Pressure coefficient#

$$C_p \stackrel{\text{def}}{=} \frac{(p - p_\infty)}{\rho U^{2}} \sim \frac{\text{local pressure difference}}{\text{dynamic pressure}}$$

Measures static pressure variation normalized by dynamic pressure. It maps local pressure loading on bodies and surfaces in a flow.

Name	Symbol	SI units	Dimension
local-reference pressure difference	$p - p_\infty$	$\mathrm{Pa}$	$\text L^{-1}\,\text M\,\text T^{-2}$
mass density	$\rho$	$\mathrm{kg}\,\mathrm{m}^{-3}$	$\text L^{-3}\,\text M$
velocity	$U$	$\mathrm{m}\,\mathrm{s}^{-1}$	$\text L\,\text T^{-1}$

External flow

Range	Regime	Description
0 – 0.1	weak pressure variation	Static pressure variations are small compared with the dynamic pressure scale.
0.1 – 1	moderate pressure loading	Pressure loading is an important part of the force balance on the body or surface.
1 – ∞	strong pressure loading	Pressure differences are comparable to or larger than the dynamic pressure scale.

Name	Symbol	SI units	Dimension
local-reference pressure difference	\(p - p_\infty\)	\(\mathrm{Pa}\)	\(\text L^{-1}\,\text M\,\text T^{-2}\)
mass density	\(\rho\)	\(\mathrm{kg}\,\mathrm{m}^{-3}\)	\(\text L^{-3}\,\text M\)
velocity	\(U\)	\(\mathrm{m}\,\mathrm{s}^{-1}\)	\(\text L\,\text T^{-1}\)