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 c_p / k                           (1)

where
μ = absolute or dynamic viscosity [kg/(m s)], [lb_m/(ft h)]
c_p = specific heat [J/(kg K)], [Btu/(lb_m ^oF)]
k = thermal conductivity [W/(m K)], [Btu/(h ft^{2 o}F/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.

See also other properties of Water at varying temperature and pressure: Boiling points at high pressure, Boiling points at vacuum pressure, Density and specific weight,  Dynamic and kinematic viscosity, Enthalpy and entropy, Heat of vaporization, Ionization Constant, pK_w, of normal and heavy water, Melting points at high pressure, Properties at Gas-Liquid Equilibrium Conditions, Saturation pressure, Specific gravity, Specific heat (heat capacity), Specific volume, Thermal conductivity, Thermal diffusivity and Vapour pressure at gas-liquid equilibrium, and Thermophysical properties at standard conditions, 
as well as Prandtl number of Air, Ammonia, Carbon dioxide, Methane, Nitrogen and Propane.

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

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


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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

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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

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