Strouhal Number

The Strouhal number calculator compute the Strouhal number based on the frequency, characteristic length and flow velocity.

INSTRUCTIONS: Choose units and enter the following:

• (f) Frequency of Vortex Shedding
• (L)  Characteristic Length
• (U)  Flow Velocity

Strouhal number (St): The calculator returns the Strouhal number.

Related Calculators:

• Reynold's Number
• Reduced Frequency
• Strouhal number

The Math / Science

In dimensional analysis, the Strouhal number (St) is a dimensionless number describing oscillating flow mechanisms. The parameter is named after Vincenc Strouhal, a Czech physicist who experimented in 1878 with wires experiencing vortex shedding and singing in the wind. The Strouhal number is an integral part of the fundamentals of fluid mechanics.

The formula for the Strouhal number is:

    St = (f • L) / U

where 

• St is the Strouhal number
• f is the frequency of vortex shedding, 
• L is the characteristic length (e.g. hydraulic diameter) and 
• U is the flow velocity. 

Uses of Strouhal Number

The Strouhal number is used to characterize and predict the occurrence of vortex shedding and flow separation in various systems, such as flow around objects (like cylinders or airfoils) or in situations involving periodic fluid motion (like flapping wings or vibrating structures).

Applications of the Strouhal number include:

1. Vortex shedding: When an object is placed in a flowing fluid, vortices might form and detach periodically from the object's surface. The Strouhal number helps predict at what frequency this shedding will occur relative to the object's size and the fluid speed.
2. Aeroelasticity: It is used in studying the behavior of structures subjected to aerodynamic forces that cause vibrations or oscillations, like bridges, buildings, and airplane wings. The Strouhal number helps predict the occurrence of resonance and the resulting structural fatigue.
3. Biofluid dynamics: In biology and biomechanics, the Strouhal number helps analyze the movements of organisms or structures within fluids, such as fish swimming or bird flight, and understand the efficiency of their locomotion based on the frequency and speed of their movements relative to their size.

In practical terms, a particular Strouhal number range often signifies the onset of specific flow behaviors. For instance, for a flow around a cylinder, a Strouhal number around 0.2 to 0.3 often indicates the onset of significant vortex shedding.

Understanding the Strouhal number helps engineers and scientists in designing aerodynamic structures, predicting flow patterns, minimizing drag, optimizing performance, and avoiding undesired vibrations or oscillations in various engineering applications.