Drag force on a sphere using FD = CD × ½ρV² × A. Viscosity is optional — used only to compute Re for CD regime verification.
Fluid Mechanics IIIf provided, Re is computed and shown to verify whether the entered CD is appropriate.
Drag force equation:
CD for a sphere — flow regime dependence:
| Regime | Re range | CD |
|---|---|---|
| Stokes (creeping flow) | Re < 0.5 | 24 / Re |
| Intermediate | 0.5 – 1 000 | ≈ 24/Re + 6/(1+√Re) + 0.4 |
| Newton (turbulent wake) | 1 000 – 2×10⁵ | ≈ 0.44 – 0.47 |
| Post-critical (turbulent b.l.) | Re > 5×10⁵ | ≈ 0.10 – 0.20 |
The sharp drop in CD at Re ≈ 5×10⁵ is the drag crisis — the boundary layer transitions to turbulent, delaying separation and reducing the wake.
Reynolds number:
Enter viscosity μ to compute Re and verify that the selected CD is appropriate for the flow regime.
Where:
Drag force scales with V² — doubling velocity quadruples drag. The projected area for a sphere is always the circle π(D/2)², regardless of orientation.