The drag coefficient Cd is defined as

• A. Cd = Fd / (0.5 ρ v^2 A)
• B. Cd = Fd / (ρ v^2 A)
• C. Cd = Fd / (0.5 ρ v A^2)
• D. Cd = 2 Fd / (ρ v^2 A)

Answer: (A)

The main idea is that the drag coefficient is a nondimensional quantity that compares the actual drag force to a standard amount of dynamic pressure acting over a reference area. The standard amount of dynamic pressure is one-half the fluid density times the square of the velocity, written as 0.5 ρ v^2. Multiply that by the reference area A to get a characteristic drag force scale. Therefore the natural definition is Cd = Fd / (0.5 ρ v^2 A). This makes Cd independent of the object's size and the flow speed in a consistent way for similar shapes, since both the drag force and the dynamic pressure-area product scale appropriately with changes in speed and size.

The reference area A is the chosen area that represents the flow interaction with the body, often the projected cross-sectional area facing the flow or another agreed-upon silhouette area for the problem.

Other forms miss this proper normalization: omitting the 1/2 factor changes the scaling with velocity; using v instead of v^2 misrepresents how drag grows with speed; and using A^2 would not produce the correct dimensional balance or physical scaling.