Bulk Modulus

The bulk modulus is used to characterize the compressibility of a fluid, and is defined as:

$$E_v=-\frac{dp}{d\forall /\forall }$$

where $dp$ is the differential change in pressure needed to create a differential change in volume, $d\forall$, in volume $\forall$.

Since a decrease in volume of a given mass, $m=\rho \forall$, and mass is always constant such that $dm=\rho d\forall +\forall d\rho =0$, we have

$$\frac{d\forall }{\forall }=-\frac{d\rho }{\rho }$$

such that we can also write bulk modulus as

$$E_v=\frac{dp}{d\rho /\rho }$$