def viscosity_at_any_temp(viscosity40: float, viscosity100: float,
temperature: float) -> float:
"""Calculate the kinematic viscosity at any temperature (ASTM D341)."""
_viscosity40 = validate_viscosity(viscosity40, "40")
_viscosity100 = validate_viscosity(viscosity100, "100")
_temperature = validate_temperature(temperature)
x = math.log10(math.log10(_viscosity40 + 0.7))
y = math.log10(math.log10(_viscosity100 + 0.7))
t0 = math.log10(40 + _TO_KELVIN)
t1 = math.log10(100 + _TO_KELVIN)
target_t = math.log10(_temperature + _TO_KELVIN)
b = (x - y) / (t1 - t0)
a = x + b * t0
v = 10**(10**(a - b * target_t)) - 0.7
return round(v, 2)
def _viscosity_index(viscosity40: float, viscosity100: float) -> float:
"""Calculate the Viscosity Index (VI) by ASTM-D2270."""
_viscosity40 = validate_viscosity(viscosity40, "40")
_viscosity100 = validate_viscosity(viscosity100, "100")
upper = float("inf")
interpolation_coefs = {
(2.0, 3.8): (1.14673, 1.7576, -0.109, 0.84155, 1.5521, -0.077),
(3.8, 4.4): (3.38095, -15.4952, 33.196, 0.78571, 1.7929, -0.183),
(4.4, 5.0): (2.5, -7.2143, 13.812, 0.82143, 1.5679, 0.119),
(5.0, 6.4): (0.101, 16.635, -45.469, 0.04985, 9.1613, -18.557),
(6.4, 7.0): (3.35714, -23.5643, 78.466, 0.22619, 7.7369, -16.656),
(7.0, 7.7): (0.01191, 21.475, -72.870, 0.79762, -0.7321, 14.61),
(7.7, 9.0): (0.41858, 16.1558, -56.040, 0.05794, 10.5156, -28.240),
(9.0, 12.0): (0.88779, 7.5527, -16.600, 0.26665, 6.7015, -10.810),
(12.0, 15.0): (0.7672, 10.7972, -38.180, 0.20073, 8.4658, -22.490),
(15.0, 18.0): (0.97305, 5.3135, -2.200, 0.28889, 5.9741, -4.930),
(18.0, 22.0): (0.97256, 5.25, -0.980, 0.24504, 7.416, -16.730),
(22.0, 28.0): (0.91413, 7.4759, -21.820, 0.20323, 9.1267, -34.230),
(28.0, 40.0): (0.87031, 9.7157, -50.770, 0.18411, 10.1015, -46.750),
(40.0, 55.0): (0.84703, 12.6752, -133.310, 0.17029, 11.4866, -80.620),
(55.0, 70.0): (0.85921, 11.1009, -83.19, 0.1713, 11.368, -76.940),
(70.0, upper): (0.83531, 14.6731, -216.246, 0.16841, 11.8493, -96.947),
}
a, b, c, d, e, f = [0.0] * 6
for k, v in interpolation_coefs.items():
if k[0] <= _viscosity100 < k[1]:
a, b, c, d, e, f = v
break
L = a * _viscosity100**2 + b * _viscosity100 + c
H = d * _viscosity100**2 + e * _viscosity100 + f
if _viscosity40 >= H:
return round(((L - _viscosity40) / (L - H)) * 100)
N = (math.log10(H) - math.log10(_viscosity40)) / math.log10(_viscosity100)
return round(((10**N - 1) / 0.00715) + 100)
def viscosity_at_40(viscosity100: float, index: float) -> float:
"""Calculate the Kinematic Viscosity (KV) at 40°C.
Valid for viscosities under 2000 cSt at 40°C.
"""
_viscosity = _viscosity100 = validate_viscosity(viscosity100, "100")
_index = validate_viscosity_index(index)
while (_viscosity_index(_viscosity, _viscosity100) >= _index
and _viscosity <= MAX_VISCOSITY_40):
_viscosity += 0.05
return round((_viscosity * 100 + 0.1) / 100, 2)
def viscosity_at_100(viscosity40: float, index: float) -> float:
"""Calculate the Kinematic Viscosity (KV) at 100°C.
Valid for viscosities between 2 and 500 cSt at 100°C.
"""
_viscosity = MIN_VISCOSITY
_viscosity40 = validate_viscosity(viscosity40, "40")
_index = validate_viscosity_index(index)
while (_viscosity_index(_viscosity40, _viscosity) <= _index
and _viscosity <= MAX_VISCOSITY_100):
_viscosity += 0.01
return round((_viscosity * 100 + 0.01) / 100, 2)
def test_viscosity100_wrong_value(self, viscosity100, temp):
with pytest.raises(ConceptError):
validate_viscosity(viscosity100, temp)
def test_viscosity100(self, viscosity100, temp, expected):
assert validate_viscosity(viscosity100, temp) == expected
def test_viscosity40_wrong_number(self, viscosity40, temp):
with pytest.raises(ValidationError):
validate_viscosity(viscosity40, temp)