Calculator Inputs
Example Data Table
| Scenario | Key Inputs | Formula | Vortex Strength Γ |
|---|---|---|---|
| Tangential velocity mode | Vθ = 12 m/s, r = 0.35 m | Γ = 2πrVθ | 26.3894 m²/s |
| Angular velocity mode | ω = 20 rad/s, r = 0.50 m | Γ = 2πωr² | 31.4159 m²/s |
| Lift relation mode | L′ = 185 N/m, ρ = 1.20 kg/m³, U∞ = 15 m/s | Γ = L′/(ρU∞) | 10.2778 m²/s |
| Uniform vorticity mode | ζ = 8 1/s, A = 1.80 m² | Γ = ζA | 14.4000 m²/s |
Formula Used
Circulation definition: Γ = ∮V·dl
From tangential speed: Γ = 2πrVθ
From angular speed: Γ = 2πωr²
From lift per unit span: Γ = L′/(ρU∞)
From uniform vorticity over area: Γ = ζA
All inputs are converted to SI units internally. The result is reported in square meters per second.
How to Use This Calculator
- Select the input method that matches your fluid problem.
- Enter the known values and choose proper units.
- Set density and freestream velocity for lift estimation.
- Choose a graph radius range for the profile plot.
- Press the calculate button to show the result above the form.
- Export the result table using the CSV or PDF buttons.
Frequently Asked Questions
1. What is vortex strength?
Vortex strength is circulation around a closed loop. It measures rotational flow intensity and is commonly written as Γ. Larger values indicate stronger swirl in the fluid field.
2. What unit does the result use?
The calculator reports vortex strength in m²/s. That unit comes from integrating velocity around a length or from equivalent relations such as lift per unit span.
3. When should I use tangential velocity mode?
Use that mode when you know the swirl speed at a specific radius. It is ideal for measured velocity data, lab probes, or velocity estimates around a vortex core.
4. When should I use angular velocity mode?
Use angular velocity mode for forced vortices or solid-body rotation. In that case, tangential velocity grows linearly with radius, and Γ depends on ω and r².
5. Why are density and freestream velocity included?
They allow an estimated lift per unit span using Kutta-Joukowski. This is useful for aerodynamics checks, rotating flow analysis, and comparing circulation to lifting performance.
6. Does the graph always show a free vortex?
Not always. The graph shows a forced-vortex profile for angular velocity mode. Other modes use an equivalent circulation-based profile to visualize tangential speed versus radius.
7. Can I use non-SI units?
Yes. The page accepts several common length, velocity, density, lift, and area units. Inputs are converted internally before the final vortex strength is calculated.
8. What assumptions affect accuracy?
Accuracy depends on model choice, steady-flow assumptions, and data quality. Uniform vorticity, ideal swirl profiles, or two-dimensional lift relations may not match complex turbulent flows exactly.