Aerodynamics of bluff bodies: Pressure (form) drag predominantly depends on flow separation and body shape. Which of the following has the least influence on pressure drag?

Introduction / Context:
Total drag on a body in a fluid consists of skin-friction (viscous) drag and pressure (form) drag. Separating which parameters mainly affect pressure drag is essential for designing streamlined bodies and reducing energy consumption in flow systems.

Given Data / Assumptions:

• External flow over a body at moderate to high Reynolds number.
• Comparison between effects of shape/length and surface roughness.
• Focus on pressure drag, not skin-friction drag.

Concept / Approach:
Pressure drag results from separation and the large-scale wake; it depends strongly on body shape, bluffness, and length in the flow direction (which affects separation and pressure recovery). Surface roughness primarily influences skin-friction drag. While roughness can sometimes alter separation for spheres/cylinders, its first-order effect relates to viscous drag, not pressure drag, for many engineering shapes; thus, it is the least influential of the listed factors on pressure drag.

Step-by-Step Solution:

Verification / Alternative check:
Wind-tunnel data for streamlined vs bluff bodies show significant pressure-drag reduction with elongation; roughness changes mainly shift friction coefficients.

Why Other Options Are Wrong:

• Length in flow direction: Directly alters separation and pressure recovery.
• Pressure of main flow only: By itself does not define drag without geometry, but compared to roughness, shape-related parameters govern form drag more strongly.
• All of these: Not correct since one factor (roughness) is least relevant to pressure drag.

Common Pitfalls:
Conflating skin friction with form drag; they respond to different geometric and surface factors. Also, special cases exist where controlled roughness triggers earlier transition and changes separation, but the general rule remains.

Final Answer:
roughness of surface of the body