# Pressure Coefficient

Written by Jerry Ratzlaff on . Posted in Dimensionless Numbers

Pressure coefficient, abbreviated as $$C_p$$, a dimensionless number, about the relative pressures throughout a flow field in fluid mechanics.

## Pressure Coefficient formula

 $$\large{ C_p = \frac { p \;-\; p_{\infty} } { \frac {1}{2} \; \rho_{\infty} \; v_{\infty}^2 } }$$

### Where:

 Units English Metric $$\large{ C_p }$$ = pressure coefficient $$\large{dimensionless}$$ $$\large{ p }$$ = pressure $$\large{\frac{lbf}{in^2}}$$ $$\large{Pa}$$ $$\large{ p_{\infty} }$$ = free stream pressure $$\large{\frac{lbf}{in^2}}$$ $$\large{Pa}$$ $$\large{ \rho _{\infty} }$$  (Greek symbol rho) = free stream density $$\large{\frac{lbm}{ft^3}}$$ $$\large{\frac{kg}{m^3}}$$ $$\large{ v_{\infty} }$$ = free stream velocity $$\large{\frac{ft^3}{sec}}$$ $$\large{\frac{m^3}{s}}$$