Drag Force

Aerodynamic and hydrodynamic drag forces opposing body motion through fluid media.

General idea of the topic

Drag is the resistance that a fluid, air or liquid, opposes to the motion of a body moving through it. It always points opposite to the relative velocity and, unlike weight, grows with speed: that is why a falling body ends up reaching a limiting speed at which drag and weight balance.

The topic goes through the two usual models. At low speed, with laminar flow, drag is proportional to speed; at high speed, with turbulent flow, it is proportional to its square. The Reynolds number tells which model applies and the drag coefficient summarises the shape of the body.

What the student is expected to understand

By the end, the student should be able to choose between linear and quadratic drag according to the regime, compute the terminal velocity and describe qualitatively how the speed of a body falling or launched in a fluid evolves.

The student should also be able to interpret the drag coefficient and the Reynolds number to decide which model is reasonable in each problem.

Recommended learning route

1. Linear Drag: studies drag proportional to speed, valid for laminar flow and low speeds.
2. Quadratic Drag: analyses drag proportional to the square of the speed, typical of large or fast bodies.
3. Terminal Velocity: computes the limiting speed a body reaches when drag equals the driving force.
4. Reynolds Number and Drag Regimes: introduces the Reynolds number to decide the regime and which drag model applies.
5. Drag Coefficient: treats the drag coefficient as a measure of the body's shape and of its behaviour in the fluid.

Physical criterion to acquire

The essential criterion is to decide the regime first. With a low Reynolds number linear drag is used and with a high one, quadratic; applying the wrong model gives errors of orders of magnitude. Terminal velocity is not computed by kinematics, but by equating forces when the acceleration vanishes.

Connection with real problems

• skydiving, falling droplets and suspended particles.
• automotive and vehicle aerodynamics.
• sports: cycling, skiing and projectile ballistics.
• design of shapes that reduce resistance.

Final goal of the topic

The final goal is to choose and justify the appropriate drag model, compute terminal velocity and analyse with judgment the motion of a body in a fluid.