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# Water - Prandtl Number

## Figures and tables showing Prandtl Number of liquid and gaseous water at varying temperarure and pressure, SI and Imperial units

The Prandtl Number - Pr - is a dimensionless number approximating the ratio of momentum diffusivity (kinematic viscosity) to thermal diffusivity - and is often used in heat transfer and free and forced convection calculations.

The Prandtl number can for calculations be expressed as

Pr =  μ cp / k                           (1)

where
μ = absolute or dynamic viscosity [kg/(m s)], [lbm/(ft h)]
cp = specific heat [J/(kg K)], [Btu/(lbm oF)]
k = thermal conductivity [W/(m K)], [Btu/(h ft2 oF/ft)]

Below, Prandtl numbers of water at varying temperatures and 1, 10 and 100 bara (14.5, 145 and 1450 psia) are given in figures and tables.

and Thermophysical properties at standard conditions
as well as Prandtl number of Air, Ammonia, Methane, Nitrogen and Propane.

Prandtl number of water at 1 bara pressure, varying temperature given as °C or °F:

Prandtl number of water at 1, 10 and 100 bara (14.5, 145 and 1450 psia), varying temperature given as °C or °F:

Prandtl number of water at atmospheric pressure, temperature given as K, °C or °F:

 State Temperature Prandtl number Temperature Prandtl number [K] [°C] [-] [K] [°F] [-] Liquid 273 0 13.6 273 32 13.6 278 5 11.2 278 40 11.5 283 10 9.46 283 50 9.46 293 20 6.99 297 75 6.31 298 25 6.13 311 100 4.56 303 30 5.43 325 125 3.45 323 50 3.56 339 150 2.74 348 75 2.39 353 175 2.25 373 100 1.76 366 200 1.88 Gas 373 100 1.03 394 250 0.999 398 125 0.996 422 300 0.978 423 150 0.978 450 350 0.964 448 175 0.965 478 400 0.970 473 200 0.958 533 500 0.945 523 250 0.947 589 600 0.937 573 300 0.939 644 700 0.930 623 350 0.932 700 800 0.923 673 400 0.926 755 900 0.917 773 500 0.916 811 1000 0.912

Prandtl number of water at given temperatures and 1, 10 and 100 bara (14.5, 145 and 1450 psia):

 State Temperature Pressure Prandtl number [K] [°C] [°F] [bara] [psia] [-] Liquid 273.16 0.01 32.02 1 14.5 13.60 280 6.9 44.3 1 14.5 10.53 300 26.9 80.3 1 14.5 5.856 320 46.9 116 1 14.5 3.785 340 66.9 152 1 14.5 2.687 360 86.9 188 1 14.5 2.040 372.756 99.61 211.3 1 14.5 1.760 Gas 372.756 99.61 211.3 1 14.5 1.035 380 107 224 1 14.5 1.020 400 127 260 1 14.5 0.9938 450 177 350 1 14.5 0.9644 500 227 440 1 14.5 0.9512 550 277 530 1 14.5 0.9425 600 327 620 1 14.5 0.9354 650 377 710 1 14.5 0.9289 700 427 800 1 14.5 0.9231 750 477 890 1 14.5 0.9179 800 527 980 1 14.5 0.9132 900 627 1160 1 14.5 0.9053 1000 727 1340 1 14.5 0.8992 1100 827 1520 1 14.5 0.8942 1200 927 1700 1 14.5 0.8897 Liquid 273.16 0.01 32.02 10 145 13.55 280 6.9 44.3 10 145 10.50 300 26.9 80.3 10 145 5.847 320 46.9 116 10 145 3.781 340 66.9 152 10 145 2.685 360 86.9 188 10 145 2.040 380 107 224 10 145 1.632 400 127 260 10 145 1.362 450 177 350 10 145 1.000 453.028 179.9 355.8 10 145 0.9873 Gas 453.028 179.9 355.8 10 145 1.167 500 227 440 10 145 1.010 550 277 530 10 145 0.9694 600 327 620 10 145 0.9509 650 377 710 10 145 0.9395 700 427 800 10 145 0.9308 750 477 890 10 145 0.9235 800 527 980 10 145 0.9173 900 627 1160 10 145 0.9069 1000 727 1340 10 145 0.8990 1100 827 1520 10 145 0.8928 1200 927 1700 10 145 0.8875 Liquid 273.16 0.01 32.018 100 1450 13.12 280 6.9 44.3 100 1450 10.23 300 26.9 80.3 100 1450 5.761 320 46.9 116 100 1450 3.746 340 66.9 152 100 1450 2.669 360 86.9 188 100 1450 2.030 380 107 224 100 1450 1.626 400 127 260 100 1450 1.358 450 177 350 100 1450 0.9967 500 227 440 100 1450 0.8531 550 277 530 100 1450 0.8366 584.147 311.00 591.79 100 1450 0.9349 Gas 584.147 311.00 591.79 100 1450 1.841 600 327 620 100 1450 1.494 650 377 710 100 1450 1.168 700 427 800 100 1450 1.058 750 477 890 100 1450 1.003 800 527 980 100 1450 0.9686 900 627 1160 100 1450 0.9251 1000 727 1340 100 1450 0.8977 1100 827 1520 100 1450 0.8789 1200 927 1700 100 1450 0.8655

## Related Topics

• Steam Thermodynamics - Thermodynamics of steam and condensate applications
• Fluid Mechanics - The study of fluids - liquids and gases. Involves velocity, pressure, density and temperature as functions of space and time
• Material Properties - Material properties for gases, fluids and solids - densities, specific heats, viscosities and more
• Steam and Condensate - Steam & condensate systems- properties, capacities, pipe sizing, systems configuration and more
• Water Systems - Hot and cold water service systems - design properties, capacities, sizing and more
• Thermodynamics - Effects of work, heat and energy on systems

## Related Documents

• Nitrogen - Prandtl number - Figures and tables showing Prandtl number of nitrogen at varying temperarure and pressure, SI and Imperial units
• Propane - Prandtl Number - Figures and tables showing Prandtl Number of liquid and gaseous propane at varying temperarure and pressure, SI and Imperial units
• Propane - Thermal Diffusivity - Figures and tables showing thermal diffusivity of liquid and gaseous propane at varying temperarure and pressure, SI and Imperial units
• Water - Properties at Gas-Liquid Equilibrium Conditions - Figures and tables showing how the properties of water changes along the boiling/condensation curve (vapor pressure, density, viscosity, thermal conductivity, specific heat, Prandtl number, thermal diffusivity, entropy and enthalpy).

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## Citation

• Engineering ToolBox, (2018). Water - Prandtl Number. [online] Available at: https://www.engineeringtoolbox.com/water-steam-Prandtl-number-d_2059.html [Accessed Day Mo. Year].

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