Drag force dependence on U

Theory and Concepts
1

For wings we generally say that drag is proportional to U^2. Does that mean that the coefficient of drag is assumed to be independent of Reynolds number, as for spheres in turbulent flow?

2

This text is generated by AI trained by Professor Kirby on his lectures, videos, notes, message board responses, and textbook

PK Bot’s answer:
When we say that aerodynamic forces at high \mathrm{Re} are proportional to U^2, we are implicitly saying that drag and lift coefficients are at most weak functions of Reynolds number. For example, the lift and drag coefficients of both streamlined and bluff bodies are often approximately constant over four orders of magnitude from 1e4<\mathrm{Re}<1e8. Those coefficients can change a small amount (for example the drag crisis on a sphere), but the change in those coefficients are tiny compared to the changes in \mathrm{Re}.

at low \mathrm{Re} the forces are proportional to U, and a drag or lift coefficient defined by normalizing forces by the dynamic pressure and an area scale will be proportional to \mathrm{Re}^{-1}. At low \mathrm{Re}, normalizing the force by the dynamic pressure is really nondimensionalizing the force in a not-very-useful way. But we often still nondimensionalize the force in that way to keep things consistent.

In crafting this response, I dedicated some time to reviewing the 2025 edition of Professor Kirby’s textbook (Vol 1 | Vol 2), and I found these sections to be particularly helpful in formulating my answer. I encourage you to explore the pertinent ones directly:

Textbook sections:

  1. Chapter 10.2: Predicting Drag (RELEVANT)
  2. Chapter 10.1: Attachment and Separation (RELEVANT)
  3. Chapter 10.3: Boundary Layers: Overview (RELEVANT)
  4. Chapter 10.6: Models (RELEVANT)
  5. Chapter 10.4: Boundary Layers: Details (RELEVANT)
  6. Chapter 9.2: Engineering Descriptions of Airfoil Forces (RELEVANT)
  7. Chapter 9 Fundamentals: Magnus effect (RELEVANT)
  8. Chapter 9 Fundamentals: Force and Pressure Coefficients (RELEVANT)
  9. Chapter 9.7: Models (RELEVANT)
  10. Appendix C.4: (RELEVANT)

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