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# Prandtl Number of Water

Prandtl number of water

Pr = μ cp / k

Where:

cp : specific heat, (SI units: J/kg·K).

μ : dynamic viscosity, (SI units: Pa s = N s/m2).

k : thermal conductivity, (SI units: W/m·K).

The specific Heat, dynamic viscosity and the thermal conductivity required for the calculation of Prandtl number of the water were calculated based on the equations defined on the IAPWS-IF97.

These equations have a range of validity for further details please refer to IAPWS-IF97 or to International Steam Tables – Properties of Water and Steam Based on the Industrial Formulation IAPWS-IF97.

The cp,  ,μ and k were calculated for a given pressure and temperature.

The Prandtl number of water varies in a range between 13.456 and 1.9630 for the liquid phase and between 1.0239 and 0.87954 for the gas phase at 1 bar and temperature between 0 and 800 °C.

— Prandtl Number Water

The below tables and graphs shows the Prandtl number of water at varying temperature and pressure  1 bar, 5 bar, 10 bar , 20 bar , 100 bar and 200 bar:

## Prandtl Number of water from 1 to 7 bar

Temperature
T [ C ]
Temperature
T [ °F ]
p = 1 [ bar ]p = 5 [ bar ]7
03213.45213.43313.423
54111.15411.14111.134
10509.41429.40469.3998
15598.06298.05578.0521
20686.99136.98596.9831
25776.12666.12246.1203
30865.41855.41525.4136
35954.83134.82864.8273
401044.33894.33684.3357
451133.92213.92043.9195
501223.56633.56493.5641
601402.99532.99432.9938
701582.56232.56162.5613
801762.22712.22662.2264
901941.9631.96261.9624
1002121.02391.75161.7514
1252570.994741.38091.3808
1503020.978531.1511.1509
1753470.967421.03281.0727
2003920.959411.00591.03
2254370.953270.986761.0044
2504820.948220.972660.98566
2755270.94380.961990.97163
3005720.939760.953590.96087
3256170.935920.946690.9523
3506620.932210.940780.9452
3757070.928580.935530.93909
4007520.925020.930730.93364
4257970.921520.926280.92869
4508420.918090.92210.92412
4758870.914720.918130.91984
5009320.911430.914340.9158
5259770.908220.910720.91198
55010220.90510.907260.90834
57510670.902070.903940.90487
60011120.899140.900750.90155
62511570.89630.89770.89839
65012020.893570.894780.89538
67512470.890940.891980.8925
70012920.888420.889310.88976
72513370.886010.886780.88716
75013820.883720.884380.8847
77514270.881560.882120.8824
80014720.879540.880020.88025

## Prandtl Number of water from 10 to 200 bar

[ °C ]102050100200
013.4113.36313.22713.00912.606
511.12411.09210.99510.84110.553
109.39269.36889.29879.18598.975
158.04688.0297.97677.89247.7344
206.97916.96566.92576.86156.7406
256.11716.10676.07586.0265.9321
305.41115.40295.37865.33945.2653
354.82534.81884.79954.76824.7091
404.33414.32884.31334.28814.2404
453.91823.91393.90133.88073.842
503.56313.55963.54923.53243.5005
602.99312.99072.98352.97192.95
702.56082.55912.5542.54582.5304
802.2262.22472.22112.21512.204
901.96221.96121.95851.95411.9459
1001.75121.75051.74841.74511.7389
1251.38071.38021.3791.3771.3733
1501.15081.15041.14931.14761.1446
1751.00431.00381.00251.00040.99688
2001.06940.911450.909490.906490.90137
2251.03211.14580.855580.850760.84264
2501.00611.08220.835060.826710.8131
2750.986791.04331.30750.835830.81109
3000.972261.01441.18370.895890.84287
3250.961020.992871.11511.51430.93568
3500.952030.976581.06781.2981.2364
3750.944560.964021.03561.20772.2777
4000.938080.95361.00821.13031.6084
4250.932350.9450.98811.08051.3764
4500.927180.937650.972271.04351.248
4750.922420.931190.959461.01521.1639
5000.9180.925420.948820.993251.1049
5250.913860.920170.939750.975681.0615
5500.909950.915360.931880.961311.0285
5750.906260.91090.924930.949291.0027
6000.902760.906750.918710.939050.982
6250.899430.902870.91310.930160.96502
6500.896270.899230.907980.922360.95084
6750.893270.895820.903310.915440.9388
7000.890420.892610.899010.909260.92846
7250.887730.889610.895060.903710.91947
7500.885190.886790.891430.89870.91162
7750.882810.884170.88810.89420.90473
8000.88060.881750.885050.890140.89868

## Prandtl Number Water Diagram

If you want to estimate the prandtl number for water for a different condition you can always use the below diagram or use our online prandtl number calculator.

Reference:

Engineering Reference Book on Energy and Heat