Strouhal Number Calculator

Formula used

The Strouhal number is a dimensionless quantity that links unsteady flow frequency to a length scale and speed: St = (f × L) / V.

• St is the Strouhal number (dimensionless).
• f is the characteristic frequency (Hz).
• L is the characteristic length (m).
• V is the flow speed (m/s).

How to use this calculator

1. Select what you want to solve for from the dropdown.
2. Enter the other three quantities and choose their units.
3. Click Calculate to view results above the form.
4. Use the CSV or PDF buttons to save the computed summary.

Tip: For vortex shedding from a cylinder, L is usually the cylinder diameter.

Example data table

Strouhal number in practice

1) Why this dimensionless number matters

The Strouhal number compares an oscillation frequency to the flow time scale around a body. When St is stable, periodic unsteady behavior is predictable and easier to model. It is widely used for vortex shedding, acoustic tones, flow-induced vibration, and wake dynamics. This context helps you validate simulations and wind-tunnel data.

2) What your inputs represent

Use a frequency that characterizes the dominant unsteady motion, such as a shedding tone or lift/pressure peak. Choose a length that matches the physics, like cylinder diameter, airfoil chord, or jet width. Use the free-stream speed seen by the object, not a local recirculation speed.

3) Unit consistency and conversions

Because St is dimensionless, any consistent unit set is valid. This calculator converts frequency to hertz, length to meters, and speed to meters per second internally. If you mix units, you can still obtain the correct St as long as each input is converted properly.

4) Typical ranges and quick interpretation

Many bluff-body wakes show Strouhal values on the order of 0.1 to 0.3 over practical flow regimes. Values far outside that band can indicate a different length scale, a non-shedding mechanism, strong turbulence, or measurement noise dominating the spectrum.

5) Vortex shedding and wake frequency

For classic von Kármán shedding from a circular cylinder, St is often near 0.2 across a broad range of conditions. With St known, you can estimate shedding frequency as f ≈ (St × V) / L, which is useful for checking resonance risk in masts, chimneys, and heat-exchanger tubes.

6) Connection to Reynolds number

Strouhal behavior depends on the flow regime, which is commonly described by the Reynolds number. At very low Reynolds numbers, unsteady shedding may not exist. As Reynolds number increases, shedding becomes more coherent and then can broaden under turbulence and roughness.

7) Measurement tips and uncertainty

Prefer a dominant spectral peak from force, pressure, or velocity signals and report how it was extracted. Use an adequate sampling rate and record length to resolve the peak. Uncertainty in speed or length transfers directly to St, so document probe calibration and geometry.

8) Engineering checks and design use

Use Strouhal estimates to screen for flow-induced vibration, tonal noise, and lock-in with structural modes. Compare against empirical values for similar shapes and surface conditions. When St varies strongly with operating point, consider using multiple peaks or a band-limited definition.

FAQs

1) What is the Strouhal number?
It is a dimensionless ratio that relates an oscillation frequency to a characteristic length and flow speed: St = (f × L) / V.

2) Which length should I use?
Use the length that sets the wake scale, such as cylinder diameter, airfoil chord, or bluff-body height. If the mechanism is different, choose the scale that best matches the observed unsteadiness.

3) Can I compute frequency from a known St?
Yes. Rearrange the relation to f = (St × V) / L. This is common for estimating vortex shedding tones and checking resonance with natural frequencies.

4) Why is my St unusually high or low?
Common reasons are using the wrong length scale, using a local speed instead of free-stream speed, selecting a non-dominant frequency, or operating in a regime where shedding is weak or broadband.

5) Does Strouhal depend on Reynolds number?
Often, yes. Many shapes show near-constant St over a range of Reynolds numbers, but transitions, surface roughness, and turbulence intensity can shift the dominant shedding behavior and measured peaks.

6) Is Strouhal always about vortex shedding?
Not always. It can describe any periodic unsteady phenomenon in flows, including jet oscillations, cavity tones, and aerodynamic flutter signatures, as long as a representative frequency, length, and speed exist.

7) What is a reasonable St to expect for a cylinder?
A common rule-of-thumb is around 0.2 in many practical shedding regimes. The exact value can change with Reynolds number, surface condition, end effects, and measurement method.