Density of a Fluid - Changing Pressure and Temperature
Calculate the density of a fluid when changing pressure and temperature
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The density of a fluid changes when temperature or pressure on the fluid are changed. The density of water versus temperature and pressure are visualized in the diagram below.
Density and change in Temperature
The density of a fluid when the temperature is changed can be expressed as
ρ1 = ρ0 / (1 + β (t1 - t0)) (1)
where
ρ1 = final density (kg/m3)
ρ0 = initial density (kg/m3)
β = volumetric temperature expansion coefficient (m3/m3 oC)
t1 = final temperature (oC)
t0 = initial temperature (oC)
Volumetric Temperature Coefficients - β
- water : 0.88 10-4 (m3/m3 oC)
- ethyl alcohol : 110 10-5 (m3/m3 oC)
- oil : 63.3 10-5 (m3/m3 oC)
Density and change in Pressure
The density of a fluid when the pressure is changed can be expressed as
ρ1 = ρ0 / (1 - (p1 - p0) / E) (2)
where
E = bulk modulus fluid elasticity (N/m2)
p1 = final pressure (N/m2)
p0 = initial pressure (N/m2)
Bulk Modulus Fluid Elasticity some common Fluids - E
- water : 2.15 109 (N/m2)
- ethyl alcohol : 1.06 109 (N/m2)
- oil : 1.5 109 (N/m2)
Density of a fluid changing both Temperature and Pressure
The density of a fluid when changing both temperature and pressure can be expressed by combining (1) and (2)
ρ1 = [ ρ0 / (1 + β (t1 - t0)) ] / [1 - (p1 - p0) / E] (3)
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