🎯 External Flow — Drag Force Calculator

Calculate drag force on common geometries with Reynolds-dependent drag coefficient correlations.

Turbulent Wake Sphere / D U_∞ (Flow) Drag F_D F_D = C_d A (ρU²/2) A = πD²/4 (Sphere)

Drag & Aerodynamic Boundaries

Viscous friction and pressure differentials along moving shapes combine to produce a net resistance drag force. Drag coefficients correlate directly with the Reynolds number.

• Pressure Drag: Caused by separation profiles and downstream wake vacuums.
• Friction Drag: Viscous wall shear stress boundaries across surface area elements.
• Streamlining: Delaying flow separation points to minimize wake pressure differences.

📝 Configuration

Body Shape

Flow Conditions

Fluid

Drag Force:
$F_D = C_d \frac{\rho U_\infty^2}{2} A_{ref}$

Sphere:
Stokes ($Re \lt 1$): $C_d = \frac{24}{Re}$
Intermediate: $C_d = \frac{24}{Re}(1 + 0.15 Re^{0.687})$
Newton: $C_d \approx 0.44$

Cylinder: $C_d \approx 1.2$ ($Re \gt 10^3$)
Flat plate: $C_d \approx 1.17$ (normal)

📊 Results & Visualization

Configure inputs and click Calculate Drag Force to view results.

📘 Calculation Methodology

Mathematical Model & Theory

A body moving through a fluid experiences a drag force opposing its motion, defined by the drag equation:

$$F_D = C_d A_{ref} \frac{\rho U_\infty^2}{2}, \quad Re = \frac{\rho U_\infty D}{\mu}$$

Where $C_d$ is the drag coefficient, which depends on shape and the Reynolds number ($Re$). At low Reynolds numbers ($Re < 0.1$), viscous forces dominate and the drag coefficient of a sphere follows Stokes' Law ($C_d = 24/Re$). Streamlined profiles delay boundary layer separation, reducing pressure drag at high Reynolds numbers.

Assumptions

  • Steady and uniform free-stream flow conditions.
  • Rigid body with smooth surface finish (no surface roughness corrections).
  • No wall interference effects (free boundary fluid domain).

Academic References

  1. White, F. M.: Fluid Mechanics, McGraw-Hill, 8th Edition.
  2. Schlichting, H.: Boundary-Layer Theory, McGraw-Hill.

Worked Engineering Example

Problem Statement:
A 100 mm diameter sphere is placed in a wind tunnel with air flowing at 20 m/s ($\rho = 1.2$ kg/m³, $\mu = 1.8 \times 10^{-5}$ Pa·s). If the drag coefficient is $C_d = 0.45$, calculate the drag force.

Step-by-step Solution:
1. Calculate projected area $A_{ref}$:
$$A_{ref} = \frac{\pi D^2}{4} = \frac{\pi \times 0.1^2}{4} = 0.007854 \text{ m}^2$$ 2. Apply the drag equation:
$$F_D = C_d A_{ref} \frac{\rho U_\infty^2}{2}$$ $$F_D = 0.45 \times 0.007854 \times \frac{1.2 \times 20^2}{2} = 0.848 \text{ N}$$
Final Result:
The drag force is 0.848 N.