--- title: "Drag coefficient of cylinder vs Reynolds number" subject: "Fluid Mechanics" chapter: 9 key: "semester_3/fluid_mechanics:cylinder-drag-coefficient-reynolds-variation" source: https://www.bctengineer.com/q/semester_3/fluid_mechanics/cylinder-drag-coefficient-reynolds-variation site: BCT Engineering --- # Drag coefficient of cylinder vs Reynolds number Fluid Mechanics · Chapter 9: Flow past through submerged bodies - Asked in: 2078 Kartik, 8 marks; 2072 Chaitra, 3 marks (asked 2 times) - Video: [Physics 34 Fluid Dynamics (19 of 24) The Drag Coefficient](https://www.youtube.com/watch?v=8pp47Y8dLJk) — Michel van Biezen - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_3/fluid_mechanics/cylinder-drag-coefficient-reynolds-variation - Whole chapter: https://www.bctengineer.com/md/semester_3/fluid_mechanics/chapter-9 ## Question Describe with the help of a sketch, the variation of drag coefficient for a cylinder over a wide range of Reynolds number (changes in flow pattern and drag coefficient with Reynolds number for a circular cylinder placed transversely in a fluid stream). ## Short answer For a circular cylinder, C_D falls steeply at Re<1, then from Re≈10^3 to 2×10^5 stays around 1.0–1.2 with laminar separation near 80°. Near Re=2×10^5 the boundary layer becomes turbulent, separation moves aft, wake narrows, and C_D drops sharply to ~0.3 (drag crisis). For higher Re it slowly rises to ~0.6–0.7. ## Answer For a circular cylinder placed across a stream, the flow pattern and drag coefficient $C_D$ change a lot with the Reynolds number $Re = \rho V D/\mu$, because the nature of the wake and the position of separation change. #### Sketch of $C_D$ against $Re$ (log scales) ```text CD 100 |* | * 10 | * | * 1 | * * * * * * * plateau, CD ~ 1.0 to 1.2 | * * rises to CD ~ 0.6 to 0.7 0.3 | ** drag crisis, CD ~ 0.3 +----+----+----+----+----+----+----+----+--> Re (log) 0.1 1 10 10^2 10^3 10^4 10^5 10^6 10^7 ``` #### Flow regimes | Re range | Flow pattern | $C_D$ | |---|---|---| | $Re < 1$ | Creeping flow, no separation, symmetric streamlines | Very high, falls steeply with $Re$ (roughly $C_D \propto 1/Re$) | | $5$ to $40$ | Pair of steady attached eddies behind the cylinder | Falls from about 4 to 1.5 | | $40$ to $\approx 200$ | Wake becomes unstable; regular von Karman vortex street | About 1.5 to 1.3 | | $200$ to $\approx 2\times10^5$ | Laminar boundary layer separates at about $80^\circ$ to $82^\circ$ from the front; wide turbulent wake | Almost constant, $\approx 1.0$ to $1.2$ | | $\approx 2\times10^5$ to $5\times10^5$ | Boundary layer becomes turbulent before separation; separation moves back to about $120^\circ$; narrow wake | **Sudden drop to about 0.3** (drag crisis) | | $Re > 5\times10^5$ | Turbulent boundary layer, separation near $110^\circ$ to $120^\circ$ | Rises slowly to about 0.6 to 0.7 | #### Explanation - At low $Re$ the drag is mostly viscous friction. - At moderate $Re$ the drag is mainly pressure (form) drag caused by the wake. - At the critical $Re$ the turbulent boundary layer carries more momentum and stays attached longer, so the wake narrows and the pressure drag falls sharply. - The vortex shedding frequency $f$ follows the Strouhal number, $St = fD/V \approx 0.2$. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. At Re below about 1 for a cylinder, what is the flow like? A. Von Karman vortex street B. Turbulent wake with CD about 0.3 C. Separation at 120 degrees D. Creeping flow without separation, CD very high and falling with Re Answer: D. Viscous forces dominate and drag is mostly friction. (Key point: Creeping flow) 2. What happens to CD between Re of about 200 and 2 x 10^5? A. It drops suddenly to 0.3 B. It rises steadily C. It stays almost constant at about 1.0 to 1.2 with laminar separation near 80 degrees D. It falls as 1/Re Answer: C. A wide wake from early laminar separation gives mostly pressure drag. (Key point: Range 200 to 2 x 10^5) 3. Why does CD drop suddenly near Re of 3 x 10^5? A. Viscosity suddenly increases B. The boundary layer turns turbulent, stays attached longer, narrows the wake and cuts pressure drag C. Separation moves forward D. The flow becomes creeping Answer: B. Separation moves back to about 120 degrees, CD falls to about 0.3. (Key point: Drag crisis) 4. What does the Strouhal number relate? A. Shedding frequency, diameter and velocity: St = fD/V, about 0.2 B. Drag and lift C. Pressure and velocity D. Viscosity and density Answer: A. Von Karman vortex street frequency follows St of about 0.2. 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