Strouhal Number Formula & Calculator
The Strouhal number is a dimensionless measure that relates the oscillation frequency of a body to the velocity and characteristic length of the surrounding flow, and describes how periodic patterns such as vortices are generated in a fluid.
The Strouhal Number: A Bridge Between Oscillation and Flow
The Strouhal number is a fundamental parameter in fluid mechanics that describes the relationship between the oscillation frequency of a flow, the fluid velocity, and a characteristic length of the body in its path. Its importance lies in its use in the analysis of flow-induced vibrations, structural resonances, and the aerodynamic design of components exposed to air or water currents.
The interesting thing about the Strouhal number is not only its formulation, but what it reveals: a dynamic balance between inertial forces and the natural frequencies of moving bodies. For example, when air passes around a cylinder, a trail of eddies known as the von Kármán vortex street is generated. These vortices do not appear randomly; their frequency of appearance is in constant proportion to the wind speed and the size of the object. This proportion is precisely the Strouhal number.
This is especially important because, thanks to this phenomenon and because they don't appear randomly, there are measuring devices based on this operating principle, such as vortex and swirl flow meters.
Beyond theory, this number finds applications in aeronautical engineering, biomechanics, meteorology, and even the design of musical instruments. In biology, research has revealed that swimming and flying animals, from trout to hummingbirds, tend to move in ways that optimize their Strouhal number, maximizing the efficiency of their propulsion.
What is the Strouhal number?
The Strouhal number (St) is a dimensionless number that relates how often a body sheds vortices (or oscillates) to the flow velocity and the size of the body. It is named after Czech physicist Vincenc Strouhal, who studied the “singing” of wires in the wind in 1878.
Strouhal number formula
St = f · L / V
• f: vortex shedding or oscillation frequency (Hz)
• L: characteristic length, usually the diameter or width of the body (m)
• V: flow velocity (m/s)
Rearranged: f = St · V / L and V = f · L / St.
Worked example: vortex flowmeter
A vortex flowmeter has a 20 mm wide shedder bar (L = 0.02 m) and St ≈ 0.2. Water flows through the pipe at 3 m/s.
1. Vortex frequency: f = St · V / L = 0.2 × 3 / 0.02 = 30 Hz.
2. Reynolds number (water at 20 °C, ν = 1.0 × 10⁻⁶ m²/s): Re = V · L / ν = 3 × 0.02 / 1.0 × 10⁻⁶ = 60,000, inside the range where St is almost constant.
3. The other way round: if the sensor reads 45 Hz, the velocity is V = f · L / St = 45 × 0.02 / 0.2 = 4.5 m/s.
Because St stays constant over a wide Reynolds range, frequency is proportional to velocity: that is how vortex flowmeters work.
Another example: a 2 m diameter chimney in a 10 m/s wind sheds vortices at f = 0.2 × 10 / 2 = 1 Hz. If its natural frequency is close to 1 Hz, it can go into resonance.
Typical Strouhal number values
• Circular cylinder (Re ≈ 300 to 2 × 10⁵): St ≈ 0.2
• Square cylinder: St ≈ 0.13
• Flat plate normal to the flow: St ≈ 0.15
• Swimming and flying animals (fish, birds, insects): St ≈ 0.2 to 0.4 (the most efficient range)
• Below Re ≈ 47 a cylinder does not shed vortices.
Frequently asked questions
Does the Strouhal number have units?
No. It is dimensionless: Hz × m ÷ (m/s) cancels out.
Why is St ≈ 0.2 for a cylinder?
Over a wide Reynolds range the von Kármán vortex street forms the same way: in each full cycle (one vortex on each side) the flow travels about 5 diameters.
What is the difference between Strouhal and Reynolds?
Reynolds compares inertial and viscous forces and tells you whether flow is laminar or turbulent; Strouhal tells you how often the flow oscillates. St depends on Re.
What is it used for in engineering?
Designing vortex flowmeters, preventing vortex-induced vibration in chimneys, bridges, cables and thermowells, and in acoustics (the whistling of the wind).
What happens if the vortex frequency matches the natural frequency?
The structure resonates and vibrates with large amplitude; that is why it is checked for thermowells (ASME PTC 19.3 TW) and chimneys.
If you need to calculate the Reynolds number you can follow the following link:
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