1.9 Bulk Modulus and Compressibility

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Bulk modulus:

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It is defined as the ratio of change in pressure to the volumetric strain of the fluid.
It should be noted that the volumetric strain is the ratio of change in volume to its original volume.
 Bulk modulus is represented by B and by some authors as K.

This mathematically bulk modulus can be given as

where dp is the change in pressure.
 dV  is the change in volume.
V is the original volume.

It should be noted that here a negative sign is added to the bulk modulus mathematical relation(formula) because the stain is considered to be compressive strain. If the strain is tensile then the negative should not be considered. 

In SI units its dimensional formula can be given as M¹L⁻¹T⁻².

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Compressibility:

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It is defined as the inverse of the bulk modulus. Thus it can be defined as the ratio of the volumetric strain to the change in pressure. Thus mathematically it can be given as

Compressibility = 1/K or 1/B

In SI units its dimensional formula can be given as M^-1L¹T².

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References:
http://en.wikipedia.org/wiki/Bulk_modulus
http://www.britannica.com/EBchecked/topic/84278/bulk-modulus
http://dictionary.reference.com/browse/bulk+modulus
Img Credits: http://hyperphysics.phy-astr.gsu.edu/hbase/imgmec/bulk3.gif