# Drag Coefficient

on . Posted in Dimensionless Numbers

Drag coefficient, abbreviated as $$C_d$$, a dimensionless number, that characterizes the amount of aerodynamic or hydrodynamic drag experienced by an object moving through a fluid, such as air or water.  It quantifies the relationship between the drag force acting on the object and the dynamic pressure of the fluid.  In fluid dynamics, the drag force is the resistance that opposes the motion of an object through a fluid medium.  It arises due to the interactions between the object's surface and the fluid molecules.  It expresses a force in the direction of flow due and is related to the pressure and surface stress on an object.  The lower the drag coefficient, the easier the object moves throught the fluid, the higher the efficient, the more difficult it moves through the fluid.

The drag coefficient depends on various factors including the shape of the object, the flow conditions (laminar or turbulent), and the roughness of the object's surface.  It's an essential parameter in aerodynamics and hydrodynamics for predicting the drag experienced by different objects, which is crucial for designing efficient vehicles, structures, and equipment that move through fluids.

For example, a streamlined object like an airplane wing or a well designed car can have a lower drag coefficient compared to a less aerodynamic shape.  Engineers and researchers use wind tunnel tests, computational fluid dynamics simulations, and empirical data to determine and refine drag coefficients for various objects under different conditions.

### Drag coefficient formula

$$C_d \;=\; 2 \; F_d \;/\; A \; \rho \; v^2$$     (Drag Coefficient)

$$F_d \;=\; (1 \;/\; 2) \; C_d \; A \; \rho \; v^2$$

$$A \;=\; 2 \; F_d \;/\; C_d \; \rho \; v^2$$

$$\rho \;=\; 2 \; F_d \;/\; C_d \; A \; v^2$$

$$v \;=\; \sqrt{ 2 \; F_d \;/\; C_d \; A \; \rho }$$

Symbol English Metric
$$C_d$$ = drag coefficient $$dimensionless$$ $$dimensionless$$
$$F_d$$ = drag force $$lbf$$ $$N$$
$$A$$ = area  $$ft^2$$ $$m^2$$
$$\rho$$  (Greek symbol rho) = mass density $$lbm \;/\; ft^3$$ $$kg \;/\; m^3$$
$$v$$ = velocity $$ft \;/\; sec$$ $$m \;/\; s$$

Tags: Coefficient