Definition
The bulk modulus can be formally defined by the equation:
where is pressure, is volume, and denotes the derivative of pressure with respect to volume. Equivalently
where ρ is density and dP/dρ denotes the derivative of pressure with respect to density. The inverse of the bulk modulus gives a substance's compressibility.
Other moduli describe the material's response (strain) to other kinds of stress: the shear modulus describes the response to shear, and Young's modulus describes the response to linear stress. For a fluid, only the bulk modulus is meaningful. For an anisotropic solid such as wood or paper, these three moduli do not contain enough information to describe its behaviour, and one must use the full generalized Hooke's law.
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