % _Backward2a_T_Ps(0.1,7.5)
'399.517097'
>>> "%.5f" % _Backward2a_T_Ps(2.5,8)
'1039.84917'
"""
I=[-1.5, -1.5, -1.5, -1.5, -1.5, -1.5, -1.25, -1.25, -1.25, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -0.75, -0.75, -0.5, -0.5, -0.5, -0.5, -0.25, -0.25, -0.25, -0.25, 0.25, 0.25, 0.25, 0.25, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.75, 0.75, 0.75, 0.75, 1.0, 1.0, 1.25, 1.25, 1.5, 1.5]
J=[-24, -23, -19, -13, -11, -10, -19, -15, -6, -26, -21, -17, -16, -9, -8, -15, -14, -26, -13, -9, -7, -27, -25, -11, -6, 1, 4, 8, 11, 0, 1, 5, 6, 10, 14, 16, 0, 4, 9, 17, 7, 18, 3, 15, 5, 18]
n=[-0.39235983861984e6, 0.51526573827270e6, 0.40482443161048e5, -0.32193790923902e3, 0.96961424218694e2, -0.22867846371773e2, -0.44942914124357e6, -0.50118336020166e4, 0.35684463560015, 0.44235335848190e5, -0.13673388811708e5, 0.42163260207864e6, 0.22516925837475e5, 0.47442144865646e3, -0.14931130797647e3, -0.19781126320452e6, -0.23554399470760e5, -0.19070616302076e5, 0.55375669883164e5, 0.38293691437363e4, -0.60391860580567e3, 0.19363102620331e4, 0.42660643698610e4, -0.59780638872718e4, -0.70401463926862e3, 0.33836784107553e3, 0.20862786635187e2, 0.33834172656196e-1, -0.43124428414893e-4, 0.16653791356412e3, -0.13986292055898e3, -0.78849547999872, 0.72132411753872e-1, -0.59754839398283e-2, -0.12141358953904e-4, 0.23227096733871e-6, -0.10538463566194e2, 0.20718925496502e1, -0.72193155260427e-1, 0.20749887081120e-6, -0.18340657911379e-1, 0.29036272348696e-6, 0.21037527893619, 0.25681239729999e-3, -0.12799002933781e-1, -0.82198102652018e-5]
Pr=P/1
sigma=s/2
T=0
for i in range(46):
T+=n[i]*Pr**I[i]*(sigma-2)**J[i]
return T
def _Backward2b_T_Ps(P, s):
"""Backward equation for region 2b, T=f(P,s)
>>> "%.6f" % _Backward2b_T_Ps(8,6)
'600.484040'
>>> "%.5f" % _Backward2b_T_Ps(90,6)
'1038.01126'
"""
I=[-6, -6, -5, -5, -4, -4, -4, -3, -3, -3, -3, -2, -2, -2, -2, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5]
J=[0, 11, 0, 11, 0, 1, 11, 0, 1, 11, 12, 0, 1, 6, 10, 0, 1, 5, 8, 9, 0, 1, 2, 4, 5, 6, 9, 0, 1, 2, 3, 7, 8, 0, 1, 5, 0, 1, 3, 0, 1, 0, 1, 2]
n=[0.31687665083497e6, 0.20864175881858e2, -0.39859399803599e6, -0.21816058518877e2, 0.22369785194242e6, -0.27841703445817e4, 0.99207436071480e1, -0.75197512299157e5, 0.29708605951158e4, -0.34406878548526e1, 0.38815564249115, 0.17511295085750e5, -0.14237112854449e4, 0.10943803364167e1, 0.89971619308495, -0.33759740098958e4, 0.47162885818355e3, -0.19188241993679e1, 0.41078580492196, -0.33465378172097, 0.13870034777505e4, -0.40663326195838e3, 0.41727347159610e2, 0.21932549434532e1, -0.10320050009077e1, 0.35882943516703, 0.52511453726066e-2, 0.12838916450705e2, -0.28642437219381e1, 0.56912683664855, -0.99962954584931e-1, -0.32632037778459e-2, 0.23320922576723e-3, -0.15334809857450, 0.29072288239902e-1, 0.37534702741167e-3, 0.17296691702411e-2, -0.38556050844504e-3, -0.35017712292608e-4, -0.14566393631492e-4, 0.56420857267269e-5, 0.41286150074605e-7, -0.20684671118824e-7, 0.16409393674725e-8]
Pr=P/1
sigma=s/0.7853
T=0
for i in range(44):
T+=n[i]*Pr**I[i]*(10-sigma)**J[i]
return T
def _Backward2c_T_Ps(P, s):
"""Backward equation for region 2c, T=f(P,s)
>>> "%.6f" % _Backward2c_T_Ps(20,5.75)
'697.992849'
>>> "%.6f" % _Backward2c_T_Ps(80,5.75)
'949.017998'
"""
I=[-2, -2, -1, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 7, 7, 7, 7, 7]
J=[0, 1, 0, 0, 1, 2, 3, 0, 1, 3, 4, 0, 1, 2, 0, 1, 5, 0, 1, 4, 0, 1, 2, 0, 1, 0, 1, 3, 4, 5]
n=[0.90968501005365e3, 0.24045667088420e4, -0.59162326387130e3, 0.54145404128074e3, -0.27098308411192e3, 0.97976525097926e3, -0.46966772959435e3, 0.14399274604723e2, -0.19104204230429e2, 0.53299167111971e1, -0.21252975375934e2, -0.31147334413760, 0.60334840894623, -0.42764839702509e-1, 0.58185597255259e-2, -0.14597008284753e-1, 0.56631175631027e-2, -0.76155864584577e-4, 0.22440342919332e-3, -0.12561095013413e-4, 0.63323132660934e-6, -0.20541989675375e-5, 0.36405370390082e-7, -0.29759897789215e-8, 0.10136618529763e-7, 0.59925719692351e-11, -0.20677870105164e-10, -0.20874278181886e-10, 0.10162166825089e-9, -0.16429828281347e-9]
Pr=P/1
sigma=s/2.9251
T=0
for i in range(30):
T+=n[i]*Pr**I[i]*(2-sigma)**J[i]
return T
def _Backward2_T_Ps(P, s):
"""Backward equation for region 2, T=f(P,s)"""
sf=5.85
Tsat=_TSat_P(P)
if P<=4:
T=_Backward2a_T_Ps(P, s)
elif s>=sf:
T=_Backward2b_T_Ps(P, s)
else:
T=_Backward2c_T_Ps(P, s)
return max(Tsat, T)
def _Backward2a_P_hs(h, s):
"""Backward equation for region 2a, P=f(h,s)
>>> "%.9f" % _Backward2a_P_hs(2800,6.5)
'1.371012767'
>>> "%.12f" % _Backward2a_P_hs(2800,9.5)
'0.001879743844'
>>> "%.10f" % _Backward2a_P_hs(4100,9.5)
'0.1024788997'
"""
I=[0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 3, 4, 5, 5, 6, 7]
J=[1, 3, 6, 16, 20, 22, 0, 1, 2, 3, 5, 6, 10, 16, 20, 22, 3, 16, 20, 0, 2, 3, 6, 16, 16, 3, 16, 3, 1]
n=[-0.182575361923032e-1, -0.125229548799536, 0.592290437320145, 0.604769706185122e1, 0.238624965444474e3, -0.298639090222922e3, 0.512250813040750e-1, -0.437266515606486, 0.413336902999504, -0.516468254574773e1, -0.557014838445711e1, 0.128555037824478e2, 0.114144108953290e2, -0.119504225652714e3, -0.284777985961560e4, 0.431757846408006e4, 0.112894040802650e1, 0.197409186206319e4, 0.151612444706087e4, 0.141324451421235e-1, 0.585501282219601, -0.297258075863012e1, 0.594567314847319e1, -0.623656565798905e4, 0.965986235133332e4, 0.681500934948134e1, -0.633207286824489e4, -0.558919224465760e1, 0.400645798472063e-1]
nu=h/4200
sigma=s/12
suma=0
for i in range(29):
suma+=n[i]*(nu-0.5)**I[i]*(sigma-1.2)**J[i]
return 4*suma**4
def _Backward2b_P_hs(h, s):
"""Backward equation for region 2b, P=f(h,s)
>>> "%.9f" % _Backward2b_P_hs(2800,6)
'4.793911442'
>>> "%.8f" % _Backward2b_P_hs(3600,6)
'83.95519209'
>>> "%.9f" % _Backward2b_P_hs(3600,7)
'7.527161441'
"""
I=[0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 8, 12, 14]
J=[0, 1, 2, 4, 8, 0, 1, 2, 3, 5, 12, 1, 6, 18, 0, 1, 7, 12, 1, 16, 1, 12, 1, 8, 18, 1, 16, 1, 3, 14, 18, 10, 16]
n=[0.801496989929495e-1, -0.543862807146111, 0.337455597421283, 0.890555451157450e1, 0.313840736431485e3, 0.797367065977789, -0.121616973556240e1, 0.872803386937477e1, -0.169769781757602e2, -0.186552827328416e3, 0.951159274344237e5, -0.189168510120494e2, -0.433407037194840e4, 0.543212633012715e9, 0.144793408386013, 0.128024559637516e3, -0.672309534071268e5, 0.336972380095287e8, -0.586634196762720e3, -0.221403224769889e11, 0.171606668708389e4, -0.570817595806302e9, -0.312109693178482e4, -0.207841384633010e7, 0.305605946157786e13, 0.322157004314333e4, 0.326810259797295e12, -0.144104158934487e4, 0.410694867802691e3, 0.109077066873024e12, -0.247964654258893e14, 0.188801906865134e10, -0.123651009018773e15]
nu=h/4100
sigma=s/7.9
suma=0
for i in range(33):
suma+=n[i]*(nu-0.6)**I[i]*(sigma-1.01)**J[i]
return 100*suma**4
def _Backward2c_P_hs(h, s):
"""Backward equation for region 2c, P=f(h,s)
>>> "%.8f" % _Backward2c_P_hs(2800,5.1)
'94.39202060'
>>> "%.9f" % _Backward2c_P_hs(2800,5.8)
'8.414574124'
>>> "%.8f" % _Backward2c_P_hs(3400,5.8)
'83.76903879'
"""
I=[0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 5, 5, 5, 5, 6, 6, 10, 12, 16]
J=[0, 1, 2, 3, 4, 8, 0, 2, 5, 8, 14, 2, 3, 7, 10, 18, 0, 5, 8, 16, 18, 18, 1, 4, 6, 14, 8, 18, 7, 7, 10]
n=[0.112225607199012, -0.339005953606712e1, -0.320503911730094e2, -0.197597305104900e3, -0.407693861553446e3, 0.132943775222331e5, 0.170846839774007e1, 0.373694198142245e2, 0.358144365815434e4, 0.423014446424664e6, -0.751071025760063e9, 0.523446127607898e2, -0.228351290812417e3, -0.960652417056937e6, -0.807059292526074e8, 0.162698017225669e13, 0.772465073604171, 0.463929973837746e5, -0.137317885134128e8, 0.170470392630512e13, -0.251104628187308e14, 0.317748830835520e14, 0.538685623675312e2, -0.553089094625169e5, -0.102861522421405e7, 0.204249418756234e13, 0.273918446626977e9, -0.263963146312685e16, -0.107890854108088e10, -0.296492620980124e11, -0.111754907323424e16]
nu=h/3500
sigma=s/5.9
suma=0
for i in range(31):
suma+=n[i]*(nu-0.7)**I[i]*(sigma-1.1)**J[i]
return 100*suma**4
def _Backward2_P_hs(h, s):
"""Backward equation for region 2, P=f(h,s)"""
sfbc=5.85
hamin=_hab_s(s)
if h<=hamin:
P=_Backward2a_P_hs(h, s)
elif s>=sfbc:
P=_Backward2b_P_hs(h, s)
else:
P=_Backward2c_P_hs(h, s)
return P
#Region 3
def _Region3(rho, T):
"""Basic equation for region 3
>>> "%.7f" % _Region3(500,650)["P"]
'25.5837018'
>>> "%.5f" % _Region3(500,650)["h"]
'1863.43019'
>>> "%.5f" % (_Region3(500,650)["h"]-_Region3(500,650)["P"]*1000*_Region3(500,650)["v"], )
'1812.26279'
>>> "%.8f" % _Region3(200,650)["s"]
'4.85438792'
>>> "%.7f" % _Region3(200,650)["cp"]
'44.6579342'
>>> "%.8f" % _Region3(200,650)["cv"]
'4.04118076'
>>> "%.6f" % _Region3(200,650)["w"]
'383.444594'
>>> "%.11f" % _Region3(500,750)["alfav"]
'0.00441515098'
>>> "%.11f" % _Region3(500,750)["kt"]
'0.00806710817'
>>> "%.11f" % _Region3(500,750)["alfap"]
'0.00698896514'
>>> "%.6f" % _Region3(500,750)["betap"]
'791.475213'
"""
I=[None, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 8, 9, 9, 10, 10, 11]
J=[None, 0, 1, 2, 7, 10, 12, 23, 2, 6, 15, 17, 0, 2, 6, 7, 22, 26, 0, 2, 4, 16, 26, 0, 2, 4, 26, 1, 3, 26, 0, 2, 26, 2, 26, 2, 26, 0, 1, 26]
n=[0.10658070028513e1, -0.15732845290239e2, 0.20944396974307e2, -0.76867707878716e1, 0.26185947787954e1, -0.28080781148620e1, 0.12053369696517e1, -0.84566812812502e-2, -0.12654315477714e1, -0.11524407806681e1, 0.88521043984318, -0.64207765181607, 0.38493460186671, -0.85214708824206, 0.48972281541877e1, -0.30502617256965e1, 0.39420536879154e-1, 0.12558408424308, -0.27999329698710, 0.13899799569460e1, -0.20189915023570e1, -0.82147637173963e-2, -0.47596035734923, 0.43984074473500e-1, -0.44476435428739, 0.90572070719733, 0.70522450087967, 0.10770512626332, -0.32913623258954, -0.50871062041158, -0.22175400873096e-1, 0.94260751665092e-1, 0.16436278447961, -0.13503372241348e-1, -0.14834345352472e-1, 0.57922953628084e-3, 0.32308904703711e-2, 0.80964802996215e-4, -0.16557679795037e-3, -0.44923899061815e-4]
d=rho/rhoc
Tr=Tc/T
g=n[0]*log(d)
gd=n[0]*d**-1
gdd=-n[0]*d**-2
gt=gtt=gdt=0
for i in range(1, 40):
g+=n[i]*d**I[i]*Tr**J[i]
gd+=n[i]*I[i]*d**(I[i]-1)*Tr**J[i]
gdd+=n[i]*I[i]*(I[i]-1)*d**(I[i]-2)*Tr**J[i]
gt+= n[i] * d**I[i] * J[i] * Tr**(J[i]-1)
gtt+=n[i]*d**I[i]*J[i]*(J[i]-1)*Tr**(J[i]-2)
gdt+=n[i]*I[i]*d**(I[i]-1)*J[i]*Tr**(J[i]-1)
propiedades={}
propiedades["T"]=T
propiedades["P"]=d*gd*R*T*rho/1000
propiedades["v"]=1/rho
propiedades["h"]=R*T*(Tr*gt+d*gd)
propiedades["s"]=R*(Tr*gt-g)
propiedades["cp"]=R*(-Tr**2*gtt+(d*gd-d*Tr*gdt)**2/(2*d*gd+d**2*gdd))
propiedades["cv"]=-R*Tr**2*gtt
propiedades["w"]=sqrt(R*T*1000*(2*d*gd+d**2*gdd-(d*gd-d*Tr*gdt)**2/Tr**2/gtt))
propiedades["alfav"]=(gd-Tr*gdt)/(2*gd+d*gdd)/T
propiedades["kt"]=1/(2*d*gd+d**2*gdd)/rho/R/T*1000
propiedades["alfap"]=(1-Tr*gdt/gd)/T
propiedades["betap"]=rho*(2+d*gdd/gd)
propiedades["region"]=3
propiedades["x"]=1
return propiedades
def _h_3ab(P):
"""Define the boundary between Region 3a-3b, h=f(P)
>>> "%.6f" % _h_3ab(25)
'2095.936454'
"""
return 0.201464004206875e4+3.74696550136983*P-0.0219921901054187*P**2+0.875131686009950e-4*P**3
def _tab_P(P):
"""Define the boundary between Region 3a-3b, T=f(P)
>>> "%.7f" % _tab_P(40)
'693.0341408'
"""
I=[0, 1, 2, -1, -2]
n=[0.154793642129415e4, -0.187661219490113e3, 0.213144632222113e2, -0.191887498864292e4, 0.918419702359447e3]
Pr=P/1
T=0
for i in range(5):
T+=n[i]*log(Pr)**I[i]
return T
def _top_P(P):
"""Define the boundary between Region 3o-3p, T=f(P)
>>> "%.7f" % _top_P(22.8)
'650.0106943'
"""
I=[0, 1, 2, -1, -2]
n=[0.969461372400213e3, -0.332500170441278e3, 0.642859598466067e2, 0.773845935768222e3, -0.152313732937084e4]
Pr=P/1
T=0
for i in range(5):
T+=n[i]*log(Pr)**I[i]
return T
def _twx_P(P):
"""Define the boundary between Region 3w-3x, T=f(P)
>>> "%.7f" % _twx_P(22.3)
'648.2049480'
"""
I=[0, 1, 2, -1, -2]
n=[0.728052609145380e1, 0.973505869861952e2, 0.147370491183191e2, 0.329196213998375e3, 0.873371668682417e3]
Pr=P/1
T=0
for i in range(5):
T+=n[i]*log(Pr)**I[i]
return T
def _tef_P(P):
"""Define the boundary between Region 3e-3f, T=f(P)
>>> "%.7f" % _tef_P(40)
'713.9593992'
"""
return 3.727888004*(P-22.064)+647.096
def _txx_P(P, xx):
"""Define the boundary between 3x-3y, T=f(P) where xx represent the subregions options: cd, gh, ij, jk, mn, qu, rx, uv
>>> "%.7f" % _txx_P(25,"cd")
'649.3659208'
>>> "%.7f" % _txx_P(23,"gh")
'649.8873759'
>>> "%.7f" % _txx_P(23,"ij")
'651.5778091'
>>> "%.7f" % _txx_P(23,"jk")
'655.8338344'
>>> "%.7f" % _txx_P(22.8,"mn")
'649.6054133'
>>> "%.7f" % _txx_P(22,"qu")
'645.6355027'
>>> "%.7f" % _txx_P(22,"rx")
'648.2622754'
>>> "%.7f" % _txx_P(22.3,"uv")
'647.7996121'
"""
ng={"cd": [0.585276966696349e3, 0.278233532206915e1, -0.127283549295878e-1, 0.159090746562729e-3],
"gh": [-0.249284240900418e5, 0.428143584791546e4, -0.269029173140130e3, 0.751608051114157e1, -0.787105249910383e-1],
"ij": [0.584814781649163e3, -0.616179320924617, 0.260763050899562, -0.587071076864459e-2, 0.515308185433082e-4],
"jk": [0.617229772068439e3, -0.770600270141675e1, 0.697072596851896, -0.157391839848015e-1, 0.137897492684194e-3],
"mn": [0.535339483742384e3, 0.761978122720128e1, -0.158365725441648, 0.192871054508108e-2],
"qu": [0.565603648239126e3, 0.529062258221222e1, -0.102020639611016, 0.122240301070145e-2],
"rx": [0.584561202520006e3, -0.102961025163669e1, 0.243293362700452, -0.294905044740799e-2],
"uv": [0.528199646263062e3, 0.890579602135307e1, -0.222814134903755, 0.286791682263697e-2]}
n=ng[xx]
Pr=P/1
T=0
for i in range(len(n)):
T+=n[i]*Pr**i
return T
def _Backward3a_v_Ph(P, h):
"""Backward equation for region 3a, v=f(P,h)
>>> "%.12f" % _Backward3a_v_Ph(20,1700)
'0.001749903962'
>>> "%.12f" % _Backward3a_v_Ph(100,2100)
'0.001676229776'
"""
I=[-12, -12, -12, -12, -10, -10, -10, -8, -8, -6, -6, -6, -4, -4, -3, -2, -2, -1, -1, -1, -1, 0, 0, 1, 1, 1, 2, 2, 3, 4, 5, 8]
J=[6, 8, 12, 18, 4, 7, 10, 5, 12, 3, 4, 22, 2, 3, 7, 3, 16, 0, 1, 2, 3, 0, 1, 0, 1, 2, 0, 2, 0, 2, 2, 2]
n=[0.529944062966028e-2, -0.170099690234461, 0.111323814312927e2, -0.217898123145125e4, -0.506061827980875e-3, 0.556495239685324, -0.943672726094016e1, -0.297856807561527, 0.939353943717186e2, 0.192944939465981e-1, 0.421740664704763, -0.368914126282330e7, -0.737566847600639e-2, -0.354753242424366, -0.199768169338727e1, 0.115456297059049e1, 0.568366875815960e4, 0.808169540124668e-2, 0.172416341519307, 0.104270175292927e1, -0.297691372792847, 0.560394465163593, 0.275234661176914, -0.148347894866012, -0.651142513478515e-1, -0.292468715386302e1, 0.664876096952665e-1, 0.352335014263844e1, -0.146340792313332e-1, -0.224503486668184e1, 0.110533464706142e1, -0.408757344495612e-1]
Pr=P/100
nu=h/2100
suma=0
for i in range(32):
suma+=n[i]*(Pr+0.128)**I[i]*(nu-0.727)**J[i]
return 0.0028*suma
def _Backward3b_v_Ph(P, h):
"""Backward equation for region 3b, v=f(P,h)
>>> "%.12f" % _Backward3b_v_Ph(20,2500)
'0.006670547043'
>>> "%.12f" % _Backward3b_v_Ph(100,2700)
'0.002404234998'
"""
I=[-12, -12, -8, -8, -8, -8, -8, -8, -6, -6, -6, -6, -6, -6, -4, -4, -4, -3, -3, -2, -2, -1, -1, -1, -1, 0, 1, 1, 2, 2]
J=[0, 1, 0, 1, 3, 6, 7, 8, 0, 1, 2, 5, 6, 10, 3, 6, 10, 0, 2, 1, 2, 0, 1, 4, 5, 0, 0, 1, 2, 6]
n=[-0.225196934336318e-8, 0.140674363313486e-7, 0.233784085280560e-5, -0.331833715229001e-4, 0.107956778514318e-2, -0.271382067378863, 0.107202262490333e1, -0.853821329075382, -0.215214194340526e-4, 0.769656088222730e-3, -0.431136580433864e-2, 0.453342167309331, -0.507749535873652, -0.100475154528389e3, -0.219201924648793, -0.321087965668917e1, 0.607567815637771e3, 0.557686450685932e-3, 0.187499040029550, 0.905368030448107e-2, 0.285417173048685, 0.329924030996098e-1, 0.239897419685483, 0.482754995951394e1, -0.118035753702231e2, 0.169490044091791, -0.179967222507787e-1, 0.371810116332674e-1, -0.536288335065096e-1, 0.160697101092520e1]
Pr=P/100
nu=h/2800
suma=0
for i in range(30):
suma+=n[i]*(Pr+0.0661)**I[i]*(nu-0.72)**J[i]
return 0.0088*suma
def _Backward3_v_Ph(P, h):
"""Backward equation for region 3, v=f(P,h)"""
hf=_h_3ab(P)
if h<=hf:
return _Backward3a_v_Ph(P, h)
else:
return _Backward3b_v_Ph(P, h)
def _Backward3a_T_Ph(P, h):
"""Backward equation for region 3a, T=f(P,h)
>>> "%.7f" % _Backward3a_T_Ph(20,1700)
'629.3083892'
>>> "%.7f" % _Backward3a_T_Ph(100,2100)
'733.6163014'
"""
I=[-12, -12, -12, -12, -12, -12, -12, -12, -10, -10, -10, -8, -8, -8, -8, -5, -3, -2, -2, -2, -1, -1, 0, 0, 1, 3, 3, 4, 4, 10, 12]
J=[0, 1, 2, 6, 14, 16, 20, 22, 1, 5, 12, 0, 2, 4, 10, 2, 0, 1, 3, 4, 0, 2, 0, 1, 1, 0, 1, 0, 3, 4, 5]
n=[-0.133645667811215e-6, 0.455912656802978e-5, -0.146294640700979e-4, 0.639341312970080e-2, 0.372783927268847e3, -0.718654377460447e4, 0.573494752103400e6, -0.267569329111439e7, -0.334066283302614e-4, -0.245479214069597e-1, 0.478087847764996e2, 0.764664131818904e-5, 0.128350627676972e-2, 0.171219081377331e-1, -0.851007304583213e1, -0.136513461629781e-1, -0.384460997596657e-5, 0.337423807911655e-2, -0.551624873066791, 0.729202277107470, -0.992522757376041e-2, -0.119308831407288, 0.793929190615421, 0.454270731799386, 0.209998591259910, -0.642109823904738e-2, -0.235155868604540e-1, 0.252233108341612e-2, -0.764885133368119e-2, 0.136176427574291e-1, -0.133027883575669e-1]
Pr=P/100
nu=h/2300
suma=0
for i in range(31):
suma+=n[i]*(Pr+0.240)**I[i]*(nu-0.615)**J[i]
return 760*suma
def _Backward3b_T_Ph(P, h):
"""Backward equation for region 3b, T=f(P,h)
>>> "%.7f" % _Backward3b_T_Ph(20,2500)
'641.8418053'
>>> "%.7f" % _Backward3b_T_Ph(100,2700)
'842.0460876'
"""
I=[-12, -12, -10, -10, -10, -10, -10, -8, -8, -8, -8, -8, -6, -6, -6, -4, -4, -3, -2, -2, -1, -1, -1, -1, -1, -1, 0, 0, 1, 3, 5, 6, 8]
J=[0, 1, 0, 1, 5, 10, 12, 0, 1, 2, 4, 10, 0, 1, 2, 0, 1, 5, 0, 4, 2, 4, 6, 10, 14, 16, 0, 2, 1, 1, 1, 1, 1]
n=[0.323254573644920e-4, -0.127575556587181e-3, -0.475851877356068e-3, 0.156183014181602e-2, 0.105724860113781, -0.858514221132534e2, 0.724140095480911e3, 0.296475810273257e-2, -0.592721983365988e-2, -0.126305422818666e-1, -0.115716196364853, 0.849000969739595e2, -0.108602260086615e-1, 0.154304475328851e-1, 0.750455441524466e-1, 0.252520973612982e-1, -0.602507901232996e-1, -0.307622221350501e1, -0.574011959864879e-1, 0.503471360939849e1, -0.925081888584834, 0.391733882917546e1, -0.773146007130190e2, 0.949308762098587e4, -0.141043719679409e7, 0.849166230819026e7, 0.861095729446704, 0.323346442811720, 0.873281936020439, -0.436653048526683, 0.286596714529479, -0.131778331276228, 0.676682064330275e-2]
Pr=P/100
nu=h/2800
suma=0
for i in range(33):
suma+=n[i]*(Pr+0.298)**I[i]*(nu-0.72)**J[i]
return 860*suma
def _Backward3_T_Ph(P, h):
"""Backward equation for region 3, T=f(P,h)"""
hf=_h_3ab(P)
Tsat=_TSat_P(P)
if h<=hf:
T=_Backward3a_T_Ph(P, h)
else:
T=_Backward3b_T_Ph(P, h)
return max(Tsat, T)
def _Backward3a_v_Ps(P, s):
"""Backward equation for region 3a, v=f(P,s)
>>> "%.12f" % _Backward3a_v_Ps(20,3.8)
'0.001733791463'
>>> "%.12f" % _Backward3a_v_Ps(100,4)
'0.001555893131'
"""
I=[-12, -12, -12, -10, -10, -10, -10, -8, -8, -8, -8, -6, -5, -4, -3, -3, -2, -2, -1, -1, 0, 0, 0, 1, 2, 4, 5, 6]
J=[10, 12, 14, 4, 8, 10, 20, 5, 6, 14, 16, 28, 1, 5, 2, 4, 3, 8, 1, 2, 0, 1, 3, 0, 0, 2, 2, 0]
n=[0.795544074093975e2, -0.238261242984590e4, 0.176813100617787e5, -0.110524727080379e-2, -0.153213833655326e2, 0.297544599376982e3, -0.350315206871242e8, 0.277513761062119, -0.523964271036888, -0.148011182995403e6, 0.160014899374266e7, 0.170802322663427e13, 0.246866996006494e-3, 0.165326084797980e1, -0.118008384666987, 0.253798642355900e1, 0.965127704669424, -0.282172420532826e2, 0.203224612353823, 0.110648186063513e1, 0.526127948451280, 0.277000018736321, 0.108153340501132e1, -0.744127885357893e-1, 0.164094443541384e-1, -0.680468275301065e-1, 0.257988576101640e-1, -0.145749861944416e-3]
Pr=P/100
sigma=s/4.4
suma=0
for i in range(28):
suma+=n[i]*(Pr+0.187)**I[i]*(sigma-0.755)**J[i]
return 0.0028*suma
def _Backward3b_v_Ps(P, s):
"""Backward equation for region 3b, v=f(P,s)
>>> "%.12f" % _Backward3b_v_Ps(20,5)
'0.006262101987'
>>> "%.12f" % _Backward3b_v_Ps(100,5)
'0.002449610757'
"""
I=[-12, -12, -12, -12, -12, -12, -10, -10, -10, -10, -8, -5, -5, -5, -4, -4, -4, -4, -3, -2, -2, -2, -2, -2, -2, 0, 0, 0, 1, 1, 2]
J=[0, 1, 2, 3, 5, 6, 0, 1, 2, 4, 0, 1, 2, 3, 0, 1, 2, 3, 1, 0, 1, 2, 3, 4, 12, 0, 1, 2, 0, 2, 2]
n=[0.591599780322238e-4, -0.185465997137856e-2, 0.104190510480013e-1, 0.598647302038590e-2, -0.771391189901699, 0.172549765557036e1, -0.467076079846526e-3, 0.134533823384439e-1, -0.808094336805495e-1, 0.508139374365767, 0.128584643361683e-2, -0.163899353915435e1, 0.586938199318063e1, -0.292466667918613e1, -0.614076301499537e-2, 0.576199014049172e1, -0.121613320606788e2, 0.167637540957944e1, -0.744135838773463e1, 0.378168091437659e-1, 0.401432203027688e1, 0.160279837479185e2, 0.317848779347728e1, -0.358362310304853e1, -0.115995260446827e7, 0.199256573577909, -0.122270624794624, -0.191449143716586e2, -0.150448002905284e-1, 0.146407900162154e2, -0.327477787188230e1]
Pr=P/100
sigma=s/5.3
suma=0
for i in range(31):
suma+=n[i]*(Pr+0.298)**I[i]*(sigma-0.816)**J[i]
return 0.0088*suma
def _Backward3_v_Ps(P, s):
"""Backward equation for region 3, v=f(P,s)"""
if s<=sc:
return _Backward3a_v_Ps(P, s)
else:
return _Backward3b_v_Ps(P, s)
def _Backward3a_T_Ps(P, s):
"""Backward equation for region 3a, T=f(P,s)
>>> "%.7f" % _Backward3a_T_Ps(20,3.8)
'628.2959869'
>>> "%.7f" % _Backward3a_T_Ps(100,4)
'705.6880237'
"""
I=[-12, -12, -10, -10, -10, -10, -8, -8, -8, -8, -6, -6, -6, -5, -5, -5, -4, -4, -4, -2, -2, -1, -1, 0, 0, 0, 1, 2, 2, 3, 8, 8, 10]
J=[28, 32, 4, 10, 12, 14, 5, 7, 8, 28, 2, 6, 32, 0, 14, 32, 6, 10, 36, 1, 4, 1, 6, 0, 1, 4, 0, 0, 3, 2, 0, 1, 2]
n=[0.150042008263875e10, -0.159397258480424e12, 0.502181140217975e-3, -0.672057767855466e2, 0.145058545404456e4, -0.823889534888890e4, -0.154852214233853, 0.112305046746695e2, -0.297000213482822e2, 0.438565132635495e11, 0.137837838635464e-2, -0.297478527157462e1, 0.971777947349413e13, -0.571527767052398e-4, 0.288307949778420e5, -0.744428289262703e14, 0.128017324848921e2, -0.368275545889071e3, 0.664768904779177e16, 0.449359251958880e-1, -0.422897836099655e1, -0.240614376434179, -0.474341365254924e1, 0.724093999126110, 0.923874349695897, 0.399043655281015e1, 0.384066651868009e-1, -0.359344365571848e-2, -0.735196448821653, 0.188367048396131, 0.141064266818704e-3, -0.257418501496337e-2, 0.123220024851555e-2]
Pr=P/100
sigma=s/4.4
suma=0
for i in range(33):
suma+=n[i]*(Pr+0.240)**I[i]*(sigma-0.703)**J[i]
return 760*suma
def _Backward3b_T_Ps(P, s):
"""Backward equation for region 3b, T=f(P,s)
>>> "%.7f" % _Backward3b_T_Ps(20,5)
'640.1176443'
>>> "%.7f" % _Backward3b_T_Ps(100,5)
'847.4332825'
"""
I=[-12, -12, -12, -12, -8, -8, -8, -6, -6, -6, -5, -5, -5, -5, -5, -4, -3, -3, -2, 0, 2, 3, 4, 5, 6, 8, 12, 14]
J=[1, 3, 4, 7, 0, 1, 3, 0, 2, 4, 0, 1, 2, 4, 6, 12, 1, 6, 2, 0, 1, 1, 0, 24, 0, 3, 1, 2]
n=[0.527111701601660, -0.401317830052742e2, 0.153020073134484e3, -0.224799398218827e4, -0.193993484669048, -0.140467557893768e1, 0.426799878114024e2, 0.752810643416743, 0.226657238616417e2, -0.622873556909932e3, -0.660823667935396, 0.841267087271658, -0.253717501764397e2, 0.485708963532948e3, 0.880531517490555e3, 0.265015592794626e7, -0.359287150025783, -0.656991567673753e3, 0.241768149185367e1, 0.856873461222588, 0.655143675313458, -0.213535213206406, 0.562974957606348e-2, -0.316955725450471e15, -0.699997000152457e-3, 0.119845803210767e-1, 0.193848122022095e-4, -0.215095749182309e-4]
Pr=P/100
sigma=s/5.3
suma=0
for i in range(28):
suma+=n[i]*(Pr+0.760)**I[i]*(sigma-0.818)**J[i]
return 860*suma
def _Backward3_T_Ps(P, s):
"""Backward equation for region 3, T=f(P,s)"""
sc=4.41202148223476
Tsat=_TSat_P(P)
if s<=sc:
T=_Backward3a_T_Ps(P, s)
else:
T=_Backward3b_T_Ps(P, s)
return max(Tsat, T)
def _Backward3a_P_hs(h, s):
"""Backward equation for region 3a, P=f(h,s)
>>> "%.8f" % _Backward3a_P_hs(1700,3.8)
'25.55703246'
>>> "%.8f" % _Backward3a_P_hs(2000,4.2)
'45.40873468'
>>> "%.8f" % _Backward3a_P_hs(2100,4.3)
'60.78123340'
"""
I=[0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 6, 7, 8, 10, 10, 14, 18, 20, 22, 22, 24, 28, 28, 32, 32]
J=[0, 1, 5, 0, 3, 4, 8, 14, 6, 16, 0, 2, 3, 0, 1, 4, 5, 28, 28, 24, 1, 32, 36, 22, 28, 36, 16, 28, 36, 16, 36, 10, 28]
n=[0.770889828326934e1, -0.260835009128688e2, 0.267416218930389e3, 0.172221089496844e2, -0.293542332145970e3, 0.614135601882478e3, -0.610562757725674e5, -0.651272251118219e8, 0.735919313521937e5, -0.116646505914191e11, 0.355267086434461e2, -0.596144543825955e3, -0.475842430145708e3, 0.696781965359503e2, 0.335674250377312e3, 0.250526809130882e5, 0.146997380630766e6, 0.538069315091534e20, 0.143619827291346e22, 0.364985866165994e20, -0.254741561156775e4, 0.240120197096563e28, -0.393847464679496e30, 0.147073407024852e25, -0.426391250432059e32, 0.194509340621077e39, 0.666212132114896e24, 0.706777016552858e34, 0.175563621975576e42, 0.108408607429124e29, 0.730872705175151e44, 0.159145847398870e25, 0.377121605943324e41]
nu=h/2300
sigma=s/4.4
suma=0
for i in range(33):
suma+=n[i]*(nu-1.01)**I[i]*(sigma-0.75)**J[i]
return 99*suma
def _Backward3b_P_hs(h, s):
"""Backward equation for region 3b, P=f(h,s)
>>> "%.8f" % _Backward3b_P_hs(2400,4.7)
'63.63924887'
>>> "%.8f" % _Backward3b_P_hs(2600,5.1)
'34.34999263'
>>> "%.8f" % _Backward3b_P_hs(2700,5.0)
'88.39043281'
"""
I=[-12, -12, -12, -12, -12, -10, -10, -10, -10, -8, -8, -6, -6, -6, -6, -5, -4, -4, -4, -3, -3, -3, -3, -2, -2, -1, 0, 2, 2, 5, 6, 8, 10, 14, 14]
J=[2, 10, 12, 14, 20, 2, 10, 14, 18, 2, 8, 2, 6, 7, 8, 10, 4, 5, 8, 1, 3, 5, 6, 0, 1, 0, 3, 0, 1, 0, 1, 1, 1, 3, 7]
n=[0.125244360717979e-12, -0.126599322553713e-1, 0.506878030140626e1, 0.317847171154202e2, -0.391041161399932e6, -0.975733406392044e-10, -0.186312419488279e2, 0.510973543414101e3, 0.373847005822362e6, 0.299804024666572e-7, 0.200544393820342e2, -0.498030487662829e-5, -0.102301806360030e2, 0.552819126990325e2, -0.206211367510878e3, -0.794012232324823e4, 0.782248472028153e1, -0.586544326902468e2, 0.355073647696481e4, -0.115303107290162e-3, -0.175092403171802e1, 0.257981687748160e3, -0.727048374179467e3, 0.121644822609198e-3, 0.393137871762692e-1, 0.704181005909296e-2, -0.829108200698110e2, -0.265178818131250, 0.137531682453991e2, -0.522394090753046e2, 0.240556298941048e4, -0.227361631268929e5, 0.890746343932567e5, -0.239234565822486e8, 0.568795808129714e10]
nu=h/2800
sigma=s/5.3
suma=0
for i in range(35):
suma+=n[i]*(nu-0.681)**I[i]*(sigma-0.792)**J[i]
return 16.6/suma
def _Backward3_P_hs(h, s):
"""Backward equation for region 3, P=f(h,s)"""
sc=4.41202148223476
if s<=sc:
return _Backward3a_P_hs(h, s)
else:
return _Backward3b_P_hs(h, s)
def _Backward3_v_PT(T, P):
"""Backward equation for region 3, v=f(P,T)"""
if P>40:
if T<=_tab_P(P): region="a"
else: region="b"
elif 25_TSat_P(P):
if _PSat_T(643.15)>> "%.12f" % _Backward3x_v_PT(630,50,"a")
'0.001470853100'
>>> "%.12f" % _Backward3x_v_PT(670,80,"a")
'0.001503831359'
>>> "%.12f" % _Backward3x_v_PT(710,50,"b")
'0.002204728587'
>>> "%.12f" % _Backward3x_v_PT(750,80,"b")
'0.001973692940'
>>> "%.12f" % _Backward3x_v_PT(630,20,"c")
'0.001761696406'
>>> "%.12f" % _Backward3x_v_PT(650,30,"c")
'0.001819560617'
>>> "%.12f" % _Backward3x_v_PT(656,26,"d")
'0.002245587720'
>>> "%.12f" % _Backward3x_v_PT(670,30,"d")
'0.002506897702'
>>> "%.12f" % _Backward3x_v_PT(661,26,"e")
'0.002970225962'
>>> "%.12f" % _Backward3x_v_PT(675,30,"e")
'0.003004627086'
>>> "%.12f" % _Backward3x_v_PT(671,26,"f")
'0.005019029401'
>>> "%.12f" % _Backward3x_v_PT(690,30,"f")
'0.004656470142'
>>> "%.12f" % _Backward3x_v_PT(649,23.6,"g")
'0.002163198378'
>>> "%.12f" % _Backward3x_v_PT(650,24,"g")
'0.002166044161'
>>> "%.12f" % _Backward3x_v_PT(652,23.6,"h")
'0.002651081407'
>>> "%.12f" % _Backward3x_v_PT(654,24,"h")
'0.002967802335'
>>> "%.12f" % _Backward3x_v_PT(653,23.6,"i")
'0.003273916816'
>>> "%.12f" % _Backward3x_v_PT(655,24,"i")
'0.003550329864'
>>> "%.12f" % _Backward3x_v_PT(655,23.5,"j")
'0.004545001142'
>>> "%.12f" % _Backward3x_v_PT(660,24,"j")
'0.005100267704'
>>> "%.12f" % _Backward3x_v_PT(660,23,"k")
'0.006109525997'
>>> "%.12f" % _Backward3x_v_PT(670,24,"k")
'0.006427325645'
>>> "%.12f" % _Backward3x_v_PT(646,22.6,"l")
'0.002117860851'
>>> "%.12f" % _Backward3x_v_PT(646,23,"l")
'0.002062374674'
>>> "%.12f" % _Backward3x_v_PT(648.6,22.6,"m")
'0.002533063780'
>>> "%.12f" % _Backward3x_v_PT(649.3,22.8,"m")
'0.002572971781'
>>> "%.12f" % _Backward3x_v_PT(649,22.6,"n")
'0.002923432711'
>>> "%.12f" % _Backward3x_v_PT(649.7,22.8,"n")
'0.002913311494'
>>> "%.12f" % _Backward3x_v_PT(649.1,22.6,"o")
'0.003131208996'
>>> "%.12f" % _Backward3x_v_PT(649.9,22.8,"o")
'0.003221160278'
>>> "%.12f" % _Backward3x_v_PT(649.4,22.6,"p")
'0.003715596186'
>>> "%.12f" % _Backward3x_v_PT(650.2,22.8,"p")
'0.003664754790'
>>> "%.12f" % _Backward3x_v_PT(640,21.1,"q")
'0.001970999272'
>>> "%.12f" % _Backward3x_v_PT(643,21.8,"q")
'0.002043919161'
>>> "%.12f" % _Backward3x_v_PT(644,21.1,"r")
'0.005251009921'
>>> "%.12f" % _Backward3x_v_PT(648,21.8,"r")
'0.005256844741'
>>> "%.12f" % _Backward3x_v_PT(635,19.1,"s")
'0.001932829079'
>>> "%.12f" % _Backward3x_v_PT(638,20,"s")
'0.001985387227'
>>> "%.12f" % _Backward3x_v_PT(626,17,"t")
'0.008483262001'
>>> "%.12f" % _Backward3x_v_PT(640,20,"t")
'0.006227528101'
>>> "%.12f" % _Backward3x_v_PT(644.6,21.5,"u")
'0.002268366647'
>>> "%.12f" % _Backward3x_v_PT(646.1,22,"u")
'0.002296350553'
>>> "%.12f" % _Backward3x_v_PT(648.6,22.5,"v")
'0.002832373260'
>>> "%.12f" % _Backward3x_v_PT(647.9,22.3,"v")
'0.002811424405'
>>> "%.12f" % _Backward3x_v_PT(647.5,22.15,"w")
'0.003694032281'
>>> "%.12f" % _Backward3x_v_PT(648.1,22.3,"w")
'0.003622226305'
>>> "%.12f" % _Backward3x_v_PT(648,22.11,"x")
'0.004528072649'
>>> "%.12f" % _Backward3x_v_PT(649,22.3,"x")
'0.004556905799'
>>> "%.12f" % _Backward3x_v_PT(646.84,22,"y")
'0.002698354719'
>>> "%.12f" % _Backward3x_v_PT(647.05,22.064,"y")
'0.002717655648'
>>> "%.12f" % _Backward3x_v_PT(646.89,22,"z")
'0.003798732962'
>>> "%.12f" % _Backward3x_v_PT(647.15,22.064,"z")
'0.003701940009'
"""
par={
"a": [0.0024, 100, 760, 30, 0.085, 0.817, 1, 1, 1],
"b": [0.0041, 100, 860, 32, 0.280, 0.779, 1, 1, 1],
"c": [0.0022, 40, 690, 35, 0.259, 0.903, 1, 1, 1],
"d": [0.0029, 40, 690, 38, 0.559, 0.939, 1, 1, 4],
"e": [0.0032, 40, 710, 29, 0.587, 0.918, 1, 1, 1],
"f": [0.0064, 40, 730, 42, 0.587, 0.891, 0.5, 1, 4],
"g": [0.0027, 25, 660, 38, 0.872, 0.971, 1, 1, 4],
"h": [0.0032, 25, 660, 29, 0.898, 0.983, 1, 1, 4],
"i": [0.0041, 25, 660, 42, 0.910, 0.984, 0.5, 1, 4],
"j": [0.0054, 25, 670, 29, 0.875, 0.964, 0.5, 1, 4],
"k": [0.0077, 25, 680, 34, 0.802, 0.935, 1, 1, 1],
"l": [0.0026, 24, 650, 43, 0.908, 0.989, 1, 1, 4],
"m": [0.0028, 23, 650, 40, 1.000, 0.997, 1, 0.25, 1],
"n": [0.0031, 23, 650, 39, 0.976, 0.997, None, None, None],
"o": [0.0034, 23, 650, 24, 0.974, 0.996, 0.5, 1, 1],
"p": [0.0041, 23, 650, 27, 0.972, 0.997, 0.5, 1, 1],
"q": [0.0022, 23, 650, 24, 0.848, 0.983, 1, 1, 4],
"r": [0.0054, 23, 650, 27, 0.874, 0.982, 1, 1, 1],
"s": [0.0022, 21, 640, 29, 0.886, 0.990, 1, 1, 4],
"t": [0.0088, 20, 650, 33, 0.803, 1.020, 1, 1, 1],
"u": [0.0026, 23, 650, 38, 0.902, 0.988, 1, 1, 1],
"v": [0.0031, 23, 650, 39, 0.960, 0.995, 1, 1, 1],
"w": [0.0039, 23, 650, 35, 0.959, 0.995, 1, 1, 4],
"x": [0.0049, 23, 650, 36, 0.910, 0.988, 1, 1, 1],
"y": [0.0031, 22, 650, 20, 0.996, 0.994, 1, 1, 4],
"z": [0.0038, 22, 650, 23, 0.993, 0.994, 1, 1, 4],
}
I={
"a": [-12, -12, -12, -10, -10, -10, -8, -8, -8, -6, -5, -5, -5, -4, -3, -3, -3, -3, -2, -2, -2, -1, -1, -1, 0, 0, 1, 1, 2, 2],
"b": [-12, -12, -10, -10, -8, -6, -6, -6, -5, -5, -5, -4, -4, -4, -3, -3, -3, -3, -3, -2, -2, -2, -1, -1, 0, 0, 1, 1, 2, 3, 4, 4],
"c": [-12, -12, -12, -10, -10, -10, -8, -8, -8, -6, -5, -5, -5, -4, -4, -3, -3, -2, -2, -2, -1, -1, -1, 0, 0, 0, 1, 1, 2, 2, 2, 2, 3, 3, 8],
"d": [-12, -12, -12, -12, -12, -12, -10, -10, -10, -10, -10, -10, -10, -8, -8, -8, -8, -6, -6, -5, -5, -5, -5, -4, -4, -4, -3, -3, -2, -2, -1, -1, -1, 0, 0, 1, 1, 3],
"e": [-12, -12, -10, -10, -10, -10, -10, -8, -8, -8, -6, -5, -4, -4, -3, -3, -3, -2, -2, -2, -2, -1, 0, 0, 1, 1, 1, 2, 2],
"f": [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 3, 3, 3, 4, 5, 5, 6, 7, 7, 10, 12, 12, 12, 14, 14, 14, 14, 14, 16, 16, 18, 18, 20, 20, 20, 22, 24, 24, 28, 32],
"g": [-12, -12, -12, -12, -12, -12, -10, -10, -10, -8, -8, -8, -8, -6, -6, -5, -5, -4, -3, -2, -2, -2, -2, -1, -1, -1, 0, 0, 0, 1, 1, 1, 3, 5, 6, 8, 10, 10],
"h": [-12, -12, -10, -10, -10, -10, -10, -10, -8, -8, -8, -8, -8, -6, -6, -6, -5, -5, -5, -4, -4, -3, -3, -2, -1, -1, 0, 1, 1],
"i": [0, 0, 0, 1, 1, 1, 1, 2, 3, 3, 4, 4, 4, 5, 5, 5, 7, 7, 8, 8, 10, 12, 12, 12, 14, 14, 14, 14, 18, 18, 18, 18, 18, 20, 20, 22, 24, 24, 32, 32, 36, 36],
"j": [0, 0, 0, 1, 1, 1, 2, 2, 3, 4, 4, 5, 5, 5, 6, 10, 12, 12, 14, 14, 14, 16, 18, 20, 20, 24, 24, 28, 28],
"k": [-2, -2, -1, -1, 0, -0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 5, 5, 5, 6, 6, 6, 6, 8, 10, 12],
"l": [-12, -12, -12, -12, -12, -10, -10, -8, -8, -8, -8, -8, -8, -8, -6, -5, -5, -4, -4, -3, -3, -3, -3, -2, -2, -2, -1, -1, -1, 0, 0, 0, 0, 1, 1, 2, 4, 5, 5, 6, 10, 10, 14],
"m": [0, 3, 8, 20, 1, 3, 4, 5, 1, 6, 2, 4, 14, 2, 5, 3, 0, 1, 1, 1, 28, 2, 16, 0, 5, 0, 3, 4, 12, 16, 1, 8, 14, 0, 2, 3, 4, 8, 14, 24],
"n": [0, 3, 4, 6, 7, 10, 12, 14, 18, 0, 3, 5, 6, 8, 12, 0, 3, 7, 12, 2, 3, 4, 2, 4, 7, 4, 3, 5, 6, 0, 0, 3, 1, 0, 1, 0, 1, 0, 1],
"o": [0, 0, 0, 2, 3, 4, 4, 4, 4, 4, 5, 5, 6, 7, 8, 8, 8, 10, 10, 14, 14, 20, 20, 24],
"p": [0, 0, 0, 0, 1, 2, 3, 3, 4, 6, 7, 7, 8, 10, 12, 12, 12, 14, 14, 14, 16, 18, 20, 22, 24, 24, 36],
"q": [-12, -12, -10, -10, -10, -10, -8, -6, -5, -5, -4, -4, -3, -2, -2, -2, -2, -1, -1, -1, 0, 1, 1, 1],
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"m": [0.811384363481847, -0.568199310990094e4, -0.178657198172556e11, 0.795537657613427e32, -0.814568209346872e5, -0.659774567602874e8, -0.152861148659302e11, -0.560165667510446e12, 0.458384828593949e6, -0.385754000383848e14, 0.453735800004273e8, 0.939454935735563e12, 0.266572856432938e28, -0.547578313899097e10, 0.200725701112386e15, 0.185007245563239e13, 0.185135446828337e9, -0.170451090076385e12, 0.157890366037614e15, -0.202530509748774e16, 0.368193926183570e60, 0.170215539458936e18, 0.639234909918741e42, -0.821698160721956e15, -0.795260241872306e24, 0.233415869478510e18, -0.600079934586803e23, 0.594584382273384e25, 0.189461279349492e40, -0.810093428842645e46, 0.188813911076809e22, 0.111052244098768e36, 0.291133958602503e46, -0.329421923951460e22, -0.137570282536696e26, 0.181508996303902e28, -0.346865122768353e30, -0.211961148774260e38, -0.128617899887675e49, 0.479817895699239e65],
"n": [0.280967799943151e-38, 0.614869006573609e-30, 0.582238667048942e-27, 0.390628369238462e-22, 0.821445758255119e-20, 0.402137961842776e-14, 0.651718171878301e-12, -0.211773355803058e-7, 0.264953354380072e-2, -0.135031446451331e-31, -0.607246643970893e-23, -0.402352115234494e-18, -0.744938506925544e-16, 0.189917206526237e-12, 0.364975183508473e-5, 0.177274872361946e-25, -0.334952758812999e-18, -0.421537726098389e-8, -0.391048167929649e-1, 0.541276911564176e-13, 0.705412100773699e-11, 0.258585887897486e-8, -0.493111362030162e-10, -0.158649699894543e-5, -0.525037427886100, 0.220019901729615e-2, -0.643064132636925e-2, 0.629154149015048e2, 0.135147318617061e3, 0.240560808321713e-6, -0.890763306701305e-3, -0.440209599407714e4, -0.302807107747776e3, 0.159158748314599e4, 0.232534272709876e6, -0.792681207132600e6, -0.869871364662769e11, 0.354542769185671e12, 0.400849240129329e15],
"o": [0.128746023979718e-34, -0.735234770382342e-11, 0.289078692149150e-2, 0.244482731907223, 0.141733492030985e-23, -0.354533853059476e-28, -0.594539202901431e-17, -0.585188401782779e-8, 0.201377325411803e-5, 0.138647388209306e1, -0.173959365084772e-4, 0.137680878349369e-2, 0.814897605805513e-14, 0.425596631351839e-25, -0.387449113787755e-17, 0.139814747930240e-12, -0.171849638951521e-2, 0.641890529513296e-21, 0.118960578072018e-10, -0.155282762571611e-17, 0.233907907347507e-7, -0.174093247766213e-12, 0.377682649089149e-8, -0.516720236575302e-10],
"p": [-0.982825342010366e-4, 0.105145700850612e1, 0.116033094095084e3, 0.324664750281543e4, -0.123592348610137e4, -0.561403450013495e-1, 0.856677401640869e-7, 0.236313425393924e3, 0.972503292350109e-2, -0.103001994531927e1, -0.149653706199162e-8, -0.215743778861592e-4, -0.834452198291445e1, 0.586602660564988, 0.343480022104968e-25, 0.816256095947021e-5, 0.294985697916798e-2, 0.711730466276584e-16, 0.400954763806941e-9, 0.107766027032853e2, -0.409449599138182e-6, -0.729121307758902e-5, 0.677107970938909e-8, 0.602745973022975e-7, -0.382323011855257e-10, 0.179946628317437e-2, -0.345042834640005e-3],
"q": [-0.820433843259950e5, 0.473271518461586e11, -0.805950021005413e-1, 0.328600025435980e2, -0.356617029982490e4, -0.172985781433335e10, 0.351769232729192e8, -0.775489259985144e6, 0.710346691966018e-4, 0.993499883820274e5, -0.642094171904570, -0.612842816820083e4, 0.232808472983776e3, -0.142808220416837e-4, -0.643596060678456e-2, -0.428577227475614e1, 0.225689939161918e4, 0.100355651721510e-2, 0.333491455143516, 0.109697576888873e1, 0.961917379376452, -0.838165632204598e-1, 0.247795908411492e1, -0.319114969006533e4],
"r": [0.144165955660863e-2, -0.701438599628258e13, -0.830946716459219e-16, 0.261975135368109, 0.393097214706245e3, -0.104334030654021e5, 0.490112654154211e9, -0.147104222772069e-3, 0.103602748043408e1, 0.305308890065089e1, -0.399745276971264e7, 0.569233719593750e-11, -0.464923504407778e-1, -0.535400396512906e-17, 0.399988795693162e-12, -0.536479560201811e-6, 0.159536722411202e-1, 0.270303248860217e-14, 0.244247453858506e-7, -0.983430636716454e-5, 0.663513144224454e-1, -0.993456957845006e1, 0.546491323528491e3, -0.143365406393758e5, 0.150764974125511e6, -0.337209709340105e-9, 0.377501980025469e-8],
"s": [-0.532466612140254e23, 0.100415480000824e32, -0.191540001821367e30, 0.105618377808847e17, 0.202281884477061e59, 0.884585472596134e8, 0.166540181638363e23, -0.313563197669111e6, -0.185662327545324e54, -0.624942093918942e-1, -0.504160724132590e10, 0.187514491833092e5, 0.121399979993217e-2, 0.188317043049455e1, -0.167073503962060e4, 0.965961650599775, 0.294885696802488e1, -0.653915627346115e5, 0.604012200163444e50, -0.198339358557937, -0.175984090163501e58, 0.356314881403987e1, -0.575991255144384e3, 0.456213415338071e5, -0.109174044987829e8, 0.437796099975134e34, -0.616552611135792e46, 0.193568768917797e10, 0.950898170425042e54],
"t": [0.155287249586268e1, 0.664235115009031e1, -0.289366236727210e4, -0.385923202309848e13, -0.291002915783761e1, -0.829088246858083e12, 0.176814899675218e1, -0.534686695713469e9, 0.160464608687834e18, 0.196435366560186e6, 0.156637427541729e13, -0.178154560260006e1, -0.229746237623692e16, 0.385659001648006e8, 0.110554446790543e10, -0.677073830687349e14, -0.327910592086523e31, -0.341552040860644e51, -0.527251339709047e21, 0.245375640937055e24, -0.168776617209269e27, 0.358958955867578e29, -0.656475280339411e36, 0.355286045512301e39, 0.569021454413270e58, -0.700584546433113e48, -0.705772623326374e65, 0.166861176200148e53, -0.300475129680486e61, -0.668481295196808e51, 0.428432338620678e69, -0.444227367758304e72, -0.281396013562745e77],
"u": [0.122088349258355e18, 0.104216468608488e10, -0.882666931564652e16, 0.259929510849499e20, 0.222612779142211e15, -0.878473585050085e18, -0.314432577551552e22, -0.216934916996285e13, 0.159079648196849e21, -0.339567617303423e3, 0.884387651337836e13, -0.843405926846418e21, 0.114178193518022e2, -0.122708229235641e-3, -0.106201671767107e3, 0.903443213959313e25, -0.693996270370852e28, 0.648916718965575e-8, 0.718957567127851e4, 0.105581745346187e-2, -0.651903203602581e15, -0.160116813274676e25, -0.510254294237837e-8, -0.152355388953402, 0.677143292290144e12, 0.276378438378930e15, 0.116862983141686e-1, -0.301426947980171e14, 0.169719813884840e-7, 0.104674840020929e27, -0.108016904560140e5, -0.990623601934295e-12, 0.536116483602738e7, 0.226145963747881e22, -0.488731565776210e-9, 0.151001548880670e-4, -0.227700464643920e5, -0.781754507698846e28],
"v": [-0.415652812061591e-54, 0.177441742924043e-60, -0.357078668203377e-54, 0.359252213604114e-25, -0.259123736380269e2, 0.594619766193460e5, -0.624184007103158e11, 0.313080299915944e17, 0.105006446192036e-8, -0.192824336984852e-5, 0.654144373749937e6, 0.513117462865044e13, -0.697595750347391e19, -0.103977184454767e29, 0.119563135540666e-47, -0.436677034051655e-41, 0.926990036530639e-29, 0.587793105620748e21, 0.280375725094731e-17, -0.192359972440634e23, 0.742705723302738e27, -0.517429682450605e2, 0.820612048645469e7, -0.188214882341448e-8, 0.184587261114837e-1, -0.135830407782663e-5, -0.723681885626348e17, -0.223449194054124e27, -0.111526741826431e-34, 0.276032601145151e-28, 0.134856491567853e15, 0.652440293345860e-9, 0.510655119774360e17, -0.468138358908732e32, -0.760667491183279e16, -0.417247986986821e-18, 0.312545677756104e14, -0.100375333864186e15, 0.247761392329058e27],
"w": [-0.586219133817016e-7, -0.894460355005526e11, 0.531168037519774e-30, 0.109892402329239, -0.575368389425212e-1, 0.228276853990249e5, -0.158548609655002e19, 0.329865748576503e-27, -0.634987981190669e-24, 0.615762068640611e-8, -0.961109240985747e8, -0.406274286652625e-44, -0.471103725498077e-12, 0.725937724828145, 0.187768525763682e-38, -0.103308436323771e4, -0.662552816342168e-1, 0.579514041765710e3, 0.237416732616644e-26, 0.271700235739893e-14, -0.907886213483600e2, -0.171242509570207e-36, 0.156792067854621e3, 0.923261357901470, -0.597865988422577e1, 0.321988767636389e7, -0.399441390042203e-29, 0.493429086046981e-7, 0.812036983370565e-19, -0.207610284654137e-11, -0.340821291419719e-6, 0.542000573372233e-17, -0.856711586510214e-12, 0.266170454405981e-13, 0.858133791857099e-5],
"x": [0.377373741298151e19, -0.507100883722913e13, -0.103363225598860e16, 0.184790814320773e-5, -0.924729378390945e-3, -0.425999562292738e24, -0.462307771873973e-12, 0.107319065855767e22, 0.648662492280682e11, 0.244200600688281e1, -0.851535733484258e10, 0.169894481433592e22, 0.215780222509020e-26, -0.320850551367334, -0.382642448458610e17, -0.275386077674421e-28, -0.563199253391666e6, -0.326068646279314e21, 0.397949001553184e14, 0.100824008584757e-6, 0.162234569738433e5, -0.432355225319745e11, -0.592874245598610e12, 0.133061647281106e1, 0.157338197797544e7, 0.258189614270853e14, 0.262413209706358e25, -0.920011937431142e-1, 0.220213765905426e-2, -0.110433759109547e2, 0.847004870612087e7, -0.592910695762536e9, -0.183027173269660e-4, 0.181339603516302, -0.119228759669889e4, 0.430867658061468e7],
"y": [-0.525597995024633e-9, 0.583441305228407e4, -0.134778968457925e17, 0.118973500934212e26, -0.159096490904708e27, -0.315839902302021e-6, 0.496212197158239e3, 0.327777227273171e19, -0.527114657850696e22, 0.210017506281863e-16, 0.705106224399834e21, -0.266713136106469e31, -0.145370512554562e-7, 0.149333917053130e28, -0.149795620287641e8, -0.381881906271100e16, 0.724660165585797e-4, -0.937808169550193e14, 0.514411468376383e10, -0.828198594040141e5],
"z": [0.244007892290650e-10, -0.463057430331242e7, 0.728803274777712e10, 0.327776302858856e16, -0.110598170118409e10, -0.323899915729957e13, 0.923814007023245e16, 0.842250080413712e-12, 0.663221436245506e12, -0.167170186672139e15, 0.253749358701391e4, -0.819731559610523e-20, 0.328380587890663e12, -0.625004791171543e8, 0.803197957462023e21, -0.204397011338353e-10, -0.378391047055938e4, 0.972876545938620e-2, 0.154355721681459e2, -0.373962862928643e4, -0.682859011374572e11, -0.248488015614543e-3, 0.394536049497068e7]}
I=I[x]
J=J[x]
n=n[x]
v_, P_, T_, N, a, b, c, d, e=par[x]
Pr=P/P_
Tr=T/T_
suma=0
if x=="n":
for i in range(N):
suma+=n[i]*(Pr-a)**I[i]*(Tr-b)**J[i]
return v_*exp(suma)
else:
for i in range(N):
suma+=n[i]*(Pr-a)**(c*I[i])*(Tr-b)**(J[i]*d)
return v_*suma**e
#Region 4
def _Region4(P, x):
"""Basic equation for region 4"""
T=_TSat_P(P)
P1=_Region1(T, P)
P2=_Region2(T, P)
propiedades={}
propiedades["T"]=T
propiedades["P"]=P
propiedades["v"]=P1["v"]+x*(P2["v"]-P1["v"])
propiedades["h"]=P1["h"]+x*(P2["h"]-P1["h"])
propiedades["s"]=P1["s"]+x*(P2["s"]-P1["s"])
propiedades["cp"]=None
propiedades["cv"]=None
propiedades["w"]=None
propiedades["alfa"]=None
propiedades["kt"]=None
propiedades["region"]=4
propiedades["x"]=x
return propiedades
def _Backward4_T_hs(h, s):
"""Backward equation for region 4, T=f(h,s)
>>> "%.7f" % _Backward4_T_hs(1800,5.3)
'346.8475498'
>>> "%.7f" % _Backward4_T_hs(2400,6.0)
'425.1373305'
>>> "%.7f" % _Backward4_T_hs(2500,5.5)
'522.5579013'
"""
I=[0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 6, 8, 10, 10, 12, 14, 14, 16, 16, 18, 18, 18, 20, 28]
J=[0, 3, 12, 0, 1, 2, 5, 0, 5, 8, 0, 2, 3, 4, 0, 1, 1, 2, 4, 16, 6, 8, 22, 1, 20, 36, 24, 1, 28, 12, 32, 14, 22, 36, 24, 36]
n=[0.179882673606601, -0.267507455199603, 0.116276722612600e1, 0.147545428713616, -0.512871635973248, 0.421333567697984, 0.563749522189870, 0.429274443819153, -0.335704552142140e1, 0.108890916499278e2, -0.248483390456012, 0.304153221906390, -0.494819763939905, 0.107551674933261e1, 0.733888415457688e-1, 0.140170545411085e-1, -0.106110975998808, 0.168324361811875e-1, 0.125028363714877e1, 0.101316840309509e4, -0.151791558000712e1, 0.524277865990866e2, 0.230495545563912e5, 0.249459806365456e-1, 0.210796467412137e7, 0.366836848613065e9, -0.144814105365163e9, -0.179276373003590e-2, 0.489955602100459e10, 0.471262212070518e3, -0.829294390198652e11, -0.171545662263191e4, 0.355777682973575e7, 0.586062760258436e12, -0.129887635078195e8, 0.317247449371057e11]
nu=h/2800
sigma=s/9.2
suma=0
for i in range(36):
suma+=n[i]*(nu-0.119)**I[i]*(sigma-1.07)**J[i]
return 550*suma
#Region 5
def _Region5(T, P):
"""Basic equation for region 5
>>> "%.8f" % _Region5(1500,0.5)["v"]
'1.38455090'
>>> "%.5f" % _Region5(1500,0.5)["h"]
'5219.76855'
>>> "%.5f" % (_Region5(1500,0.5)["h"]-500*_Region5(1500,0.5)["v"], )
'4527.49310'
>>> "%.8f" % _Region5(1500,30)["s"]
'7.72970133'
>>> "%.8f" % _Region5(1500,30)["cp"]
'2.72724317'
>>> "%.8f" % _Region5(1500,30)["cv"]
'2.19274829'
>>> "%.5f" % _Region5(2000,30)["w"]
'1067.36948'
>>> "%.12f" % _Region5(2000,30)["alfav"]
'0.000508830641'
>>> "%.10f" % _Region5(2000,30)["kt"]
'0.0329193892'
"""
Tr=1000/T
Pr=P/1
Jo=[0, 1, -3, -2, -1, 2]
no=[-0.13179983674201e2, 0.68540841634434e1, -0.24805148933466e-1, 0.36901534980333, -0.31161318213925e1, -0.32961626538917]
go=log(Pr)
gop=Pr**-1
gopp=-Pr**-2
got=gott=gopt=0
for i in range(6):
go+=no[i]*Tr**Jo[i]
got+=no[i]*Jo[i]*Tr**(Jo[i]-1)
gott+=no[i]*Jo[i]*(Jo[i]-1)*Tr**(Jo[i]-2)
Ir=[1, 1, 1, 2, 2, 3]
Jr=[1, 2, 3, 3, 9, 7]
nr=[0.15736404855259e-2, 0.90153761673944e-3, -0.50270077677648e-2, 0.22440037409485e-5, -0.41163275453471e-5, 0.37919454822955e-7]
gr=grp=grpp=grt=grtt=grpt=0
for i in range(6):
gr+=nr[i]*Pr**Ir[i]*Tr**Jr[i]
grp+=nr[i]*Ir[i]*Pr**(Ir[i]-1)*Tr**Jr[i]
grpp+=nr[i]*Ir[i]*(Ir[i]-1)*Pr**(Ir[i]-2)*Tr**Jr[i]
grt+=nr[i]*Pr**Ir[i]*Jr[i]*Tr**(Jr[i]-1)
grtt+=nr[i]*Pr**Ir[i]*Jr[i]*(Jr[i]-1)*Tr**(Jr[i]-2)
grpt+=nr[i]*Ir[i]*Pr**(Ir[i]-1)*Jr[i]*Tr**(Jr[i]-1)
propiedades={}
propiedades["T"]=T
propiedades["P"]=P
propiedades["v"]=Pr*(gop+grp)*R*T/P/1000
propiedades["h"]=Tr*(got+grt)*R*T
propiedades["s"]=R*(Tr*(got+grt)-(go+gr))
propiedades["cp"]=-R*Tr**2*(gott+grtt)
propiedades["cv"]=R*(-Tr**2*(gott+grtt)+((gop+grp)-Tr*(gopt+grpt))**2/(gopp+grpp))
propiedades["w"]=(R*T*1000*(1+2*Pr*grp+Pr**2*grp**2)/(1-Pr**2*grpp+(1+Pr*grp-Tr*Pr*grpt)**2/Tr**2/(gott+grtt)))**0.5
propiedades["alfav"]=(1+Pr*grp-Tr*Pr*grpt)/(1+Pr*grp)/T
propiedades["kt"]=(1-Pr**2*grpp)/(1+Pr*grp)/P
propiedades["region"]=5
propiedades["x"]=1
return propiedades
#Transport properties
def _Viscosity(rho, T):
"""Equation for the Viscosity
>>> "%.12f" % _Viscosity(997.047435,298.15)
'0.000890022551'
>>> "%.13f" % _Viscosity(54.9921814,873.15)
'0.0000339743835'
"""
Tr=T/Tc
Dr=rho/rhoc
no=[1.67752, 2.20462, 0.6366564, -0.241605]
suma=0
for i in range(4):
suma+=no[i]/Tr**i
fi0=100*Tr**0.5/suma
I=[0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 4, 4, 5, 6, 6]
J=[0, 1, 2, 3, 0, 1, 2, 3, 5, 0, 1, 2, 3, 4, 0, 1, 0, 3, 4, 3, 5]
nr=[0.520094, 0.850895e-1, -0.108374e1, -0.289555, 0.222531, 0.999115, 0.188797e1, 0.126613e1, 0.120573, -0.281378, -0.906851, -0.772479, -0.489837, -0.257040, 0.161913, 0.257399, -0.325372e-1, 0.698452e-1, 0.872102e-2, -0.435673e-2, -0.593264e-3]
suma=0
for i in range(21):
suma+=nr[i]*(Dr-1)**I[i]*(1/Tr-1)**J[i]
fi1=exp(Dr*suma)
if 645.911:
Lw=log((1+w)/(1-w))
else:
Lw=2*atan(abs(w))
Y=sin(3*Fid)/12-sin(2*Fid)/4/qc/X+(1-5/4*(qc*X)**2)/(qc*X)**2*sin(Fid)-((1-3/2*(qc*X)**2)*Fid-abs((qc*X)**2-1)**1.5*Lw)/(qc*X)**3
fi2=exp(xu*Y)
else:
fi2=1
return fi0*fi1*fi2*1e-6
def _ThCond(rho, T):
"""Equation for the thermal conductivity
>>> "%.9f" % _ThCond(997.047435,298.15)
'0.607509806'
>>> "%.10f" % _ThCond(26.0569558,873.15)
'0.0867570353'
"""
d=rho/317.7
Tr=T/647.26
no=[0.102811e-1, 0.299621e-1, 0.156146e-1, -0.422464e-2]
suma=0
for i in range(4):
suma+=no[i]*Tr**i
L0=Tr**0.5*suma
n1=[0, -0.397070, 0.400302, 0.106e1, -0.171587, 0.239219e1]
L1=n1[1]+n1[2]*d+n1[3]*exp(n1[4]*(d+n1[5])**2)
n2=[0, 0.701309e-1, 0.118520e-1, 0.642857, 0.169937e-2, -0.102000e1, -0.411717e1, -0.617937e1, 0.822994e-1, 0.100932e2, 0.308976e-2]
DT=abs(Tr-1)+n2[10]
A=2+n2[8]/DT**0.6
if Tr<1:
B=n2[9]/DT**0.6
else:
B=1/DT
L2=(n2[1]/Tr**10+n2[2])*d**1.8*exp(n2[3]*(1-d**2.8)) + n2[4]*B*d**A*exp(A/(1+A)*(1-d**(1+A)))+n2[5]*exp(n2[6]*Tr**1.5+n2[7]*d**-5)
return L0+L1+L2
def _Tension(T):
"""Equation for the surface tension
>>> "%.10f" % _Tension(300)
'0.0716859625'
>>> "%.10f" % _Tension(450)
'0.0428914992'
"""
Tr=T/Tc
return 1e-3*(235.8*(1-Tr)**1.256*(1-0.625*(1-Tr)))
def _Dielectric(rho, T):
"""Equation for the Dielectric constant
>>> "%.7f" % _Dielectric(999.242866, 298.15)
'78.5907250'
>>> "%.8f" % _Dielectric(26.0569558, 873.15)
'1.12620970'
"""
k=1.380658e-23
Na=6.0221367e23
alfa=1.636e-40
epsilon0=8.854187817e-12
mu=6.138e-30
M=0.018015268
d=rho/rhoc
Tr=Tc/T
I=[1, 1, 1, 2, 3, 3, 4, 5, 6, 7, 10, None]
J=[0.25, 1, 2.5, 1.5, 1.5, 2.5, 2, 2, 5, 0.5, 10, None]
n=[0.978224486826, -0.957771379375, 0.237511794148, 0.714692244396, -0.298217036956, -0.108863472196, 0.949327488264e-1, -0.980469816509e-2, 0.165167634970e-4, 0.937359795772e-4, -0.123179218720e-9, 0.196096504426e-2]
g=1+n[11]*d/(Tc/228/Tr-1)**1.2
for i in range(11):
g+=n[i]*d**I[i]*Tr**J[i]
A=Na*mu**2*rho*g/M/epsilon0/k/T
B=Na*alfa*rho/3/M/epsilon0
return (1+A+5*B+(9+2*A+18*B+A**2+10*A*B+9*B**2)**0.5)/4/(1-B)
def _Refractive(rho, T, l=0.5893):
"""Equation for the refractive index
>>> "%.8f" % _Refractive(997.047435, 298.15, 0.2265)
'1.39277824'
>>> "%.8f" % _Refractive(30.4758534, 773.15, 0.5893)
'1.00949307'
"""
Lir=5.432937
Luv=0.229202
d=rho/1000
Tr=T/273.15
L=l/0.589
a=[0.244257733, 0.974634476e-2, -0.373234996e-2, 0.268678472e-3, 0.158920570e-2, 0.245934259e-2, 0.900704920, -0.166626219e-1]
A=d*(a[0]+a[1]*d+a[2]*Tr+a[3]*L**2*Tr+a[4]/L**2+a[5]/(L**2-Luv**2)+a[6]/(L**2-Lir**2)+a[7]*d**2)
return ((2*A+1)/(1-A))**0.5
#Region definitions
def _Bound_TP(T, P):
"""Region definition for input T and P"""
region=None
if 1073.15=273.15 and Pt<=P<=100:
hs=_h1_s(s)
if h>=hs: region=1
elif hmin<=hh13 and _Backward3_P_hs(h, s)<=100: region=3
elif hs<=h<=h13: region=1
elif hmin4<=h=hs and _Backward3_P_hs(h, s)<=100: region=3
elif hmin4<=h=hs and _Backward3_P_hs(h, s)<=100: region=3
elif hmin4<=h=Pmin and T<=1073.15: region=2
if not region and _Region5(1073.15, 50)["s"]