# Oil quadratic viscosity¶

With this model the oil viscosity has a quadratic dependence with respect to the pressure and temperature. Two reference values are required for both pressure and temperature, plus corresponding coefficients.

See an example below:

EOS OIL
DENSITY CONSTANT 734.29d0 !kg/m3
ENTHALPY LINEAR_TEMP 1.d3 !c oil [J/kg/°C]
REFERENCE_VALUE 2.94d-3
PRES_REF_VALUES 1.d5 0.0
TEMP_REF_VALUES 10.0 0.0
PRES_COEFFICIENTS 0.0d0 0.0d0
TEMP_COEFFICIENTS -0.01522d-3 0.0d0
END
END


The mathematical expression of the model is as follows:

$\mu (P ,T )=\mu_0 +a_1 ( P − P_1 ) +b_1 ( T −T_1 ) + a_2 ( P− P_2 )^2 +b_2 ( T −T_2 )^2$

where

$\begin{split}\begin{split} &\mu &= \mbox{viscosity [Pa.s]} \\ &\mu_0 &= \mbox{reference viscosity [Pa.s]} \\ &P_1 &= \mbox{linear pressure reference [Pa]} \\ &P_2 &= \mbox{quadratic pressure reference [Pa]} \\ &a_1 &= \mbox{linear pressure coefficient [s]} \\ &a_2 &= \mbox{quadratic pressure pressure coefficient [s/Pa]} \\ &T_1 &= \mbox{linear temperature reference [°C]} \\ &T_2 &= \mbox{quadratic temperature reference [°C]} \\ &b_1 &= \mbox{linear temperature coefficient [Pa.s/°C]} \\ &b_2 &= \mbox{quadratic temperature coefficient [Pa.s/(°C)^2]} \end{split}\end{split}$

Setting to zero the quadratic coefficients the quadratic model simplifies to a linear model. Units cannot be specified, therefore values must be entered in the units prescribed above.