Fluid Compressibility

$$ c = – \frac{1}{v} \left. \frac{\partial v}{\partial p} \right|_{T} $$

For water, \( c \approx 1 \times 10^{-5} \text{/psi} \)

For an isothermal ideal gas

$$ c \propto \frac{1}{p} $$

For an adiabatic ideal gas, where \( k \) is the taio of specific heats (1.4 for air)

$$ c \propto \frac{1}{k p } $$

From this can be derived the speed of sound in an ideal gas

$$ a = \sqrt{\frac{k R T}{MW} } $$