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Next: Thermal conductivity of water Up: Derivation of curve fits Previous: Viscosity of water at Contents Index

Viscosity of steam at saturation

According to White [28, p. 28] we could fit the viscosity data to a model function of the form

$\begin{displaymath} \frac{\mu}{\mu_0} = \left( \frac{T}{T_0} \right)^n \end{displaymath}$

(B4)

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

It however turns out that a quadratic model function of the form

$\begin{displaymath} \mu_i^* = a + b T_i^* + c (T_i^*)^2 \end{displaymath}$

(B5)

does a much better job. The quantities $\mu_i^*$ and T_i^* is a transformation of the original variables $\mu_i$ and T_i given by

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

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

Running a least square fit on the transformed data originating from data in [25, Table 6, Db 5] in the temperature range from 210 ${}^\circ\mbox{C}$ to 300 ${}^\circ\mbox{C}$ results in the following coefficients

$\begin{eqnarray*} a &=& -0.4914429395 \\ b &=& 0.3707909076 \\ c &=& 0.1212... ... (18.38\cdot 10^{-5} {\mbox{P}}, 270\mbox{${}^\circ\mbox{C}$}) \end{eqnarray*}$

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

The resulting fit has an error less than 0.11 percent in the temperature range [210 ${}^\circ\mbox{C}$ ;300 ${}^\circ\mbox{C}$ ].

In the figures B.5 and B.6 we see the a comparison of the fit and the data and the error of the fit as a function of temperature respectively.

$\begin{figure} % latex2html id marker 47045\rule{\textwidth}{0.2mm} \rule{0cm}... ...\mu_g(t)$(\raise0.5ex\hbox{$.....$}) and the data points ($\cdot$).}\end{figure}$

$\begin{figure} % latex2html id marker 47065\rule{\textwidth}{0.2mm} \rule{0cm}... ...rve fit formula of the viscosity of steam at saturation $\mu_g(t)$.}\end{figure}$

Next: Thermal conductivity of water Up: Derivation of curve fits Previous: Viscosity of water at Contents Index

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