Enter values and calculate
Result
Your inputs are calculated by your browser on this page; the operator does not receive or store them.
Reading St as a ratio of times
St = fL/v is the transit time L/v divided by the oscillation period 1/f. St = 0.2 means that while the fluid travels one cylinder diameter, the oscillation advances one fifth of a cycle. Expressed this way, frequencies from experiments of different size and speed collapse to a single comparable number.
Rearranged as f = St·v/L, it gives a rough frequency estimate when St is known. At constant St, doubling the speed doubles the frequency.
Variables and SI units
| Symbol | Meaning | SI unit | Example |
|---|---|---|---|
| f | Frequency of the oscillation of interest, such as vortex shedding | Hz = 1/s | 10 |
| L | Diameter for a cylinder | m | 0.1 |
| v | Free-stream speed | m/s | 5 |
Entering the frequency
- f is in hertz (cycles per second). Divide rpm by 60 to get Hz; 3000 rpm is 50 Hz.
- An angular frequency ω in rad/s must be divided by 2π. Entering ω directly makes St about 6.28 times too large.
- Behind a cylinder, lift fluctuates at the shedding frequency while drag fluctuates at twice that frequency. For the same reason the NASA NPARC cylinder case reads the frequency from wake velocity off the centreline rather than from the drag coefficient.
- Use the diameter for a cylinder, or the width across the flow for other bodies.
How to treat the value 0.2
NASA TM 107730 reports that St from the peak cylinder noise frequency stays nearly constant at 0.2 over 60 < Re < 10⁶. The Re = 150 experiment cited in the NASA NPARC case, by contrast, gives 0.179–0.182. A result that differs from 0.2 is not automatically wrong: first match the Re, the geometry, the definition of L and the measured signal. A result near 0.4 usually means a 2f signal was read.
Examples you can follow with the calculator
Example 1. Reading the fill-in values as a real case
Given. The "Fill example values" button enters f = 10 Hz, L = 0.1 m and v = 5 m/s. Take it as a 100 mm post in 5 m/s wind with a 10 Hz wake fluctuation (assumed).
Calculation. St = 10 × 0.1 ÷ 5 = 0.2. With ν = 1.5104 × 10⁻⁵ m²/s for air at 20 °C and 1 atm (from IAEA Table 3.1 viscosity and density), Re = 5 × 0.1 ÷ (1.5104 × 10⁻⁵) ≈ 33,104.
Interpretation. Re lies within 60 < Re < 10⁶, so St = 0.2 agrees with NASA TM 107730. If the wind rises to 15 m/s, constant St predicts f = 0.2 × 15 ÷ 0.1 = 30 Hz; change v to 15 and f to 30 in the calculator and St stays 0.2.
Example 2. Entering angular frequency or the drag signal by mistake
Given. A 20 mm cylinder is tested at 12 m/s in a wind tunnel, and the spectral peak of a hot-wire signal on one side of the wake reads ω = 754 rad/s (diameter, speed and reading are assumed).
Unit conversion. L = 20 mm = 0.02 m; f = ω/(2π) = 754 ÷ 6.2832 ≈ 120.0 Hz.
Calculation. Correct inputs give St = 120.0 × 0.02 ÷ 12 ≈ 0.200, at Re = 12 × 0.02 ÷ (1.5104 × 10⁻⁵) ≈ 15,890. Entering ω in the f box gives St ≈ 1.257. Entering the drag-signal peak of 240.0 Hz from the same test gives St ≈ 0.400.
Interpretation. 1.257 flags a unit error and 0.400 a signal-choice error. When a cylinder gives about 2π times or twice 0.2, check the inputs before the formula.
Using the Strouhal number calculator
Which speed goes into v?
For a single cylinder, the undisturbed free-stream speed upstream. For a probe in a pipe the section-mean and local speeds can differ, and data for tube bundles often use the gap velocity, so follow the definition of the data you compare with.
How do I get a frequency from a known St?
The calculator returns St, so compute f = St·v/L by hand and enter it to confirm. A 30 mm cable in 10 m/s wind gives f ≈ 66.7 Hz at St = 0.2.
Why does a zero speed or frequency give an error?
Zero speed puts zero in the denominator, and zero frequency means there is no periodic event to compare. For a body oscillating in still fluid, choose another reference speed such as the oscillation velocity amplitude.
What should I watch when comparing CFD St with experiment?
Compare at the same Re and from the same signal. In the NASA NPARC case the Re = 150 experiment gave 0.179–0.182, first-order time integration 0.161 and second order 0.180, so time-integration order and record length matter.
Related guides and calculators
Guide
- Strouhal number guide: worked example and cautions: cable, thermowell and NASA CFD examples on when St ≈ 0.2 holds.
Calculation notes
- Surface tension and unsteady flow: connect force ratios to time ratios: rechecks a St from this calculator as transit time over period and compares it with capillary time.
Related calculators
- Reynolds number (Re): St for vortex shedding behind a cylinder depends on Re, so report both values together.
- Weber number (We): The squared ratio of capillary time √(ρL³/σ) to transit time L/v is We, so compare interface oscillations alongside St.
- Froude number (Fr): For periodic free-surface motion, check gravity effects (Fr) together with oscillation time (St).
References
- NASA Langley: Reynolds Number Influences in Aeronautics (NASA TM 107730). Cylinder noise-peak St near 0.2 for 60 < Re < 10⁶
- NASA Glenn / NPARC Alliance: Laminar Flow over a Circular Cylinder: Study #1. Re 150 experiment 0.179–0.182, CFD 0.161 and 0.180, drag at twice the frequency
- IAEA: Thermophysical Properties of Materials for Nuclear Engineering (2008). Table 3.1 air at 20 °C: viscosity 1.819 × 10⁻⁵ Pa·s, density 1.166 kg/m³ (98.1 kPa)