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Drag coefficient of cylinder vs Reynolds number

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.

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).

For a circular cylinder placed across a stream, the flow pattern and drag coefficient CDC_D change a lot with the Reynolds number Re=ρVD/μRe = \rho V D/\mu, because the nature of the wake and the position of separation change.

Sketch of CDC_D against ReRe (log scales)

  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 rangeFlow patternCDC_D
Re<1Re < 1Creeping flow, no separation, symmetric streamlinesVery high, falls steeply with ReRe (roughly CD∝1/ReC_D \propto 1/Re)
55 to 4040Pair of steady attached eddies behind the cylinderFalls from about 4 to 1.5
4040 to ≈200\approx 200Wake becomes unstable; regular von Karman vortex streetAbout 1.5 to 1.3
200200 to ≈2×105\approx 2\times10^5Laminar boundary layer separates at about 80∘80^\circ to 82∘82^\circ from the front; wide turbulent wakeAlmost constant, ≈1.0\approx 1.0 to 1.21.2
≈2×105\approx 2\times10^5 to 5×1055\times10^5Boundary layer becomes turbulent before separation; separation moves back to about 120∘120^\circ; narrow wakeSudden drop to about 0.3 (drag crisis)
Re>5×105Re > 5\times10^5Turbulent boundary layer, separation near 110∘110^\circ to 120∘120^\circRises slowly to about 0.6 to 0.7

Explanation

  • At low ReRe the drag is mostly viscous friction.
  • At moderate ReRe the drag is mainly pressure (form) drag caused by the wake.
  • At the critical ReRe 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 ff follows the Strouhal number, St=fD/V≈0.2St = fD/V \approx 0.2.

✓ Answer checked by Claude Opus 5.5 (high effort)

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