When is isothermal compressibility used for a fluid?

In fluid mechanics, isothermal compressibility (${\beta }_T$) is used to describe how the density of a fluid changes when the pressure is altered by a small amount under conditions where the temperature remains essentially constant.1

This quantity is specifically applied when an element of fluid is compressed and the heat generated by the work done on the fluid has sufficient time to drain away to the surroundings, ensuring the temperature does not change throughout the process. In contrast, if the process occurs such that virtually no heat escapes—which is common in many flow problems due to the poor thermal conductivity of most fluids—the process is considered adiabatic, and adiabatic compressibility (${\beta }_S$) is used instead.1