Density of Fluids - Changing Pressure and Temperature
Calculating density of fluids when changing pressure and temperature
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The density of a fluid changes with temperature and pressure. The density of water versus temperature and pressure is indicated in the chart below:
Density and change in Temperature
When temperature is changed the density of a fluid 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 : 0.0002 (m3/m3 oC)
- ethyl alcohol : 0.0011 (m3/m3 oC)
Density and change in Pressure
When pressure is changed the density of a fluid 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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