Which of the following expresses the drag coefficient in terms of drag force, fluid density, velocity, and reference area?

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

Answer: (A)

The drag coefficient is found by normalizing the drag force with the dynamic pressure of the flow and the reference area. Dynamic pressure is q = 0.5 ρ v^2, where ρ is fluid density and v is velocity. Since Fd = Cd q A, solving for Cd gives Cd = Fd / (q A) = Fd / (0.5 ρ v^2 A). This form yields a dimensionless Cd and uses the standard dynamic-pressure definition, making it the correct expression for expressing drag coefficient in terms of drag force, density, velocity, and reference area.

If the 1/2 factor were omitted, you’d still get a dimensionless result but the numeric value would be off by a factor of 2. Using A^2 in the denominator would remove the proper dimensional balance, giving a non-dimensionless quantity, and placing a 2 in the numerator would simply double the result, giving an incorrect Cd.