The density of a fluid when changing both temperature and pressure can be expressed combining (4b) and (6b) : Bulk modulus for water - Imperial Unitsĭensity of a fluid changing both Temperature and Pressure Note! Bulk modulus for liquids varies with pressure and temperature. Ρ 1 = ρ 0 / (1 - (p 1 - p 0 ) / E) (6b) Bulk Modulus Fluid Elasticity some common Fluids - E

or combined with (2) - the final density can be expressed as With (5) - the final volume after pressure change can be expressed asĬombining (5b) with (1) - the final density can be expressed as: The minus sign corresponds to the fact that an increase in the pressure leads to a decrease in volume. = - (p 1 - p 0 ) / ((V 1 - V 0 ) / V 0 ) (5)Į = bulk modulus - liquid elasticity (N/m 2 ) The influence of pressure on the volume of a liquid can be expressed with the three dimensional Hooke's law Note! - volumetric temperature coefficients may vary strongly with temperature.

volumetric expansion coefficient for some commonly used materials.Ρ 0 = initial density (kg/m 3 ) Volumetric Temperature Coefficients - β With (1) and (3b) the final density after a temperature change can be expressed as Β = volumetric temperature expansion coefficient (m 3 /m 3 o C)ĭt = t 1 - t 0 = change in temperature - difference between final and initial temperature ( o C) When temperature increases - most liquids expands:ĭV = V 1 - V 0 = change in volume - difference between final and initial volume (m 3 ) V = specific volume (m 3 /kg) Volume and change in Temperature The inverse of density is specific volume: The density of a liquid can be expressed as See also Water - Density, Specific Weight and Thermal Expantion Coefficient, for online calculator, figures and tables showing changes with temperature. The density of water versus temperature and pressure is indicated below: The density of a liquid will change with temperature and pressure.

Density of water in imperial units