Bulk Modulus, $E_v$

Bulk Modulus determines how compressible a fluid is. In other words, it tells us how the density of a fluid changes when the fluid is subjected to pressure. It is defined as

$$E_v = - {{dp} \over {d\forall /\forall}}= {{dp} \over {d\rho /\rho}}$$ (1.19)

where dp is the pressure change that is required in order to change the volume by $d \forall$, $\forall$ being the initial volume. The negative sign indicates that an increase in pressure is accompanied by a decrease in volume.

The dimensions of Bulk Modulus are $FL^{-2}$; the units being $N/m^2$. Higher the value of Bulk Modulus indicates that it is difficult to compress the fluid. Take water for example. Its Bulk Modulus is $2.15 \times 10^9 N/m^2$ meaning that it requires an enormous pressure to change the volume of water by a small amount. For all practical purposes water (and many other liquids as well) is treated as being incompressible.

(c) Aerospace, Mechanical & Mechatronic Engg. 2005
University of Sydney