🎯 External Flow — Drag Force Calculator
Calculate drag force on common geometries with Reynolds-dependent drag coefficient correlations.
📝 Configuration
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)
$F_D = C_d \frac{\rho U_\infty^2}{2} A_{ref}$
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 the inputs and click Calculate to see results.
ℹ️ About External Flow Drag
Drag is the resistance force exerted on a body moving through a fluid. It depends on shape, velocity, and fluid properties.
Applications:
• Automotive aerodynamics
• Settling velocity of particles
• Wind loading on structures
• Projectile ballistics
• Parachute design
Drag is the resistance force exerted on a body moving through a fluid. It depends on shape, velocity, and fluid properties.
Applications:
• Automotive aerodynamics
• Settling velocity of particles
• Wind loading on structures
• Projectile ballistics
• Parachute design
📘 Calculation Methodology
Mathematical Model & Theory
A body moving through a fluid experiences a drag force opposing its motion, defined by the drag equation:
$$F_D = C_D A \frac{\rho U^2}{2}$$
Where $C_D$ is the drag coefficient, which depends on shape and the Reynolds number ($Re_D = \rho U D / \mu$). For a sphere at low $Re < 0.1$, $C_D = 24/Re$ (Stokes' Law).
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 $A$:
$$A = \frac{\pi D^2}{4} = \frac{\pi \times 0.1^2}{4} = 0.007854 \text{ m}^2$$ 2. Apply the drag equation:
$$F_D = C_D A \frac{\rho U^2}{2} = 0.45 \times 0.007854 \times \frac{1.2 \times 20^2}{2} = 0.848 \text{ N}$$
Final Result:
The drag force is 0.848 N.
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 $A$:
$$A = \frac{\pi D^2}{4} = \frac{\pi \times 0.1^2}{4} = 0.007854 \text{ m}^2$$ 2. Apply the drag equation:
$$F_D = C_D A \frac{\rho U^2}{2} = 0.45 \times 0.007854 \times \frac{1.2 \times 20^2}{2} = 0.848 \text{ N}$$
Final Result:
The drag force is 0.848 N.