Strouhal Number Calculator

St = fL/V — dimensionless vortex-shedding frequency. Predict shedding frequency, critical wind speed, or diagnose vortex-induced vibration (VIV) resonance risk.

Dimensional Analysis · Specialized

Inputs

Solve for:

Characteristic length (diameter) L (mm)

Free-stream velocity V (m/s)

Strouhal number St (dimensionless)

Check for VIV resonance — enter structural natural frequency f_n

Theory

Strouhal number and vortex shedding:

St = f × L / V [dimensionless]

f = St × V / L [Hz] — predict shedding frequency

V_crit = f_n × L / St [m/s] — critical resonance velocity

Typical St values for bluff bodies:

Body	St	Valid Re range
Circular cylinder (Re 300 – 2×10⁵)	0.20	Re 300 – 2×10⁵
Square cylinder	0.14	Re 300 – 2×10⁵
D-section cylinder	0.19	Re 300 – 2×10⁵
Flat plate (normal to flow)	0.13	Re 300 – 2×10⁵
Equilateral triangle (apex upstream)	0.17	Re 300 – 2×10⁵
Two-dimensional airfoil at stall	0.12	Re 300 – 2×10⁵

St ≈ 0.2 for a circular cylinder is approximately constant over a wide Re range, but varies at very low Re (creeping flow) and above Re ≈ 5×10⁵ (turbulent boundary layer).

Vortex-induced vibration (VIV) and lock-in:

Resonance when: f_shedding ≈ f_n (structural natural frequency)

Lock-in range: 0.8 ≤ f/f_n ≤ 1.2

In the lock-in range, shedding frequency couples with structural vibration and can cause large-amplitude oscillations. Classic examples: Tacoma Narrows bridge, power-line galloping, offshore riser vibration.

Where:

St = Strouhal number (dimensionless)
f = vortex shedding frequency [Hz]
L = characteristic length (body diameter or width) [m]
V = free-stream velocity [m/s]
f_n = structural natural frequency [Hz]
V_crit = critical velocity at which shedding matches f_n [m/s]