# Compressibility

Written by Jerry Ratzlaff 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 formulas

 $$\large{ \beta = - \frac{1}{V} \; \frac{\Delta V}{ \Delta p} }$$ $$\large{ \beta = \frac{1}{K} }$$

### Where:

 Units English Metric $$\large{ \beta }$$  (Greek symbol beta) = compressibility $$\large{ dimensionless }$$ $$\large{ K }$$ = bulk modulus $$\large{\frac{lbm}{in^2}}$$ $$\large{ Pa }$$ $$\large{ \Delta p }$$ = pressure rate of change $$\large{\frac{lbf}{in^2}}$$ $$\large{ Pa }$$ $$\large{ \Delta V }$$ = volume rate of change $$\large{ in^3 }$$ $$\large{ mm^3 }$$ $$\large{ V }$$ = volume $$\large{ in^3 }$$ $$\large{ mm^3 }$$ 