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Liquid Water properties : correlations as a function of temperature

Formula for calculating Density, viscosity, thermal conductivity of water

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1. Liquid Water density correlation : ρ=f(T)

2. Liquid water viscosity correlation : μ=f(T)

3. Liquid water thermal conductivity correlation : λ=f(T)

4. Water saturated vapor pressure : Psat=f(T)

5. Water properties : Free Excel calculation tool

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Water critical parameters : [Dincer]

• Tc = 373.984 c
• Pc = 220.64 bar
• vc = 3.106 dm3/kg

Water triple point parameters : [Dincer]

• Tt = 0.01 c
• Pt = 611.732 Pa

1. Liquid Water density correlation : ρ=f(T)

How does the density of liquid water vary with temperature ? What is the equation to calculate the density of water ?

ρ=[((((a*T+b)*T+c)*T+d)*T+e)*T+f] / (1+g*T) [Kell]

With

ρ = density (kg/m3)
T = temperature (c)
a= -2.8054253⋅10^-10
b = 1.0556302⋅10-7
c = -4.6170461⋅10-5
d = -0.0079870401
e = 16.945176
f = 999.83952
g = 0.01687985
Range of validity : [-30 ; 150] c

Note that another equation, equivalent can be found in the literature :

ρ= = (f + e*T + d*T² + c*T³ + b*T⁴ + a*T⁵)/(1+g*T)

2. Liquid water viscosity correlation : μ=f(T)

How does the viscosity of liquid water vary with temperature ? What is the equation to calculate the viscosity of water ?

μ = exp(-3.7188+578.919/(-137.546+T))

With

μ = viscosity (mPa.s)
T = temperature (K)
A = -3.7188
B = 578.919
C = -137.546
Range of validity : [273 ; 373] K

3. Liquid water thermal conductivity correlation : λ=f(T)

How does the thermal conductivity of liquid water vary with temperature ? What is the equation to calculate the thermal conductivity of water ?

λ'=-1.48445+4.12292*T'-1.63866*T'2 [NIST]

With

λ' = λ(T)/λ(298.15)
λ(298.15) = 0.6065 W.m^-1.K^-1
λ(T) = thermal conductivity of water at temperature T (W.m^-1.K-1)
T' = T/298.15
T = temperature of water (K)
Range of validity : [274 ; 370] K

4. Water saturated vapor pressure : Psat=f(T)

How does the vapor pressure of water vary with temperature ? What is the equation to calculate the vapor pressure of water ?

log(Ps) = 8.07131 - 1730.63 / (233.426 + T) 

With

Ps = Saturation pressure (mmHg) - note, to switch to Pa, multiply by 133.322 Pa/mmHg
T = temperature (°c)
A = 8.07131
B = 1730.63
C = 233.426
Range of validity : [1 ; 100] °c

5. Water properties : Free Excel calculation tool

You can access an Excel tool to apply the formula detailed above and make calculations.

Warning : this calculator is provided to illustrate the concepts mentioned in this webpage, it is not intended for detail design. It is not a commercial product, no guarantee is given on the results. Please consult a reputable designer for all detail design you may need.

Source

[Dincer] Drying Phenomena: Theory and Applications, First Edition. İbrahim Dinçer and Calin Zamfirescu, John Wiley & Sons (excerpt available online)
[NIST] Standard reference data for the thermal conductivity of water, Ramires et al, American Institute of Physics and American Chemical Society, 1995

[DDN] Dortmund Data Bank (online)