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# Water - Prandtl Number vs. Temperature and Pressure

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 ft2oF/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 .

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:

Water - Prandtl Number vs. Temperature at Atmospheric Pressure
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):

Water - Prandtl Number vs. Temperature and Pressure
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

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