Pressure Coefficient

Overview

The pressure coefficient ($C_p$) is a dimensionless number describing the relative pressure at a point in a flow field compared to the freestream dynamic pressure.

Variables

Formula

$C_p = \frac{P - P_\infty}{\frac{1}{2}\rho v_\infty^2}$

Calculator

Notes

• Results are approximate and should be verified for critical applications
• Input values should be within reasonable engineering ranges

Key Principles

The pressure coefficient is a dimensionless number that characterizes the relationship between pressure forces and inertial forces in a fluid flow system. Its practical significance includes:

• Similarity and Modeling: It allows for the comparison of pressure fields between different flow systems (e.g., model vs. prototype) if the geometry and Reynolds number are similar.
• Predictive Analysis: It helps predict pressure changes around objects (like airfoils or pipe fittings) based on the free-stream velocity and fluid density.
• Component Performance: It is used to evaluate the pressure drop or lift characteristics of components in hydraulic and aerodynamic systems.

Dimensional Analysis

The formula $C_p = \frac{\Delta p}{\frac{1}{2} \rho v^2}$ is inherently dimensionless, as shown:

• Pressure difference $\Delta p$ has units of $\text{N/m}^2$ or $\text{kg/(m·s}^2)$.
• Dynamic pressure $\frac{1}{2} \rho v^2$ has units of $\text{kg/m}^3 \cdot (\text{m/s})^2 = \text{kg/(m·s}^2)$. The ratio therefore cancels all units, resulting in a pure number.

References

• Original Source