Formula
Properties are evaluated from the IAPWS-IF97 equations, not from a fitted curve:
\(p_{sat} = p_s(T) \;\text{(IF97 Eq. 30)} \qquad h_f, s_f, v_f, c_p = f(p_{sat}, T) \;\text{(IF97 region 1)} \qquad h_{fg} = h_g - h_f\)
\(\nu = \frac{\mu}{\rho} \qquad Pr = \frac{c_p\,\mu}{k}\)
Variables
| Symbol | Meaning | SI unit |
|---|---|---|
| \(T\) | water temperature | K |
| \(p_{sat}\) | saturation (boiling) pressure at \(T\) | Pa |
| \(h_f\) | specific enthalpy of saturated liquid | J/kg |
| \(s_f\) | specific entropy of saturated liquid | J/(kg·K) |
| \(\rho\) | density | kg/m³ |
| \(v_f\) | specific volume | m³/kg |
| \(c_p\) | isobaric specific heat capacity | J/(kg·K) |
| \(\mu\) | dynamic viscosity | Pa·s |
| \(\nu\) | kinematic viscosity | m²/s |
| \(k\) | thermal conductivity | W/(m·K) |
| \(Pr\) | Prandtl number | – |
| \(h_{fg}\) | latent heat of vaporisation | J/kg |
Method and standards
Thermodynamic properties from the IAPWS Industrial Formulation 1997 (region 1 and the region 4 saturation line; region 3 by iteration above 350 °C). Viscosity from the IAPWS 2008 formulation and thermal conductivity from the IAPWS 2011 formulation, both evaluated at the IF97 density. The code is FireCAD's own implementation, verified against the check values printed in the IAPWS releases.
Assumptions and limits
- 0.01 °C to 373.946 °C (the critical point). Transport properties omit the critical enhancement, which matters only within about 2 K of the critical temperature.
- Pure water; dissolved solids change density and boiling point slightly.
References
- IAPWS R7-97(2012) IF97
- IAPWS R12-08 viscosity
- IAPWS R15-11 thermal conductivity
Questions and answers
Is the water at its saturation pressure or at atmospheric pressure?
At its saturation pressure, i.e. on the boiling line. Below 100 °C the difference from atmospheric-pressure water is negligible for density, viscosity and heat capacity (well under 0.1 %).
Why does the Prandtl number fall so steeply with temperature?
Viscosity drops by a factor of six between 20 °C and 150 °C while conductivity and heat capacity change little, so Pr = cp·μ/k falls from about 7 to about 1.1.