# Compressibility

on . Posted in Thermodynamics

Compressibility, abbreviated as $$\beta$$ (Greek symbol beta), also called coefficient of compressibility, a dimensionless number, measures the change in volume under external forces for any liquid.  Compressibility of a fluid increases with pressure and temperature and results in loss of volume output of pumps.  In control systems, compression of fluid provides a mass spring condition that limits system response.

## Compressibility formula

$$\large{ \beta = \frac{1}{K} }$$
Symbol English Metric
$$\large{ \beta }$$  (Greek symbol beta) = compressibility $$\large{ dimensionless }$$
$$\large{ K }$$ = bulk modulus $$\large{\frac{lbm}{in^2}}$$  $$\large{ Pa }$$

## Compressibility formula

$$\large{ \beta = -\; \frac{1}{V_i} \; \frac{\Delta V}{\Delta p} }$$
Symbol English Metric
$$\large{ \beta }$$  (Greek symbol beta) = compressibility $$\large{ dimensionless }$$
$$\large{ \Delta p }$$ = pressure change $$\large{\frac{lbm}{in^2}}$$  $$\large{ Pa }$$
$$\large{ V_i }$$ = initial volume $$\large{ in^3 }$$ $$\large{ mm^3 }$$
$$\large{ \Delta V }$$ = volume change $$\large{ in^3 }$$ $$\large{ mm^3 }$$