Cavitation number#

$$\sigma_c \stackrel{\text{def}}{=} \frac{(p - p_v)}{\rho U^{2}} \sim \frac{\text{pressure margin to vapor pressure}}{\text{dynamic pressure}}$$

Measures pressure margin above vapor pressure relative to dynamic pressure. It indicates how close a liquid flow is to forming vapor cavities.

Name	Symbol	SI units	Dimension
pressure margin to vapor pressure	$p - p_v$	$\mathrm{Pa}$	$\text L^{-1}\,\text M\,\text T^{-2}$
mass density	$\rho$	$\mathrm{kg}\,\mathrm{m}^{-3}$	$\text L^{-3}\,\text M$
velocity	$U$	$\mathrm{m}\,\mathrm{s}^{-1}$	$\text L\,\text T^{-1}$

Cavitating flow

Range	Regime	Description
0 – 1	cavitation prone	Dynamic pressure is large compared with the pressure margin to vapor pressure. Cavitation is likely in low-pressure regions.
1 – 10	incipient or partial cavitation	Cavitation may appear locally depending on geometry, nuclei, and unsteady pressure fluctuations.
10 – ∞	cavitation suppressed	The pressure margin is large relative to dynamic pressure. Cavitation is generally suppressed.

Name	Symbol	SI units	Dimension
pressure margin to vapor pressure	\(p - p_v\)	\(\mathrm{Pa}\)	\(\text L^{-1}\,\text M\,\text T^{-2}\)
mass density	\(\rho\)	\(\mathrm{kg}\,\mathrm{m}^{-3}\)	\(\text L^{-3}\,\text M\)
velocity	\(U\)	\(\mathrm{m}\,\mathrm{s}^{-1}\)	\(\text L\,\text T^{-1}\)