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 |
|---|---|---|---|---|
| 0 | 32 | 13.452 | 13.433 | 13.423 |
| 5 | 41 | 11.154 | 11.141 | 11.134 |
| 10 | 50 | 9.4142 | 9.4046 | 9.3998 |
| 15 | 59 | 8.0629 | 8.0557 | 8.0521 |
| 20 | 68 | 6.9913 | 6.9859 | 6.9831 |
| 25 | 77 | 6.1266 | 6.1224 | 6.1203 |
| 30 | 86 | 5.4185 | 5.4152 | 5.4136 |
| 35 | 95 | 4.8313 | 4.8286 | 4.8273 |
| 40 | 104 | 4.3389 | 4.3368 | 4.3357 |
| 45 | 113 | 3.9221 | 3.9204 | 3.9195 |
| 50 | 122 | 3.5663 | 3.5649 | 3.5641 |
| 60 | 140 | 2.9953 | 2.9943 | 2.9938 |
| 70 | 158 | 2.5623 | 2.5616 | 2.5613 |
| 80 | 176 | 2.2271 | 2.2266 | 2.2264 |
| 90 | 194 | 1.963 | 1.9626 | 1.9624 |
| 100 | 212 | 1.0239 | 1.7516 | 1.7514 |
| 125 | 257 | 0.99474 | 1.3809 | 1.3808 |
| 150 | 302 | 0.97853 | 1.151 | 1.1509 |
| 175 | 347 | 0.96742 | 1.0328 | 1.0727 |
| 200 | 392 | 0.95941 | 1.0059 | 1.03 |
| 225 | 437 | 0.95327 | 0.98676 | 1.0044 |
| 250 | 482 | 0.94822 | 0.97266 | 0.98566 |
| 275 | 527 | 0.9438 | 0.96199 | 0.97163 |
| 300 | 572 | 0.93976 | 0.95359 | 0.96087 |
| 325 | 617 | 0.93592 | 0.94669 | 0.9523 |
| 350 | 662 | 0.93221 | 0.94078 | 0.9452 |
| 375 | 707 | 0.92858 | 0.93553 | 0.93909 |
| 400 | 752 | 0.92502 | 0.93073 | 0.93364 |
| 425 | 797 | 0.92152 | 0.92628 | 0.92869 |
| 450 | 842 | 0.91809 | 0.9221 | 0.92412 |
| 475 | 887 | 0.91472 | 0.91813 | 0.91984 |
| 500 | 932 | 0.91143 | 0.91434 | 0.9158 |
| 525 | 977 | 0.90822 | 0.91072 | 0.91198 |
| 550 | 1022 | 0.9051 | 0.90726 | 0.90834 |
| 575 | 1067 | 0.90207 | 0.90394 | 0.90487 |
| 600 | 1112 | 0.89914 | 0.90075 | 0.90155 |
| 625 | 1157 | 0.8963 | 0.8977 | 0.89839 |
| 650 | 1202 | 0.89357 | 0.89478 | 0.89538 |
| 675 | 1247 | 0.89094 | 0.89198 | 0.8925 |
| 700 | 1292 | 0.88842 | 0.88931 | 0.88976 |
| 725 | 1337 | 0.88601 | 0.88678 | 0.88716 |
| 750 | 1382 | 0.88372 | 0.88438 | 0.8847 |
| 775 | 1427 | 0.88156 | 0.88212 | 0.8824 |
| 800 | 1472 | 0.87954 | 0.88002 | 0.88025 |
Prandtl Number of water from 10 to 200 bar
| [ °C ] | 10 | 20 | 50 | 100 | 200 |
|---|---|---|---|---|---|
| 0 | 13.41 | 13.363 | 13.227 | 13.009 | 12.606 |
| 5 | 11.124 | 11.092 | 10.995 | 10.841 | 10.553 |
| 10 | 9.3926 | 9.3688 | 9.2987 | 9.1859 | 8.975 |
| 15 | 8.0468 | 8.029 | 7.9767 | 7.8924 | 7.7344 |
| 20 | 6.9791 | 6.9656 | 6.9257 | 6.8615 | 6.7406 |
| 25 | 6.1171 | 6.1067 | 6.0758 | 6.026 | 5.9321 |
| 30 | 5.4111 | 5.4029 | 5.3786 | 5.3394 | 5.2653 |
| 35 | 4.8253 | 4.8188 | 4.7995 | 4.7682 | 4.7091 |
| 40 | 4.3341 | 4.3288 | 4.3133 | 4.2881 | 4.2404 |
| 45 | 3.9182 | 3.9139 | 3.9013 | 3.8807 | 3.842 |
| 50 | 3.5631 | 3.5596 | 3.5492 | 3.5324 | 3.5005 |
| 60 | 2.9931 | 2.9907 | 2.9835 | 2.9719 | 2.95 |
| 70 | 2.5608 | 2.5591 | 2.554 | 2.5458 | 2.5304 |
| 80 | 2.226 | 2.2247 | 2.2211 | 2.2151 | 2.204 |
| 90 | 1.9622 | 1.9612 | 1.9585 | 1.9541 | 1.9459 |
| 100 | 1.7512 | 1.7505 | 1.7484 | 1.7451 | 1.7389 |
| 125 | 1.3807 | 1.3802 | 1.379 | 1.377 | 1.3733 |
| 150 | 1.1508 | 1.1504 | 1.1493 | 1.1476 | 1.1446 |
| 175 | 1.0043 | 1.0038 | 1.0025 | 1.0004 | 0.99688 |
| 200 | 1.0694 | 0.91145 | 0.90949 | 0.90649 | 0.90137 |
| 225 | 1.0321 | 1.1458 | 0.85558 | 0.85076 | 0.84264 |
| 250 | 1.0061 | 1.0822 | 0.83506 | 0.82671 | 0.8131 |
| 275 | 0.98679 | 1.0433 | 1.3075 | 0.83583 | 0.81109 |
| 300 | 0.97226 | 1.0144 | 1.1837 | 0.89589 | 0.84287 |
| 325 | 0.96102 | 0.99287 | 1.1151 | 1.5143 | 0.93568 |
| 350 | 0.95203 | 0.97658 | 1.0678 | 1.298 | 1.2364 |
| 375 | 0.94456 | 0.96402 | 1.0356 | 1.2077 | 2.2777 |
| 400 | 0.93808 | 0.9536 | 1.0082 | 1.1303 | 1.6084 |
| 425 | 0.93235 | 0.945 | 0.9881 | 1.0805 | 1.3764 |
| 450 | 0.92718 | 0.93765 | 0.97227 | 1.0435 | 1.248 |
| 475 | 0.92242 | 0.93119 | 0.95946 | 1.0152 | 1.1639 |
| 500 | 0.918 | 0.92542 | 0.94882 | 0.99325 | 1.1049 |
| 525 | 0.91386 | 0.92017 | 0.93975 | 0.97568 | 1.0615 |
| 550 | 0.90995 | 0.91536 | 0.93188 | 0.96131 | 1.0285 |
| 575 | 0.90626 | 0.9109 | 0.92493 | 0.94929 | 1.0027 |
| 600 | 0.90276 | 0.90675 | 0.91871 | 0.93905 | 0.982 |
| 625 | 0.89943 | 0.90287 | 0.9131 | 0.93016 | 0.96502 |
| 650 | 0.89627 | 0.89923 | 0.90798 | 0.92236 | 0.95084 |
| 675 | 0.89327 | 0.89582 | 0.90331 | 0.91544 | 0.9388 |
| 700 | 0.89042 | 0.89261 | 0.89901 | 0.90926 | 0.92846 |
| 725 | 0.88773 | 0.88961 | 0.89506 | 0.90371 | 0.91947 |
| 750 | 0.88519 | 0.88679 | 0.89143 | 0.8987 | 0.91162 |
| 775 | 0.88281 | 0.88417 | 0.8881 | 0.8942 | 0.90473 |
| 800 | 0.8806 | 0.88175 | 0.88505 | 0.89014 | 0.89868 |
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