Compressibility

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	\(\large{ in^3 }\)	\(\large{ mm^3 }\)