# Bulk Modulus

Written by Jerry Ratzlaff on . Posted in Fluid Dynamics

Bulk modulus, abbreviated as B or K, also called bulk modulus of elasticity, is the elastic relationship between an applied pressure that acts to change the volume of the substance and the ability of a substance to withstand changes in volume when under compression.

### Bulk Modulus Formula

$$\large{ K = p\; \frac {V_i}{ V_c} }$$

$$\large{ K = \frac { 1 }{ \beta } }$$

Where:

$$\large{ K }$$ = bulk modulus

$$\large{ V_c }$$ = change in volume (volume differential)

$$\large{ \beta }$$   (Greek symbol beta) = compressibility

$$\large{ V_i }$$ = initial volume

$$\large{ p }$$ = pressure

Solve for:

$$\large{ V_c = \frac {p \; V_i}{ K} }$$

$$\large{ \beta = \frac{1}{K} }$$

$$\large{ V_i = K\; \frac {V_c}{ p} }$$

$$\large{ p = K \; \frac{V_c}{V_i} }$$