def specific_volume(self, p=None, T=None):
"""Returns the specific volume in m³/kg"""
if p is None:
p = self.p
else:
p = Pressure(p)
if T is None:
T = self.T
else:
T = Temperature(T)
if self._is_in_region() == 1:
pi = self.p / Pressure(16.53).unit('MPa')
return (self._basic_equation1('gamma_pi') * self.R * self.T * pi /
self.p * 1e3) # because of kJ in R
elif self._is_in_region() == 2:
pi = self.p / Pressure(1).unit('MPa')
return (pi * (self._basic_equation2('gamma_0_pi') +
self._basic_equation2('gamma_r_pi')) * self.R *
self.T / self.p * 1e3)
elif self._is_in_region() == 3:
return None
elif self._is_in_region() == 4:
pass
elif self._is_in_region() == 5:
pass
return -1
def entropy(self, p=None, T=None):
"""NOT IMPLEMENTED"""
if p is None:
p = self.p
else:
p = Pressure(p)
if T is None:
T = self.T
else:
T = Temperature(T)
if self._is_in_region() == 1:
pi = self.p / Pressure(16.53).unit('MPa')
tau = Temperature(1386) / self.T
return (tau * self._basic_equation1('gamma_tau') -
self._basic_equation1('gamma')) * self.R
elif self._is_in_region() == 2:
pi = self.p / Pressure(1).unit('MPa')
tau = 540 / self.T
return ((tau * (self._basic_equation2('gamma_0_tau') +
self._basic_equation2('gamma_r_tau')) -
(self._basic_equation2('gamma_0') +
self._basic_equation2('gamma_r'))) * self.R)
elif self._is_in_region() == 3:
pass
elif self._is_in_region() == 4:
pass
elif self._is_in_region() == 5:
pass
return -1
def temperature_saturation(self, p=None):
"""Yields Tsat given a pressure p."""
# module deals with pressure in MPa
if p is None:
p = self.p.MPa
else:
p = Pressure(p).MPa
if p < Pressure(611.213).unit('Pa').MPa or p > self.pc:
raise ValueError('Pressure out of range.')
# table 34
ni = array([
1167.0521452767, -724213.16703206, -17.073846940092,
12020.82470247, -3232555.0322333, 14.91510861353, -4823.2657361591,
405113.40542057, -0.23855557567849, 650.17534844798
],
dtype='d')
beta = p**0.25
E = 1 * beta**2 + ni[2] * beta + ni[5]
F = ni[0] * beta**2 + ni[3] * beta + ni[6]
G = ni[1] * beta**2 + ni[4] * beta + ni[7]
D = 2 * G / (-F - (F**2 - 4 * E * G)**0.5)
return Temperature((ni[9] + D - ((ni[9] + D)**2 - 4 *
(ni[8] + ni[9] * D))**0.5) * 0.5)
def heat_capacity_constant_v(self, p=None, T=None):
"""NOT IMPLEMENTED"""
if p is None:
p = self.p
else:
p = Pressure(p)
if T is None:
T = self.T
else:
T = Temperature(T)
if self._is_in_region() == 1:
pi = self.p / Pressure(16.53).unit('MPa')
tau = Temperature(1386) / self.T
return (-(tau**2) * self._basic_equation1('gamma_tau_tau') +
((self._basic_equation1('gamma_pi') -
tau * self._basic_equation1('gamma_pi_tau'))**2) /
self._basic_equation1('gamma_pi_pi')) * self.R
elif self._is_in_region() == 2:
pass
elif self._is_in_region() == 3:
pass
elif self._is_in_region() == 4:
pass
elif self._is_in_region() == 5:
pass
return -1
def speed_of_sound(self, p=None, T=None):
"""NOT IMPLEMENTED"""
if p is None:
p = self.p
else:
p = Pressure(p)
if T is None:
T = self.T
else:
T = Temperature(T)
if self._is_in_region() == 1:
pi = self.p / Pressure(16.53).unit('MPa')
tau = Temperature(1386) / self.T
inside_frac = (((self._basic_equation1('gamma_pi') -
tau * self._basic_equation1('gamma_tau_pi'))**2) /
((tau**2) * self._basic_equation1('gamma_tau_tau')))
return sqrt(
((self._basic_equation1('gamma_pi')**2) /
(inside_frac - self._basic_equation1('gamma_pi_pi'))) *
self.R * self.T * 1000)
elif self._is_in_region() == 2:
pass
elif self._is_in_region() == 3:
pass
elif self._is_in_region() == 4:
pass
elif self._is_in_region() == 5:
pass
return -1
def test_units():
"""Test units."""
Tkel = Temperature(273.15).unit('K')
Tcel = Temperature(0).unit('C')
assert Tkel == Tcel
pressuremmhg = Pressure(760).unit('torr')
pressureatm = Pressure(1).unit('atm')
assert pressuremmhg == pressureatm
def _is_in_region(self):
"""Finds a region for the (T, p) point (see IAPWS-IF97 for details).
The usefulness of these regions are to divide the physical properties
of water into different sets of coefficients and equations."""
# for the 2 - 3 boundary line
ni = array([
348.05185628969, -1.1671859879975, 0.0010192970039326,
572.54459862746, 13.91883977887
],
dtype='d')
theta = self.T
pressure23 = Pressure(ni[0] + ni[1] * theta +
ni[2] * theta**2).unit('MPa')
# exceptional cases
if self.T == self.Tt and self.p == self.pt:
return 1
# regular cases
if self.T >= Temperature(273.15) and self.T <= Temperature(623.15):
if self.T < self.temperature_saturation(self.p):
return 1
else:
return 2
elif self.T > Temperature(623.15) and self.T <= Temperature(1073.15):
if self.p > pressure23:
return 3
else:
return 2
elif self.T >= Temperature(1073.15) and self.T <= Temperature(2273.15):
return 5
else:
raise Exception('Cannot assign region to the parameters p = ' +
str(self.p) + 'T = ' + str(self.T) + 'given.')
def heat_capacity(self, p=None, T=None):
"""Returns the isobaric heat capacity given p and T in kJ/(kg K)."""
if p is None:
p = self.p
else:
p = Pressure(p)
if T is None:
T = self.T
else:
T = Temperature(T)
if self._is_in_region() == 1:
tau = 1386 / T
return (-1 * tau * tau * self.R *
self._basic_equation1('gamma_tau_tau'))
elif self._is_in_region() == 2:
pass
elif self._is_in_region() == 3:
delta = rho / self.rhoc
tau = self.Tc / self.T
return (
-tau**2 / self._basic_equation3('PHI_tau_tau') +
(delta * self._basic_equation3('PHI_delta') -
delta * tau * self._basic_equation3('PHI_tau_delta'))**2 /
(2 * delta * self._basic_equation3('PHI_delta') +
delta**2 * self._basic_equation3('PHI_delta_delta'))) * self.R
elif self._is_in_region() == 4:
pass
elif self._is_in_region() == 5:
pass
return -1
def __init__(self, p, T, massic_basis=False):
u"""Initializes a Water object."""
self.p = Pressure(p)
self.T = Temperature(T)
# check if water is specified by IAPWS-IF97 for these values
if self.T < Temperature(273.15) or self.T > Temperature(2273.15):
raise ValueError('Temperature ' + str(T) +
' out of range (273.15 - 2273.15K)')
if self.p > Pressure(100).unit('MPa') or self.p < 0:
raise ValueError('Pressure ' + str(p) +
' out of range (0 - 100 MPa)')
if self.T > 1073.15 and self.p > Pressure(50).unit('MPa'):
raise ValueError('p or T value out of range')
# adjust R to mass or molar basis
if massic_basis is True:
self.R = ideal_gas_constant_massic_basis[0] # kJ/(kg K);
elif massic_basis is False:
self.R = ideal_gas_constant[0]
def _basic_equation1(self, value='gamma'):
"""Returns basic equation 1 and its derivatives, ex: 'gamma',
'gamma_tau', 'gamma_tau_pi', etc."""
# region1
Ii = array([
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
],
dtype='int')
Ji = array([
-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
],
dtype='int')
ni = array([
0.14632971213167, -0.84548187169114, -3.756360367204,
3.3855169168385, -0.95791963387872, 0.15772038513228,
-0.016616417199501, 0.00081214629983568, 0.00028319080123804,
-0.00060706301565874, -0.018990068218419, -0.032529748770505,
-0.021841717175414, -5.283835796993e-05, -0.00047184321073267,
-0.00030001780793026, 4.7661393906987e-05, -4.4141845330846e-06,
-7.2694996297594e-16, -3.1679644845054e-05, -2.8270797985312e-06,
-8.5205128120103e-10, -2.2425281908e-06, -6.5171222895601e-07,
-1.4341729937924e-13, -4.0516996860117e-07, -1.2734301741641e-09,
-1.7424871230634e-10, -6.8762131295531e-19, 1.4478307828521e-20,
2.6335781662795e-23, -1.1947622640071e-23, 1.8228094581404e-24,
-9.3537087292458e-26
],
dtype='d')
pi = self.p / Pressure(16.53).unit('MPa')
tau = Temperature(1386) / self.T
if value == 'gamma':
return sum(ni * ((7.1 - pi)**Ii) * ((tau - 1.222)**Ji))
elif value == 'gamma_tau':
return sum(ni * ((7.1 - pi)**Ii) * Ji * ((tau - 1.222)**(Ji - 1)))
elif value == 'gamma_tau_tau':
return sum(ni * ((7.1 - pi)**Ii) * Ji * (Ji - 1) *
((tau - 1.222)**(Ji - 2)))
elif value == 'gamma_pi':
return -1 * sum(ni * Ii * ((7.1 - pi)**(Ii - 1)) *
(tau - 1.222)**Ji)
elif value == 'gamma_pi_pi':
return sum(ni * Ii * (Ii - 1) * (7.1 - pi)**(Ii - 2) *
(tau - 1.222)**Ji)
elif value == 'gamma_pi_tau' or value == 'gamma_tau_pi':
return -1 * sum(ni * Ii * (7.1 - pi)**(Ii - 1) * Ji *
(tau - 1.222)**(Ji - 1))
else:
raise Exception('Function not assigned in _basic_equation1()')
def enthalpy(self, p=None, T=None):
"""Returns the enthalpy given p and T in kJ/kg."""
if p is None:
p = self.p
else:
p = Pressure(p)
if T is None:
T = self.T
else:
T = Temperature(T)
if self._is_in_region() == 1:
return Enthalpy(self._basic_equation1('gamma_tau') * 1386 * self.R)
elif self._is_in_region() == 2:
return Enthalpy(540 * self.R *
(self._basic_equation2('gamma_0_tau') +
self._basic_equation2('gamma_r_tau')))
elif self._is_in_region() == 3:
# for region 3 rho needs to be solved numerically
reg3_solved = self._basic_equation3('PHI_delta')
delta = reg3_solved[1] / self.rhoc
tau = self.Tc / self.T
return Enthalpy((tau * self._basic_equation3('PHI_tau')[0] +
delta * reg3_solved[0]) * self.R * self.T)
elif self._is_in_region() == 4:
return None
elif self._is_in_region() == 5:
pi = self.p / Pressure(1).unit('MPa')
tau = Temperature(1000) / self.T
return (tau * (self._basic_equation5('gamma_0_tau') +
self._basic_equation5('gamma_r_tau')) * self.R *
self.T)
def _basic_equation5(self, value='gamma'):
"""Returns equation 1 and its derivatives, ex: 'gamma',
'gamma_tau', 'gamma_tau_pi', etc."""
J0 = array([0, 1, -3, -2, -1, 2], dtype='d')
n0 = array([
-13.179983674201, 6.8540841634434, -0.024805148933466,
0.36901534980333, -3.1161318213925, -0.32961626538917
],
dtype='d')
Ii = array([1, 1, 1, 2, 2, 3], dtype='d')
Ji = array([1, 2, 3, 3, 9, 7], dtype='d')
ni = array([
0.0015736404855259, 0.00090153761673944, -0.0050270077677648,
2.2440037409485e-06, -4.1163275453471e-06, 3.7919454822955e-08
],
dtype='d')
pi = self.p / Pressure(1).unit('MPa')
tau = Temperature(1000) / self.T
if value == 'gamma':
return (self._basic_equation5('gamma_0') +
self._basic_equation5('gamma_r'))
elif value == 'gamma_0':
return log(pi) + sum(n0 * (tau**J0))
elif value == 'gamma_r':
return sum(ni * (pi**Ii) * (tau**Ji))
elif value == 'gamma_0_pi':
return 1 / pi
elif value == 'gamma_0_pi_pi':
return -1 / (pi**2)
elif value == 'gamma_0_tau':
return sum(n0 * J0 * (tau**(J0 - 1)))
elif value == 'gamma_0_tau_tau':
sum(n0 * J0 * (J0 - 1) * (tau**(J0 - 2)))
elif value == 'gamma_0_tau_pi' or value == 'gamma_0_pi_tau':
return 0 + 0
elif value == 'gamma_r_pi':
return sum(ni * Ii * (pi**(Ii - 1)) * (tau**Ji))
elif value == 'gamma_r_tau':
return sum(ni * (pi**Ii) * Ji * (tau**(Ji - 1)))
elif value == 'gamma_r_pi_pi':
return sum(ni * Ii * (Ii - 1) * (pi**(Ii - 2)) * (tau**Ji))
elif value == 'gamma_r_tau_tau':
return sum(ni * (pi**Ii) * Ji * (Ji - 1) * (tau**(Ji - 2)))
elif value == 'gamma_r_tau_pi' or 'gamma_r_pi_tau':
return sum(ni * Ii * (pi**(Ii - 1)) * Ji * (tau**(Ji - 1)))
def gibbs_energy(self, p=None, T=None):
"""Returns the Gibbs Energy given p and T in kJ/kg."""
if p is None:
p = self.p
else:
p = Pressure(p)
if T is None:
T = self.T
else:
T = Temperature(T)
if self._is_in_region() == 1:
return self._basic_equation1('gamma') * self.R * T
elif self._is_in_region() == 2:
return self._basic_equation2('gamma') * self.R * T
elif self._is_in_region() == 3:
pass
elif self._is_in_region() == 4:
pass
elif self._is_in_region() == 5:
pass
def pressure_saturation(self, T=None):
"""Yields Psat given a temperature T"""
if T is None:
T = self.T
else:
T = Temperature(T)
if T < 273.15 or T > self.Tc:
raise ValueError('Temperature out of range.')
# table 34
ni = array([
1167.0521452767, -724213.16703206, -17.073846940092,
12020.82470247, -3232555.0322333, 14.91510861353, -4823.2657361591,
405113.40542057, -0.23855557567849, 650.17534844798
],
dtype='d')
v = T + ni[8] / (T - ni[9])
A = 1 * v**2 + ni[0] * v + ni[1]
B = ni[2] * v**2 + ni[3] * v + ni[4]
C = ni[5] * v**2 + ni[6] * v + ni[7]
return Pressure(
(2 * C / (-B + (B**2 - 4 * A * C)**0.5))**4).unit('MPa')
class Water(object):
"""
Taken from The International Association for the Properties of Water and
Steam. Lucerne, Switzerland. August 2007. Revised Release on the IAPWS
Industrial Formulation 1997 for the Thermodynamic Properties of Water and
Steam. Reference document: IAPWS-IF97.
All units in SI and default
is molar basis."""
def __init__(self, p, T, massic_basis=False):
u"""Initializes a Water object."""
self.p = Pressure(p)
self.T = Temperature(T)
# check if water is specified by IAPWS-IF97 for these values
if self.T < Temperature(273.15) or self.T > Temperature(2273.15):
raise ValueError('Temperature ' + str(T) +
' out of range (273.15 - 2273.15K)')
if self.p > Pressure(100).unit('MPa') or self.p < 0:
raise ValueError('Pressure ' + str(p) +
' out of range (0 - 100 MPa)')
if self.T > 1073.15 and self.p > Pressure(50).unit('MPa'):
raise ValueError('p or T value out of range')
# adjust R to mass or molar basis
if massic_basis is True:
self.R = ideal_gas_constant_massic_basis[0] # kJ/(kg K);
elif massic_basis is False:
self.R = ideal_gas_constant[0]
# constants
# ideal gas constant was already instantiated
Tc = 647.096 # Critical point temperature (K)
pc = Pressure(22.064).unit('MPa') # Critical point pressure (MPa)
rhoc = 322.0 # Critical point density kg/m3
Tt = 273.16 # Triple point temperature (K)
pt = 611.657 # Triple point pressure (Pa)
ht = 0.611783 # Enthalpy at triple point (J/kg)
def temperature_saturation(self, p=None):
"""Yields Tsat given a pressure p."""
# module deals with pressure in MPa
if p is None:
p = self.p.MPa
else:
p = Pressure(p).MPa
if p < Pressure(611.213).unit('Pa').MPa or p > self.pc:
raise ValueError('Pressure out of range.')
# table 34
ni = array([
1167.0521452767, -724213.16703206, -17.073846940092,
12020.82470247, -3232555.0322333, 14.91510861353, -4823.2657361591,
405113.40542057, -0.23855557567849, 650.17534844798
],
dtype='d')
beta = p**0.25
E = 1 * beta**2 + ni[2] * beta + ni[5]
F = ni[0] * beta**2 + ni[3] * beta + ni[6]
G = ni[1] * beta**2 + ni[4] * beta + ni[7]
D = 2 * G / (-F - (F**2 - 4 * E * G)**0.5)
return Temperature((ni[9] + D - ((ni[9] + D)**2 - 4 *
(ni[8] + ni[9] * D))**0.5) * 0.5)
def pressure_saturation(self, T=None):
"""Yields Psat given a temperature T"""
if T is None:
T = self.T
else:
T = Temperature(T)
if T < 273.15 or T > self.Tc:
raise ValueError('Temperature out of range.')
# table 34
ni = array([
1167.0521452767, -724213.16703206, -17.073846940092,
12020.82470247, -3232555.0322333, 14.91510861353, -4823.2657361591,
405113.40542057, -0.23855557567849, 650.17534844798
],
dtype='d')
v = T + ni[8] / (T - ni[9])
A = 1 * v**2 + ni[0] * v + ni[1]
B = ni[2] * v**2 + ni[3] * v + ni[4]
C = ni[5] * v**2 + ni[6] * v + ni[7]
return Pressure(
(2 * C / (-B + (B**2 - 4 * A * C)**0.5))**4).unit('MPa')
def _is_in_region(self):
"""Finds a region for the (T, p) point (see IAPWS-IF97 for details).
The usefulness of these regions are to divide the physical properties
of water into different sets of coefficients and equations."""
# for the 2 - 3 boundary line
ni = array([
348.05185628969, -1.1671859879975, 0.0010192970039326,
572.54459862746, 13.91883977887
],
dtype='d')
theta = self.T
pressure23 = Pressure(ni[0] + ni[1] * theta +
ni[2] * theta**2).unit('MPa')
# exceptional cases
if self.T == self.Tt and self.p == self.pt:
return 1
# regular cases
if self.T >= Temperature(273.15) and self.T <= Temperature(623.15):
if self.T < self.temperature_saturation(self.p):
return 1
else:
return 2
elif self.T > Temperature(623.15) and self.T <= Temperature(1073.15):
if self.p > pressure23:
return 3
else:
return 2
elif self.T >= Temperature(1073.15) and self.T <= Temperature(2273.15):
return 5
else:
raise Exception('Cannot assign region to the parameters p = ' +
str(self.p) + 'T = ' + str(self.T) + 'given.')
def _basic_equation1(self, value='gamma'):
"""Returns basic equation 1 and its derivatives, ex: 'gamma',
'gamma_tau', 'gamma_tau_pi', etc."""
# region1
Ii = array([
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
],
dtype='int')
Ji = array([
-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
],
dtype='int')
ni = array([
0.14632971213167, -0.84548187169114, -3.756360367204,
3.3855169168385, -0.95791963387872, 0.15772038513228,
-0.016616417199501, 0.00081214629983568, 0.00028319080123804,
-0.00060706301565874, -0.018990068218419, -0.032529748770505,
-0.021841717175414, -5.283835796993e-05, -0.00047184321073267,
-0.00030001780793026, 4.7661393906987e-05, -4.4141845330846e-06,
-7.2694996297594e-16, -3.1679644845054e-05, -2.8270797985312e-06,
-8.5205128120103e-10, -2.2425281908e-06, -6.5171222895601e-07,
-1.4341729937924e-13, -4.0516996860117e-07, -1.2734301741641e-09,
-1.7424871230634e-10, -6.8762131295531e-19, 1.4478307828521e-20,
2.6335781662795e-23, -1.1947622640071e-23, 1.8228094581404e-24,
-9.3537087292458e-26
],
dtype='d')
pi = self.p / Pressure(16.53).unit('MPa')
tau = Temperature(1386) / self.T
if value == 'gamma':
return sum(ni * ((7.1 - pi)**Ii) * ((tau - 1.222)**Ji))
elif value == 'gamma_tau':
return sum(ni * ((7.1 - pi)**Ii) * Ji * ((tau - 1.222)**(Ji - 1)))
elif value == 'gamma_tau_tau':
return sum(ni * ((7.1 - pi)**Ii) * Ji * (Ji - 1) *
((tau - 1.222)**(Ji - 2)))
elif value == 'gamma_pi':
return -1 * sum(ni * Ii * ((7.1 - pi)**(Ii - 1)) *
(tau - 1.222)**Ji)
elif value == 'gamma_pi_pi':
return sum(ni * Ii * (Ii - 1) * (7.1 - pi)**(Ii - 2) *
(tau - 1.222)**Ji)
elif value == 'gamma_pi_tau' or value == 'gamma_tau_pi':
return -1 * sum(ni * Ii * (7.1 - pi)**(Ii - 1) * Ji *
(tau - 1.222)**(Ji - 1))
else:
raise Exception('Function not assigned in _basic_equation1()')
def _basic_equation2(self, value='gamma'):
"""Returns equation 1 and its derivatives, ex: 'gamma', 'gamma_tau',
'gamma_tau_pi', etc."""
# region2; ideal part
J0 = array([0, 1, -5, -4, -3, -2, -1, 2, 3], dtype='d')
n0 = array([
-9.6927686500217, 10.086655968018, -0.005608791128302,
0.071452738081455, -0.40710498223928, 1.4240819171444,
-4.383951131945, -0.28408632460772, 0.021268463753307
],
dtype='d')
# region2; real part
Ii = array([
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
],
dtype='d')
Ji = array([
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
],
dtype='d')
ni = array([
-0.0017731742473213, -0.017834862292358, -0.045996013696365,
-0.057581259083432, -0.05032527872793, -3.3032641670203e-05,
-0.00018948987516315, -0.0039392777243355, -0.043797295650573,
-2.6674547914087e-05, 2.0481737692309e-08, 4.3870667284435e-07,
-3.227767723857e-05, -0.0015033924542148, -0.040668253562649,
-7.8847309559367e-10, 1.2790717852285e-08, 4.8225372718507e-07,
2.2922076337661e-06, -1.6714766451061e-11, -0.0021171472321355,
-23.895741934104, -5.905956432427e-18, -1.2621808899101e-06,
-0.038946842435739, 1.1256211360459e-11, -8.2311340897998,
1.9809712802088e-08, 1.0406965210174e-19, -1.0234747095929e-13,
-1.0018179379511e-09, -8.0882908646985e-11, 0.10693031879409,
-0.33662250574171, 8.9185845355421e-25, 3.0629316876232e-13,
-4.2002467698208e-06, -5.9056029685639e-26, 3.7826947613457e-06,
-1.2768608934681e-15, 7.3087610595061e-29, 5.5414715350778e-17,
-9.436970724121e-07
],
dtype='d')
pi = self.p / Pressure(1).unit('MPa')
tau = 540 / self.T
# arrays
if value == 'gamma':
return (self._basic_equation2('gamma_0') +
self._basic_equation2('gamma_r'))
elif value == 'gamma_0':
return log(pi) + sum(n0 * (tau**J0))
elif value == 'gamma_r':
return sum(ni * (pi**Ii) * (tau - 0.5)**Ji)
elif value == 'gamma_0_pi':
return 1 / pi
elif value == 'gamme_0_pi_pi':
return -1 / (pi**2)
elif value == 'gamma_0_tau':
return 0 + sum(n0 * J0 * (tau**(J0 - 1)))
elif value == 'gamma_0_tau_tau':
return 0 + sum(n0 * J0 * (J0 - 1) * tau**(J0 - 2))
elif value == 'gamma_0_pi_tau' or value == 'gamma_0_tau_pi':
return 0
elif value == 'gamma_r_pi':
return sum(ni * Ii * (pi**(Ii - 1)) * ((tau - 0.5)**Ji))
elif value == 'gamma_r_tau':
return sum(ni * (pi**Ii) * Ji * (tau - 0.5)**(Ji - 1))
elif value == 'gamma_r_pi_pi':
return sum(ni * Ii * (Ii - 1) * (pi**(Ii - 2))(tau - 0.5)**Ji)
elif value == 'gamma_r_tau_tau':
return sum(ni * (pi**Ii) * Ji * (Ji - 1) * (tau - 0.5)**(Ji - 2))
elif value == 'gamma_pi_tau' or value == 'gamma_tau_pi':
pass
def _basic_equation3(self, value='PHI'):
"""Returns equation 3 and its derivatives, ex: 'gamma',
'gamma_tau', 'gamma_tau_pi', etc."""
# do not forget that the first term is not used
Ii = array([
-1, 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
],
dtype='d')
# do not forget that the first term is not used
Ji = array([
-1, 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
],
dtype='d')
ni = array([
1.0658070028513, -15.732845290239, 20.944396974307,
-7.6867707878716, 2.6185947787954, -2.808078114862,
1.2053369696517, -0.0084566812812502, -1.2654315477714,
-1.1524407806681, 0.88521043984318, -0.64207765181607,
0.38493460186671, -0.85214708824206, 4.8972281541877,
-3.0502617256965, 0.039420536879154, 0.12558408424308,
-0.2799932969871, 1.389979956946, -2.018991502357,
-0.0082147637173963, -0.47596035734923, 0.0439840744735,
-0.44476435428739, 0.90572070719733, 0.70522450087967,
0.10770512626332, -0.32913623258954, -0.50871062041158,
-0.022175400873096, 0.094260751665092, 0.16436278447961,
-0.013503372241348, -0.014834345352472, 0.00057922953628084,
0.0032308904703711, 8.0964802996215e-05, -0.00016557679795037,
-4.4923899061815e-05
],
dtype='d')
# it looks like the first term is never used
# except in the PHI equations
Ii = Ii[1:]
Ji = Ji[1:]
ni = ni[1:]
n1 = 1.0658070028513
tau = self.Tc / self.T
# from equations 28 and p given as input,
# calculate rho to be used in PHI
def obj(x):
print(type(self.p))
print(type(x), x)
print(type(self.rhoc), self.rhoc)
return (
self.p - 1000 * x * self.R * self.T * (x / self.rhoc) *
(n1 /
(x / self.rhoc) + sum(ni * Ii *
(x / self.rhoc)**(Ii - 1) * tau**Ji)))
for i in range(1, 580, 1):
a = i
b = a + 1
if obj(a) * obj(b) < 0:
break
rho = scipy.optimize.bisect(obj, a, b, xtol=1e-10)
delta = rho / self.rhoc
# returns PHI and found rho as tuple (PHI, rho)
if value == 'PHI':
return (n1 * log(delta) + sum(ni * delta**Ii * tau**Ji), rho)
elif value == 'PHI_delta':
return (n1 / delta + sum(ni * Ii * delta**(Ii - 1) * tau**Ji), rho)
elif value == 'PHI_delta_delta':
return (-n1 / (delta**2) +
sum(ni * Ii * (Ii - 1) * delta**(Ii - 2) * tau**Ji), rho)
elif value == 'PHI_tau':
return (sum(ni * delta**Ii * Ji * tau**(Ji - 1)), rho)
elif value == 'PHI_tau_tau':
return (sum(ni * delta**Ii * Ji * (Ji - 1) * tau**(Ji - 2)), rho)
elif value == 'PHI_delta_tau' or value == 'PHI_tau_delta':
return (sum(ni * Ii * delta**(Ii - 1) * Ji * tau**(Ji - 1)), rho)
# there is no region 4; region 4 is the saturation line of water/vapor
def _basic_equation5(self, value='gamma'):
"""Returns equation 1 and its derivatives, ex: 'gamma',
'gamma_tau', 'gamma_tau_pi', etc."""
J0 = array([0, 1, -3, -2, -1, 2], dtype='d')
n0 = array([
-13.179983674201, 6.8540841634434, -0.024805148933466,
0.36901534980333, -3.1161318213925, -0.32961626538917
],
dtype='d')
Ii = array([1, 1, 1, 2, 2, 3], dtype='d')
Ji = array([1, 2, 3, 3, 9, 7], dtype='d')
ni = array([
0.0015736404855259, 0.00090153761673944, -0.0050270077677648,
2.2440037409485e-06, -4.1163275453471e-06, 3.7919454822955e-08
],
dtype='d')
pi = self.p / Pressure(1).unit('MPa')
tau = Temperature(1000) / self.T
if value == 'gamma':
return (self._basic_equation5('gamma_0') +
self._basic_equation5('gamma_r'))
elif value == 'gamma_0':
return log(pi) + sum(n0 * (tau**J0))
elif value == 'gamma_r':
return sum(ni * (pi**Ii) * (tau**Ji))
elif value == 'gamma_0_pi':
return 1 / pi
elif value == 'gamma_0_pi_pi':
return -1 / (pi**2)
elif value == 'gamma_0_tau':
return sum(n0 * J0 * (tau**(J0 - 1)))
elif value == 'gamma_0_tau_tau':
sum(n0 * J0 * (J0 - 1) * (tau**(J0 - 2)))
elif value == 'gamma_0_tau_pi' or value == 'gamma_0_pi_tau':
return 0 + 0
elif value == 'gamma_r_pi':
return sum(ni * Ii * (pi**(Ii - 1)) * (tau**Ji))
elif value == 'gamma_r_tau':
return sum(ni * (pi**Ii) * Ji * (tau**(Ji - 1)))
elif value == 'gamma_r_pi_pi':
return sum(ni * Ii * (Ii - 1) * (pi**(Ii - 2)) * (tau**Ji))
elif value == 'gamma_r_tau_tau':
return sum(ni * (pi**Ii) * Ji * (Ji - 1) * (tau**(Ji - 2)))
elif value == 'gamma_r_tau_pi' or 'gamma_r_pi_tau':
return sum(ni * Ii * (pi**(Ii - 1)) * Ji * (tau**(Ji - 1)))
def gibbs_energy(self, p=None, T=None):
"""Returns the Gibbs Energy given p and T in kJ/kg."""
if p is None:
p = self.p
else:
p = Pressure(p)
if T is None:
T = self.T
else:
T = Temperature(T)
if self._is_in_region() == 1:
return self._basic_equation1('gamma') * self.R * T
elif self._is_in_region() == 2:
return self._basic_equation2('gamma') * self.R * T
elif self._is_in_region() == 3:
pass
elif self._is_in_region() == 4:
pass
elif self._is_in_region() == 5:
pass
def specific_volume(self, p=None, T=None):
"""Returns the specific volume in m³/kg"""
if p is None:
p = self.p
else:
p = Pressure(p)
if T is None:
T = self.T
else:
T = Temperature(T)
if self._is_in_region() == 1:
pi = self.p / Pressure(16.53).unit('MPa')
return (self._basic_equation1('gamma_pi') * self.R * self.T * pi /
self.p * 1e3) # because of kJ in R
elif self._is_in_region() == 2:
pi = self.p / Pressure(1).unit('MPa')
return (pi * (self._basic_equation2('gamma_0_pi') +
self._basic_equation2('gamma_r_pi')) * self.R *
self.T / self.p * 1e3)
elif self._is_in_region() == 3:
return None
elif self._is_in_region() == 4:
pass
elif self._is_in_region() == 5:
pass
return -1
def internal_energy(self, p=None, T=None):
"""NOT IMPLEMENTED"""
if p is None:
p = self.p
else:
p = Pressure(p)
if T is None:
T = self.T
else:
T = Temperature(T)
if self._is_in_region() == 1:
pi = self.p / Pressure(16.53).unit('MPa')
tau = Temperature(1386) / self.T
return (tau * self._basic_equation1('gamma_tau') -
pi * self._basic_equation1('gamma_pi')) * self.R * self.T
elif self._is_in_region() == 2:
pi = self.p / Pressure(1).unit('MPa')
tau = 540 / self.T
return (tau * (self._basic_equation2('gamma_0_tau') +
self._basic_equation2('gamma_r_tau')) - pi *
(self._basic_equation2('gamma_0_pi') +
self._basic_equation2('gamma_r_pi'))) * self.R * self.T
elif self._is_in_region() == 3:
pass
elif self._is_in_region() == 4:
pass
elif self._is_in_region() == 5:
pass
return -1
def entropy(self, p=None, T=None):
"""NOT IMPLEMENTED"""
if p is None:
p = self.p
else:
p = Pressure(p)
if T is None:
T = self.T
else:
T = Temperature(T)
if self._is_in_region() == 1:
pi = self.p / Pressure(16.53).unit('MPa')
tau = Temperature(1386) / self.T
return (tau * self._basic_equation1('gamma_tau') -
self._basic_equation1('gamma')) * self.R
elif self._is_in_region() == 2:
pi = self.p / Pressure(1).unit('MPa')
tau = 540 / self.T
return ((tau * (self._basic_equation2('gamma_0_tau') +
self._basic_equation2('gamma_r_tau')) -
(self._basic_equation2('gamma_0') +
self._basic_equation2('gamma_r'))) * self.R)
elif self._is_in_region() == 3:
pass
elif self._is_in_region() == 4:
pass
elif self._is_in_region() == 5:
pass
return -1
def enthalpy(self, p=None, T=None):
"""Returns the enthalpy given p and T in kJ/kg."""
if p is None:
p = self.p
else:
p = Pressure(p)
if T is None:
T = self.T
else:
T = Temperature(T)
if self._is_in_region() == 1:
return Enthalpy(self._basic_equation1('gamma_tau') * 1386 * self.R)
elif self._is_in_region() == 2:
return Enthalpy(540 * self.R *
(self._basic_equation2('gamma_0_tau') +
self._basic_equation2('gamma_r_tau')))
elif self._is_in_region() == 3:
# for region 3 rho needs to be solved numerically
reg3_solved = self._basic_equation3('PHI_delta')
delta = reg3_solved[1] / self.rhoc
tau = self.Tc / self.T
return Enthalpy((tau * self._basic_equation3('PHI_tau')[0] +
delta * reg3_solved[0]) * self.R * self.T)
elif self._is_in_region() == 4:
return None
elif self._is_in_region() == 5:
pi = self.p / Pressure(1).unit('MPa')
tau = Temperature(1000) / self.T
return (tau * (self._basic_equation5('gamma_0_tau') +
self._basic_equation5('gamma_r_tau')) * self.R *
self.T)
def heat_capacity(self, p=None, T=None):
"""Returns the isobaric heat capacity given p and T in kJ/(kg K)."""
if p is None:
p = self.p
else:
p = Pressure(p)
if T is None:
T = self.T
else:
T = Temperature(T)
if self._is_in_region() == 1:
tau = 1386 / T
return (-1 * tau * tau * self.R *
self._basic_equation1('gamma_tau_tau'))
elif self._is_in_region() == 2:
pass
elif self._is_in_region() == 3:
delta = rho / self.rhoc
tau = self.Tc / self.T
return (
-tau**2 / self._basic_equation3('PHI_tau_tau') +
(delta * self._basic_equation3('PHI_delta') -
delta * tau * self._basic_equation3('PHI_tau_delta'))**2 /
(2 * delta * self._basic_equation3('PHI_delta') +
delta**2 * self._basic_equation3('PHI_delta_delta'))) * self.R
elif self._is_in_region() == 4:
pass
elif self._is_in_region() == 5:
pass
return -1
def heat_capacity_constant_v(self, p=None, T=None):
"""NOT IMPLEMENTED"""
if p is None:
p = self.p
else:
p = Pressure(p)
if T is None:
T = self.T
else:
T = Temperature(T)
if self._is_in_region() == 1:
pi = self.p / Pressure(16.53).unit('MPa')
tau = Temperature(1386) / self.T
return (-(tau**2) * self._basic_equation1('gamma_tau_tau') +
((self._basic_equation1('gamma_pi') -
tau * self._basic_equation1('gamma_pi_tau'))**2) /
self._basic_equation1('gamma_pi_pi')) * self.R
elif self._is_in_region() == 2:
pass
elif self._is_in_region() == 3:
pass
elif self._is_in_region() == 4:
pass
elif self._is_in_region() == 5:
pass
return -1
def speed_of_sound(self, p=None, T=None):
"""NOT IMPLEMENTED"""
if p is None:
p = self.p
else:
p = Pressure(p)
if T is None:
T = self.T
else:
T = Temperature(T)
if self._is_in_region() == 1:
pi = self.p / Pressure(16.53).unit('MPa')
tau = Temperature(1386) / self.T
inside_frac = (((self._basic_equation1('gamma_pi') -
tau * self._basic_equation1('gamma_tau_pi'))**2) /
((tau**2) * self._basic_equation1('gamma_tau_tau')))
return sqrt(
((self._basic_equation1('gamma_pi')**2) /
(inside_frac - self._basic_equation1('gamma_pi_pi'))) *
self.R * self.T * 1000)
elif self._is_in_region() == 2:
pass
elif self._is_in_region() == 3:
pass
elif self._is_in_region() == 4:
pass
elif self._is_in_region() == 5:
pass
return -1
def _basic_equation2(self, value='gamma'):
"""Returns equation 1 and its derivatives, ex: 'gamma', 'gamma_tau',
'gamma_tau_pi', etc."""
# region2; ideal part
J0 = array([0, 1, -5, -4, -3, -2, -1, 2, 3], dtype='d')
n0 = array([
-9.6927686500217, 10.086655968018, -0.005608791128302,
0.071452738081455, -0.40710498223928, 1.4240819171444,
-4.383951131945, -0.28408632460772, 0.021268463753307
],
dtype='d')
# region2; real part
Ii = array([
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
],
dtype='d')
Ji = array([
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
],
dtype='d')
ni = array([
-0.0017731742473213, -0.017834862292358, -0.045996013696365,
-0.057581259083432, -0.05032527872793, -3.3032641670203e-05,
-0.00018948987516315, -0.0039392777243355, -0.043797295650573,
-2.6674547914087e-05, 2.0481737692309e-08, 4.3870667284435e-07,
-3.227767723857e-05, -0.0015033924542148, -0.040668253562649,
-7.8847309559367e-10, 1.2790717852285e-08, 4.8225372718507e-07,
2.2922076337661e-06, -1.6714766451061e-11, -0.0021171472321355,
-23.895741934104, -5.905956432427e-18, -1.2621808899101e-06,
-0.038946842435739, 1.1256211360459e-11, -8.2311340897998,
1.9809712802088e-08, 1.0406965210174e-19, -1.0234747095929e-13,
-1.0018179379511e-09, -8.0882908646985e-11, 0.10693031879409,
-0.33662250574171, 8.9185845355421e-25, 3.0629316876232e-13,
-4.2002467698208e-06, -5.9056029685639e-26, 3.7826947613457e-06,
-1.2768608934681e-15, 7.3087610595061e-29, 5.5414715350778e-17,
-9.436970724121e-07
],
dtype='d')
pi = self.p / Pressure(1).unit('MPa')
tau = 540 / self.T
# arrays
if value == 'gamma':
return (self._basic_equation2('gamma_0') +
self._basic_equation2('gamma_r'))
elif value == 'gamma_0':
return log(pi) + sum(n0 * (tau**J0))
elif value == 'gamma_r':
return sum(ni * (pi**Ii) * (tau - 0.5)**Ji)
elif value == 'gamma_0_pi':
return 1 / pi
elif value == 'gamme_0_pi_pi':
return -1 / (pi**2)
elif value == 'gamma_0_tau':
return 0 + sum(n0 * J0 * (tau**(J0 - 1)))
elif value == 'gamma_0_tau_tau':
return 0 + sum(n0 * J0 * (J0 - 1) * tau**(J0 - 2))
elif value == 'gamma_0_pi_tau' or value == 'gamma_0_tau_pi':
return 0
elif value == 'gamma_r_pi':
return sum(ni * Ii * (pi**(Ii - 1)) * ((tau - 0.5)**Ji))
elif value == 'gamma_r_tau':
return sum(ni * (pi**Ii) * Ji * (tau - 0.5)**(Ji - 1))
elif value == 'gamma_r_pi_pi':
return sum(ni * Ii * (Ii - 1) * (pi**(Ii - 2))(tau - 0.5)**Ji)
elif value == 'gamma_r_tau_tau':
return sum(ni * (pi**Ii) * Ji * (Ji - 1) * (tau - 0.5)**(Ji - 2))
elif value == 'gamma_pi_tau' or value == 'gamma_tau_pi':
pass
def test_iapws():
"""
Tests are given inside the IAPWS document. See references for more details.
"""
#test Tsat given P
assert round(Water(1e5, 373.15).temperature_saturation(0.1e6),
6) == 372.755919
assert round(Water(1e5, 373.15).temperature_saturation(1e6),
6) == 453.035632
assert round(Water(1e5, 373.15).temperature_saturation(10e6),
6) == 584.149488
#test Psat given T
assert round(Water(1e5, 373.15).pressure_saturation(300).MPa,
11) == 0.00353658941
assert round(Water(1e5, 373.15).pressure_saturation(500).MPa,
8) == 2.63889776
assert round(Water(1e5, 373.15).pressure_saturation(600).MPa,
7) == 12.3443146
#test regions
# arbitrary points
point_in_region1 = (Pressure(20e6), Temperature(300))
point_in_region2 = (Pressure(1e5), Temperature(373.15))
point_in_region3 = (Pressure(40e6), Temperature(700))
point_in_region4 = (Pressure(1).unit('atm'), Temperature(373.1243))
point_in_region5 = (Pressure(20e6), Temperature(1500))
assert Water(*point_in_region1)._is_in_region() == 1
assert Water(*point_in_region2)._is_in_region() == 2
assert Water(*point_in_region3)._is_in_region() == 3
# region 4 does not exist as a region; it is rather the saturation line
assert Water(*point_in_region5)._is_in_region() == 5
#region 1
#assert specific volume
assert round(Water(3e6, 300, massic_basis=True).specific_volume(),
11) == 0.00100215168
assert round(Water(80e6, 300, massic_basis=True).specific_volume(),
12) == 0.000971180894
assert round(Water(3e6, 500, massic_basis=True).specific_volume(),
11) == 0.00120241800
#
# #assert internal energy
assert round(Water(3e6, 300, massic_basis=True).internal_energy(),
6) == 112.324818
assert round(Water(80e6, 300, massic_basis=True).internal_energy(),
6) == 106.448356
assert round(Water(3e6, 500, massic_basis=True).internal_energy(),
6) == 971.934985
#
# #assert enthropy
assert round(Water(3e6, 300, massic_basis=True).entropy(),
9) == 0.392294792
assert round(Water(80e6, 300, massic_basis=True).entropy(),
9) == 0.368563852
assert round(Water(3e6, 500, massic_basis=True).entropy(), 8) == 2.58041912
#assert enthalpy
assert round(Water(3e6, 300, massic_basis=True).enthalpy(),
6) == 115.331273
assert round(Water(80e6, 300, massic_basis=True).enthalpy(),
6) == 184.142828
assert round(Water(3e6, 500, massic_basis=True).enthalpy(),
6) == 975.542239
#assert cp
assert round(Water(3e6, 300, massic_basis=True).heat_capacity(),
8) == 4.17301218
assert round(Water(80e6, 300, massic_basis=True).heat_capacity(),
8) == 4.01008987
assert round(Water(3e6, 500, massic_basis=True).heat_capacity(),
8) == 4.65580682
# #assert cv
# assert round(Water(3e6, 300).enthalpy(),6) == 115.331273
# assert round(Water(80e6, 300).enthalpy(),6) == 184.142828
# assert round(Water(3e6, 500).enthalpy(),6) == 975.542239
#
#assert speed of sound
assert round(Water(3e6, 300, massic_basis=True).speed_of_sound(),
5) == 1507.73921
assert round(Water(80e6, 300, massic_basis=True).speed_of_sound(),
5) == 1634.69054
assert round(Water(3e6, 500, massic_basis=True).speed_of_sound(),
5) == 1240.71337
#region 2
#assert specific volume
assert round(Water(3500, 300, massic_basis=True).specific_volume(),
7) == 39.4913866
assert round(Water(3500, 700, massic_basis=True).specific_volume(),
7) == 92.3015898
assert round(Water(30e6, 700, massic_basis=True).specific_volume(),
11) == 0.00542946619
#
# #assert internal energy
assert round(Water(3500, 300, massic_basis=True).internal_energy(),
5) == 2411.69160
assert round(Water(3500, 700, massic_basis=True).internal_energy(),
5) == 3012.62819
assert round(Water(30e6, 700, massic_basis=True).internal_energy(),
5) == 2468.61076
#
# #assert enthropy
assert round(Water(3500, 300, massic_basis=True).entropy(),
8) == 8.52238967
assert round(Water(3500, 700, massic_basis=True).entropy(),
7) == 10.1749996
assert round(Water(30e6, 700, massic_basis=True).entropy(),
8) == 5.17540298
#assert enthalpy
assert round(Water(3500, 300, massic_basis=True).enthalpy(),
5) == 2549.91145
assert round(Water(3500, 700, massic_basis=True).enthalpy(),
5) == 3335.68375
assert round(Water(30e6, 700, massic_basis=True).enthalpy(),
5) == 2631.49474
#assert cp
# assert round(Water(3e6, 300).heat_capacity(),8) == 4.17301218
# assert round(Water(80e6, 300).heat_capacity(),8) == 4.01008987
# assert round(Water(3e6, 500).heat_capacity(),8) == 4.65580682
# #assert enthalpy
# assert round(Water(3e6, 300).enthalpy(),6) == 115.331273
# assert round(Water(80e6, 300).enthalpy(),6) == 184.142828
# assert round(Water(3e6, 500).enthalpy(),6) == 975.542239
#
# #assert enthalpy
# assert round(Water(3e6, 300).enthalpy(),6) == 115.331273
# assert round(Water(80e6, 300).enthalpy(),6) == 184.142828
# assert round(Water(3e6, 500).enthalpy(),6) == 975.542239
#region 3
#assert specific volume
# assert round(Water(3500, 300).specific_volume(),7) == 39.4913866
# assert round(Water(3500, 700).specific_volume(),7) == 92.3015898
# assert round(Water(30e6, 700).specific_volume(),11) == 0.00542946619
#
# #assert internal energy
# assert round(Water(3e6, 300).enthalpy(),6) == 115.331273
# assert round(Water(80e6, 300).enthalpy(),6) == 184.142828
# assert round(Water(3e6, 500).enthalpy(),6) == 975.542239
#
# #assert enthropy
# assert round(Water(3e6, 300).enthalpy(),6) == 115.331273
# assert round(Water(80e6, 300).enthalpy(),6) == 184.142828
# assert round(Water(3e6, 500).enthalpy(),6) == 975.542239
#assert enthalpy
assert round(Water(25.5837018e6, 650, massic_basis=True).enthalpy(),
5) == 1863.43019
assert round(Water(22.2930643e6, 650, massic_basis=True).enthalpy(),
5) == round(2375.12401, 3)
assert round(Water(78.3095639e6, 750, massic_basis=True).enthalpy(),
5) == 2258.68845
#assert cp
# assert round(Water(3e6, 300).heat_capacity(),8) == 4.17301218
# assert round(Water(80e6, 300).heat_capacity(),8) == 4.01008987
# assert round(Water(3e6, 500).heat_capacity(),8) == 4.65580682
# #assert enthalpy
# assert round(Water(3e6, 300).enthalpy(),6) == 115.331273
# assert round(Water(80e6, 300).enthalpy(),6) == 184.142828
# assert round(Water(3e6, 500).enthalpy(),6) == 975.542239
#
# #assert enthalpy
# assert round(Water(3e6, 300).enthalpy(),6) == 115.331273
# assert round(Water(80e6, 300).enthalpy(),6) == 184.142828
# assert round(Water(3e6, 500).enthalpy(),6) == 975.542239
# region 4
# There is no region 4; instead region 4 is the saturation line
# region 5
#assert specific volume
# assert round(Water(3500, 300).specific_volume(),7) == 39.4913866
# assert round(Water(3500, 700).specific_volume(),7) == 92.3015898
# assert round(Water(30e6, 700).specific_volume(),11) == 0.00542946619
#
# #assert internal energy
# assert round(Water(3e6, 300).enthalpy(),6) == 115.331273
# assert round(Water(80e6, 300).enthalpy(),6) == 184.142828
# assert round(Water(3e6, 500).enthalpy(),6) == 975.542239
#
# #assert enthropy
# assert round(Water(3e6, 300).enthalpy(),6) == 115.331273
# assert round(Water(80e6, 300).enthalpy(),6) == 184.142828
# assert round(Water(3e6, 500).enthalpy(),6) == 975.542239
#assert enthalpy
assert round(Water(0.5e6, 1500, massic_basis=True).enthalpy(),
5) == 5219.76855
assert round(Water(30e6, 1500, massic_basis=True).enthalpy(),
5) == 5167.23514
assert round(Water(30e6, 2000, massic_basis=True).enthalpy(),
5) == 6571.22604