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Neglecting pressure dependence of $\mu_\ell$ and $k_\ell$

In this section we will investigate the error associated with the approximations

$$\begin{eqnarray*} \mu_\ell(p,t) &\approx& \mu_f(t)\\ k_\ell(p,t) &\approx& k_f(t) \end{eqnarray*}$$

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

ie calculation of viscosity and thermal conductivity of subcooled water where we neglect the pressure dependence and only recognize the temperature dependence.

In such an analysis it is appropriate to look at the saturation curve in Figure B.9 for steam-water because when we use the transport properties at the saturation curve we obtain properties at point $(p_{\mbox{\protect\scriptsize sat}}(t),t)$ instead of (p,t), ie we calculate the properties at the wrong pressure. The pressure difference, $\Delta p \;\hbox{$=$\kern-0.68em\raise1.1ex \hbox{$\scriptscriptstyle\triangle$}}\;p-p_{\mbox{\protect\scriptsize sat}}(t)$, is approximately

$$\Delta p \simeq (t_{\mbox{\protect\scriptsize sat}}(p)-t)\left(\frac{dp}{dt}\right)_{t_{\mbox{\protect\scriptsize sat}}(p)}$$ (B7)

where ${\mbox{dp}}/{\mbox{dt}}$ is the slope of the saturation curve.

With reference to Figure B.9 we observe that the pressure error increases with increasing temperature. For pressures around 70 bar of interest to BWR design we have a slope of approximately 1 bar/ ${}^\circ\mbox{C}$.

In Table B.1 we have compared the approximate calculation of $k_\ell$ and $\mu_\ell$ to measured values. The error, E of the approximate calculation is defined by

$$E_\xi \;\hbox{$=$\kern-0.68em\raise1.1ex \hbox{$\scriptscr... ...ct\scriptsize approx}} }{\xi_{\mbox{\protect\scriptsize tbl}}}$$ (B8)

where $\xi$ denotes the property under investigation. The indices tbl and approx denote a tabular and approximate value respectively.

^{B4 B5 B6 B7 B8 B9 B10}

The results in Table B.1 indicate that even 40 ${}^\circ\mbox{C}$ of subcooling at a pressure of 75 bar the error associated with the approximation is within the measurement error^B11. Since the error increases with temperature we estimate that in order to obtain properties within 2 percent with a subcooling of 20 ${}^\circ\mbox{C}$ we require

$$p_{\mbox{\protect\scriptsize sat}} < 90 {\mbox{ bar}} \hspa... ...box{\protect\scriptsize sat}} < 303 \mbox{${}^\circ\mbox{C}$}$$ (B9)

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