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Engineering LibreTexts

18.7: Isothermal Compressibilities

The isothermal compressibility of a fluid is defined as follows:

Contact your instructor if you are unable to see or interpret this graphic.,(18.15)

This expression can be also given in term of fluid density, as follows:

Contact your instructor if you are unable to see or interpret this graphic.(18.16)

For liquids, the value of isothermal compressibility is very small because a unitary change in pressure causes a very small change in volume for a liquid. In fact, for slightly compressible liquid, the value of compressibility (co) is usually assumed independent of pressure. Therefore, for small ranges of pressure across which co is nearly constant, Equation (18.16) can be integrated to get:

Contact your instructor if you are unable to see or interpret this graphic.(18.17)

In such a case, the following expression can be derived to relate two different liquid densities (Contact your instructor if you are unable to see or interpret this graphic.,Contact your instructor if you are unable to see or interpret this graphic.ob) at two different pressures (p, pb):

Contact your instructor if you are unable to see or interpret this graphic.(18.18)

The Vasquez-Beggs correlation is the most commonly used relationship for co.

For natural gases, isothermal compressibility varies significantly with pressure. By introducing the real gas law into Equation (18.16), it is easy to prove that, for gases:

Contact your instructor if you are unable to see or interpret this graphic.(18.19)

Note that for an ideal gas, cg is just the reciprocal of the pressure. “cg” can be readily calculated by graphical means (chart of Z versus P) or by introducing an equation of state into Equation (18.19).

Contributors

  • Prof. Michael Adewumi (The Pennsylvania State University). Some or all of the content of this module was taken from Penn State's College of Earth and Mineral Sciences' OER Initiative.