One application of fluid resistance is air drag (or drag). It's the retarding force when an object moves through a fluid. We explore more on this concept:

## Deriving the Drag Equation

Continuing from fluid resistance \(F_f\), consider a large body moving through the fluid or a relatively fast-moving object with velocity \(v\). The fluid resistance on the body is equal to:

\(F_f= kv^2\)

- \(F_f\) is the fluid resistance
- \(k\) is the constant of proportionality
- \(v\) is the velocity of the body moving through the fluid

The constant \(k\) will depend on many factors, such as the body's size and shape and the fluid's density:

\(k=\frac{1}{2} \rho A C_D\)

When we substitute this proportionality constant to \(F_f\), we have:

\(F_f=\frac{1}{2} \rho A C_D v^2\)

- \(\rho\) is the mass density of the fluid
- \(A\) is the cross-section area of the object
- \(C_D\) is the drag coefficient
- \(v\) is velocity of the object

This equation is the Drag Equation - an essential expression in many scientific fields, such as aerodynamics. From this derivation, it expands on concepts explored in fluid resistance.

## Summary

Consider a large body moving through the fluid or a relatively fast-moving object with velocity \(v\). The fluid resistance \(F_f\) on the body is equal to: \(F_f= kv^2\)

The constant \(k\) will depend on many factors, such as the body's size and shape and the fluid's density: \(k=\frac{1}{2} \rho A C_D\)

The resistance force is equal to \(F_f=\frac{1}{2} \rho A C_D v^2\) where \(\rho\) is the mass density of the fluid, \(A\) is the cross-section area of the object, and \(C_D\) is the drag coefficient. This expression is the Drag Equation.