Pressure Coefficient

on . Posted in Dimensionless Numbers

Pressure coefficient, abbreviated as $$C_p$$, a dimensionless number, is used in fluid dynamics to describe the local pressure distribution on a surface, usually around an object immersed in a fluid (such as air or water).  It's a way to quantify how the pressure at a particular point on a surface deviates from the ambient or reference pressure.  The pressure coefficient is defined as the difference between the local pressure and the reference pressure (usually the freestream or ambient pressure), divided by the dynamic pressure of the fluid flow.

The pressure coefficient provides information about the pressure distribution around an object and how the flow interacts with the surface.  Positive values of $$C_p$$ indicate that the pressure is higher than the reference pressure, while negative values indicate that the pressure is lower.

In aerodynamics and fluid dynamics, pressure coefficients are often used to analyze and design various engineering components, such as wings, airfoils, and other streamlined shapes.  They help engineers understand lift, drag, and other aerodynamic forces acting on objects in a fluid flow.  Different regions of an object may have varying pressure coefficients, which contribute to its overall aerodynamic behavior.

Pressure Coefficient formula

$$C_p \;=\; p - p_{\infty} \;/\; \frac {1}{2} \; (\rho_{\infty} \; v_{\infty}^2)$$
Symbol English Metric
$$C_p$$ = pressure coefficient  $$dimensionless$$
$$p$$ = pressure $$lbf \;/\; in^2$$ $$Pa$$
$$p_{\infty}$$ = free stream pressure $$lbf \;/\; in^2$$ $$Pa$$
$$\rho _{\infty}$$  (Greek symbol rho) = free stream density $$lbm \;/\; ft^3$$ $$kg \;/\; m^3$$
$$v_{\infty}$$ = free stream velocity $$ft^3 \;/\; sec$$  $$m^3 \;/\; s$$