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:

water density temperature pressure

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) at 20oC 
  • ethyl alcohol : 0.0011 (m3/m3 oC)

Note! - volumetric temperature coefficients varies strongly with temperature.

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)

ρ1 = final density (kg/m3)

ρ0 = initial density (kg/m3)

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 with (1) and (2) by substituting ρ0 in eq. 2 with the expression for ρ1 in eq. 1.

 ρ1 = ρ1(from eq.1) / (1 - (p1 - p0) / E)

      = ρ0 / (1 + β (t1 - t0)) / (1 - (p1 - p0) / E)   (3)

Example - Density of Water at 100 bar and 20oC

  • density of water 0oC: 999.8 (kg/m3)
  • expansion coefficent of water at 10oC: 0.000088 (m3/m3oC) (average value between 0 and 20oC)
  • bulk modulus of water: 2.15 109 (N/m2)

Density of water can be calculated with (3):

 ρ1 = 999.8 (kg/m3) / (1 + 0.000088 (m3/m3oC) (20 (oC) - 0 (oC))) / (1 - (100 105 (Pa) - 1 105 (Pa)) / 2.15 109 (N/m2))  

= 998.0 / 0.995    

= 1002.7 (kg/m3)

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Related Topics

  • Fluid Mechanics - The study of fluids - liquids and gases. Involves various properties of the fluid, such as velocity, pressure, density and temperature, as functions of space and time.
  • Thermodynamics - The effects of work, heat and energy on a system

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