Strouhal Number Calculator

The Strouhal number is a dimensionless ratio that indicates the frequency at which vortices are shed from an object in a fluid flow. The Czech physicist Vincenc Strouhal derived this number in 1878 while investigating why wires make noise in the wind. The same number explains why wires hum, why slender chimneys sometimes vibrate and collapse, and why fish and birds maintain a steady pace when they want to move efficiently.

When a fluid flows around an object, vortices are shed alternately from the back of the object and form a pattern called a von Karman vortex street. The Strouhal number relates the frequency at which the vortices are shed to the flow velocity and size of the object. If three of the four quantities below are entered, then the calculator will calculate the remaining quantity.

The importance of the Strouhal number:

The Strouhal number compares the speed at which vortices are shed from an object to the speed of the fluid flowing around the body. A small value indicates that the spacing between the vortices is large and the shedding rate is low. A high value indicates that the vortices are close together and are being shed rapidly.

For a normal cylinder hit by flow from the side this value is in a very wide range around 0.21. This stability is useful. If shape and flow speed are known, then the frequency at which vortices separate can be predicted without needing to make a measurement, and it can be checked whether that frequency is dangerously close to natural frequencies of the structure.

Formula for the Strouhal number:

The Strouhal number is the product of the frequency of vortex shedding and a characteristic length divided by the flow velocity.

where St is the Strouhal number, f is the frequency of vortex shedding, L is a characteristic length (e.g. diameter for a cylinder or width for a flat plate) and U is the flow velocity. As the product of a frequency in Hertz and a length in meters divided by a velocity in meters per second all units cancel out leaving a pure number with no unit.

Since this equation contains four variables, any one of the missing quantities can be calculated by rearranging the equation.

Example calculation:

Consider a wire with thickness of about 2 centimeters. So L = 0.02 meters. A steady wind hits the wire at speed of 10 meters per second. According to experimental data, Strouhal number for a cylinder is approximately 0.21, which means that frequency of vortex shedding will be calculated as follows:

The wire is thus oscillating with a frequency of about 105 Hertz. This corresponds to approximately one deep G and can be heard on quiet evenings in the wind. The vortices alternately separate on both sides, pushing the wire first in one direction and then in the other during each period. When this frequency matches the natural frequency of the wire, the oscillation constantly increases until eventually a part of the wire breaks.

Arrangement of formulas

The table below shows the same relationship in four different ways, each of which corresponds to one of the four sets you might be missing.

Typical Strouhal number

The Strouhal number depends mainly on the shape of the object and to a lesser extent on the Reynolds number. Engineers typically use these numbers as a first approximation.

Vortex-induced excitation and resonance

Civil engineers pay attention to the Strouhal number because vortex shedding can cause bridge decks to oscillate, offshore platforms to vibrate and several steel chimneys to collapse. Each individual shed vortex exerts a small sideways force on the structure. If the frequency of the vortex shedding gradually matches the natural frequency of the structure then these forces add up in phase with the motion and transfer energy into the structure each period.

As a rule of thumb there is normally a dead zone of about 20% on either side of the natural frequency range. A classic solution for tall chimneys is to wrap spiral guide vanes at one third up position. This disturbs regular shedding of vortices and prevents any single frequency from becoming dominant. Open the above resonance check and compare the vortex shedding frequency with the structure's natural frequency.

Animal Movement

Biologists have discovered an amazing phenomenon: animals that swim or fly efficiently move at a Strouhal number between 0.2 and 0.4, regardless of the species. Dolphins, tuna, sharks, hummingbirds, and herons all fall within this narrow range when they're moving at their preferred speed.

Biologists have discovered an amazing phenomenon: animals that swim or fly efficiently move at a Strouhal number between 0.2 and 0.4, regardless of the species. Dolphins, tuna, sharks, hummingbirds, and migrating geese all fall within this narrow range when aiming for their preferred speed.

How to use this calculator:

If you enter any three of the four values, the remaining value will be calculated automatically. If you input the frequency of vortex shedding, diameter and flow velocity, then you get the Strouhal number.

Alternatively, if the Strouhal number of the shape used is already known and you want to find out the frequency of vortex shedding for a given flow velocity and object size, then enter those values and leave the field for frequency blank. There is no mode to select as an empty field tells the calculator what to calculate. The units are automatically converted. For frequency either Hertz or cycles per minute can be used, for length meters, centimeters, feet, inches and for velocity meters per second, km/h, mph or knots.

Tips for accurate results:

Pick the correct characteristic length. For a cylinder this is its diameter, for a plate perpendicular to the flow it's the width. More complex objects require experimental data. The default value of 0.21 only applies to smooth cylinders in the subcritical Reynolds number range from about 300 to 200,000. Outside that range or with other shapes values change.

When designing, you should first perform the calculation and compare the calculated or predicted vortex shedding frequency with the natural frequencies of the structure. If the difference between these two values is about 20% or less, there is a risk of resonance. In this case, you need to change the shape, increase damping, or strengthen the structure to ensure that the natural frequency avoids this frequency.

Assumptions and limitations:

The Strouhal number characterizes periodic vortex shedding and is therefore most meaningful for relatively steady flows around blunt bodies. 0.21 is a practical average value for cylinders. The actual value varies with the Reynolds number, changing dramatically when the flow crosses Re = 200,000 into the supercritical region.

This tool treats the characteristic length, frequency and flow velocity each as a single representative value. In real structures vortices detach over a range of frequencies and a full vibration analysis also requires damping and modes of oscillation. These are aspects that cannot be captured by a single dimensionless ratio.