Water and Steam Prandtl Number vs Temperature and Pressure

The Prandtl number (Pr) is a dimensionless ratio of momentum diffusivity to thermal diffusivity. A value greater than 1 means the velocity boundary layer is thicker than the thermal boundary layer — the fluid resists shear flow more than it resists heat conduction. Liquid water at 20 °C has Pr ≈ 7, meaning heat diffuses roughly seven times more slowly than momentum through the fluid.

For liquid water, Pr falls steeply with rising temperature — from about 13.6 at 0 °C (32 °F) to 1.76 at 100 °C (212 °F) — because dynamic viscosity decreases faster than thermal conductivity. This strong temperature dependence means Prandtl number must be evaluated at actual operating temperature, not at a nominal design point.

For steam (gas phase), Pr is near 0.9–1.0 and only weakly dependent on temperature over a wide range, reflecting that momentum and thermal diffusivity are similar in magnitude for gases.

At elevated pressures the boiling point rises, so liquid water can exist above 100 °C and continues to have elevated Prandtl numbers. Near the critical point of water (373.946 °C / 705 °F, 220.6 bar) specific heat diverges, causing an anomalous spike in Pr visible in the 100 bara data. This critical-point behavior has practical implications for supercritical water reactors and supercritical boilers.

The Prandtl number appears in Nusselt number correlations for forced convection. The Dittus-Boelter equation for turbulent pipe flow is:

Nu = 0.023 × Re^0.8 × Prⁿ

where n = 0.4 for heating and n = 0.3 for cooling. For liquid water systems, the large variation of Pr with temperature means heat transfer coefficients are significantly higher at elevated temperatures, which is an important consideration in boiler and heat exchanger design.