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Engineering ToolBox > Density of a Fluid - Changing Pressure and Temperature
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.
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)
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)
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)