Strouhal Number Calculator

The Strouhal number (St) is a dimensionless number describing the frequency of vortex shedding in the wake of a body in a fluid flow. It relates the frequency of vortex shedding (f) to the velocity of the flow (v) and a characteristic length (L) of the body. This number is crucial for understanding and predicting fluid dynamics phenomena, such as the lift and drag forces experienced by the body in the flow.

Historical Background

The Strouhal number is named after Czech physicist Vincenc Strouhal, who in the 1870s investigated the whistling sounds produced by cylindrical objects in a flow and discovered the relationship between the frequency of these sounds and the speed of the flow. This relationship has since been applied broadly in fluid dynamics to characterize the oscillatory behavior of flows around objects.

Calculation Formula

The formula for calculating the Strouhal number is given by:

\[ St = \frac{fL}{v} \]

where:

• \(St\) is the Strouhal number,
• \(f\) is the frequency of vortex shedding (in Hz),
• \(L\) is the characteristic length of the body (in meters),
• \(v\) is the velocity of the flow (in m/s).

Example Calculation

If a fish's tail fin oscillates at a frequency of 2 Hz, with a characteristic length of 0.1 meters, in water flowing at 1 m/s, the Strouhal number is calculated as:

\[ St = \frac{2 \times 0.1}{1} = 0.2 \]

Importance and Usage Scenarios

The Strouhal number is used in the design and analysis of a wide range of applications, including the optimization of energy efficiency in bio-inspired propulsion systems, the study of wind loads on buildings and bridges, and the analysis of blood flow in medical research. It helps in understanding the fluid-structure interaction and predicting the forces and patterns of vortex shedding.

Common FAQs

1. What does the Strouhal number tell us?

   • The Strouhal number provides insight into the stability and pattern of vortex shedding behind a bluff body in a flow. A stable St number within a certain range indicates a regular pattern of vortices, which is important for predicting oscillatory forces on structures.

2. How does the Strouhal number affect propulsion in aquatic animals?

   • Aquatic animals, such as fish and cetaceans, utilize a range of Strouhal numbers for efficient propulsion, optimizing the trade-off between the energy they expend and the thrust they generate. Studies have shown that there's an optimal Strouhal number range for maximum efficiency in swimming and flying in nature.

3. Can the Strouhal number predict the noise generated by structures?

   • Yes, the Strouhal number can be used to predict the frequency of sound generated by vortex shedding from structures, such as chimneys and cables, when subjected to wind. This is crucial for designing structures to minimize noise pollution.

This calculator facilitates the understanding and application of the Strouhal number, making it a valuable tool for students, engineers, and researchers involved in fluid dynamics and related fields.