Drag Force

When an object moves through a fluid, the fluid exerts a drag force opposing the motion. For turbulent/high-$Re$ flow the drag is dominated by pressure drag and follows the quadratic drag law:

$F_D = \frac{1}{2} \rho v^2 C_D A$

where:

• $\rho$ — fluid density (kg/m³)
• $v$ — velocity of the object relative to the fluid (m/s)
• $C_D$ — drag coefficient (dimensionless), depends on shape and flow regime
• $A$ — reference area (m²), usually the frontal (projected) area

Note that drag grows with $v^2$ — doubling speed quadruples drag.

Common Drag Coefficients

Terminal Velocity

An object falling through a fluid accelerates until drag equals gravity ($F_D = mg$). Solving for this terminal velocity:

$v_t = \sqrt{\frac{2mg}{\rho C_D A}}$

A skydiver ($m = 70$ kg, $C_D = 1.0$, $A = 0.5$ m²) reaches about 47 m/s (~170 km/h) in air.

Your Task

Implement:

• drag_force(rho, v, Cd, A) — returns drag force $F_D$ in newtons
• terminal_velocity(m, rho, Cd, A) — returns terminal velocity $v_t$ in m/s. Use $g = 9.81$ m/s² inside the function.