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Viscosity of water at saturation

According to [28, p. 35]^B2 the viscosity of liquids may be fit accurately to a model function of the form

$$\mu(t) = \mu_0 \exp\left[ a + b \left(\frac{T}{T_0}\right) + c \left(\frac{T}{T_0}\right)^2 \right]$$ (B2)

where $(\mu_0,T_0)$ is a reference point and $a,b,c \in \Re$.

If we transform our data such that

$$\begin{eqnarray*} \mu_i &\mapsto& \mu_i^* \;\hbox{$=$\kern-0.68em\raise1.1ex \... ...e1.1ex \hbox{$\scriptscriptstyle\triangle$}}\;\frac{T_i}{T_0} \end{eqnarray*}$$

$\parbox{1.50cm}{\begin{eqnarray} \end{eqnarray}}$

we actually have to fit the transformed data points $(\mu_i^*,T_i^*)$ to the quadratic model function

m(t) = a + bT^* + c(T^*)² (B3)

If we fit data in the temperature interval 230 ${}^\circ\mbox{C}$ to 300 ${}^\circ\mbox{C}$ given by [25, Table 6, Db 5] in a least square sense to the model function we obtain the following coefficients

$$\begin{eqnarray*} a &=& 1.220692035 \\ b &=& -1.306580184 \\ c &=& 8.525375... ...& (97.4\cdot 10^{-5} {\mbox{P}}, 270\mbox{${}^\circ\mbox{C}$}) \end{eqnarray*}$$

$\parbox{1.50cm}{\begin{eqnarray} \end{eqnarray}}$

The resulting fit has an error less than 0.13 percent in the temperature range [230 ${}^\circ\mbox{C}$;300 ${}^\circ\mbox{C}$].

In the figures B.3 and B.4 we see the a comparison of the fit and the data and the error of the fit as a function of temperature respectively.

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