What equation is used to calculate liquid water density as a function of temperature?

The standard formulation used is the Kell equation (1975), which provides high accuracy density values (kg/m³) for liquid water between -30°C and 150°C at atmospheric pressure or saturation.

How does water viscosity change with temperature?

Liquid water viscosity decreases rapidly as temperature increases. It can be modeled accurately using an exponential modified Andrade/Arrhenius equation between 273 K (0°C) and 373 K (100°C).

Why does water thermal conductivity peak around 130°C?

Unlike most liquids whose thermal conductivity decreases monotonically with temperature, water exhibits a unique maximum around 130°C (403 K) due to structural hydrogen-bonding realignments before decreasing toward the critical point.

Liquid Water properties : correlations as a function of temperature

Formula for calculating Density, viscosity, thermal conductivity of water

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Liquid Water density correlation : \(\rho=f(T)\)
Liquid water viscosity correlation : \(\mu=f(T)\)
Liquid water thermal conductivity correlation : \(\lambda=f(T)\)
Water saturated vapor pressure : \(P_{\text{sat}}=f(T)\)
Interactive Water Properties Calculator & Free Excel Tool

Water critical parameters : [Dincer]

\(T_c = 373.984\ ^\circ\text{C}\) (647.134 K)
\(P_c = 220.64\ \text{bar}\) (22.064 MPa)
\(v_c = 3.106\ \text{dm}^3/\text{kg}\)

Water triple point parameters : [Dincer]

\(T_t = 0.01\ ^\circ\text{C}\) (273.16 K)
\(P_t = 611.732\ \text{Pa}\) (0.006117 bar)

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

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

\rho = \frac{((((a \cdot T + b) \cdot T + c) \cdot T + d) \cdot T + e) \cdot T + f}{1 + g \cdot T}

Water density correlation as a function of temperature

With:

\(\rho\) = density (\(\text{kg/m}^3\))
\(T\) = temperature (\(^\circ\text{C}\))
\(a = -2.8054253 \times 10^{-10}\)
\(b = 1.0556302 \times 10^{-7}\)
\(c = -4.6170461 \times 10^{-5}\)
\(d = -0.0079870401\)
\(e = 16.945176\)
\(f = 999.83952\)
\(g = 0.01687985\)
Range of validity : \([-30 ; 150]\ ^\circ\text{C}\)

Note that an equivalent alternative expanded polynomial form is frequently found in literature:

\rho = \frac{f + e \cdot T + d \cdot T^2 + c \cdot T^3 + b \cdot T^4 + a \cdot T^5}{1 + g \cdot T}

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

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

\mu = \exp\left( A + \frac{B}{C + T} \right)

Water viscosity correlation as a function of temperature

With:

\(\mu\) = dynamic viscosity (\(\text{mPa}\cdot\text{s}\) or \(\text{cP}\))
\(T\) = temperature (\(\text{K}\))
\(A = -3.7188\)
\(B = 578.919\)
\(C = -137.546\)
Range of validity : \([273 ; 373]\ \text{K}\) (\(0\) to \(100\ ^\circ\text{C}\))

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

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

\lambda' = -1.48445 + 4.12292 \cdot T' - 1.63866 \cdot {T'}^2

Water thermal conductivity correlation as a function of temperature

With:

\(\lambda' = \lambda(T) / \lambda(298.15)\)
\(\lambda(298.15) = 0.6065\ \text{W}\cdot\text{m}^{-1}\cdot\text{K}^{-1}\)
\(\lambda(T)\) = thermal conductivity of liquid water at temperature \(T\) (\(\text{W}\cdot\text{m}^{-1}\cdot\text{K}^{-1}\))
\(T' = T / 298.15\)
\(T\) = temperature of water (\(\text{K}\))
Range of validity : \([274 ; 370]\ \text{K}\) (\(1\) to \(97\ ^\circ\text{C}\))

4. Water saturated vapor pressure : \(P_{\text{sat}}=f(T)\)

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

\log_{10}(P^{\text{sat}}) = A - \frac{B}{C + T}

Antoine equation for vapor pressure

With:

\(P^{\text{sat}}\) = Saturation vapor pressure (\(\text{mmHg}\)) — To convert to \(\text{Pa}\), multiply by \(133.322\ \text{Pa/mmHg}\)
\(T\) = temperature (\(^\circ\text{C}\))
\(A = 8.07131\)
\(B = 1730.63\)
\(C = 233.426\)
Range of validity : \([1 ; 100]\ ^\circ\text{C}\)

💡 Plant Engineering Best Practices & Physical Limits

Density Anomaly: Liquid water reaches its maximum density of \(\sim 999.97\ \text{kg/m}^3\) at \(3.98\ ^\circ\text{C}\). Below this temperature, water expands upon cooling until freezing.
NPSH & Cavitation Risk: Always calculate Net Positive Suction Head Available (\(\text{NPSHa}\)) using the saturation vapor pressure (\(P_{\text{sat}}\)) at the maximum anticipated operating temperature. A sharp temperature rise drastically boosts \(P_{\text{sat}}\), triggering pump cavitation.
Viscosity Impact on Pressure Drop: Liquid water viscosity drops by over 80% between \(0\ ^\circ\text{C}\) (\(1.79\ \text{cP}\)) and \(100\ ^\circ\text{C}\) (\(0.28\ \text{cP}\)). Pipeline friction factors and motor loads for cold water systems are significantly higher than hot boiler feed systems.
Correlation Limits: Do not extrapolate these simplified industrial empirical equations above \(100\ ^\circ\text{C}\) (\(373\ \text{K}\)) for vapor pressure or thermal conductivity without checking High-Temperature IAPWS-95 formulation standards.

Warning : all correlations proposed give an approximate value of the physical properties. No guarantee is given on the results.

5. Water properties : Free Interactive Calculator & Excel Tool

Use our interactive online calculator below or download the standard Excel calculation tool to quickly execute water property calculations.

⚠️ ENGINEERING NOTICE & EDUCATIONAL DISCLAIMER: This interactive calculator is provided exclusively for preliminary estimation and educational purposes. It is not intended for detailed design or equipment procurement without certified vendor rating. No warranty, expressed or implied, is provided, and no liability is assumed.

⚡ Liquid Water Properties Calculator

Unit System:

Water Temperature (°C):

Temperature (Kelvin)

298.15 K

Absolute Temp

Liquid Density (\(\rho\))

998.9464 kg/m³

Valid: 273 - 648 K (-30 to 150 °C)

Dynamic Viscosity (\(\mu\))

0.8921 mPa·s

Valid: 273 - 373 K (0 to 100 °C)

Thermal Conductivity (\(\lambda\))

0.6064 W/m·K

Valid: 274 - 370 K (1 to 97 °C)

Saturated Vapor Pressure (\(P_{\text{sat}}\))

3158.1569 Pa

Valid: 1 to 100 °C

Excel Calculation Tool Screenshot:

Screenshot water properties calculator

References & Sources

[Dincer] Drying Phenomena: Theory and Applications, First Edition. İbrahim Dinçer and Calin Zamfirescu, John Wiley & Sons
[NIST] Standard reference data for the thermal conductivity of water, Ramires et al, American Institute of Physics and American Chemical Society, 1995
[DDB] Dortmund Data Bank (online)
[Kell] Kell, G. S. Density, Thermal Expansivity, and Compressibility of Liquid Water from 0° to 150°C: Correlations and Tables for Atmospheric Pressure and Saturation Reviewed and Expressed on 1968 Temperature Scale, J. Chem. Eng. Data, 1975, 20 (1), pp. 97-105