When a fluid flows past a blunt or bluff object, alternating vortices can peel away from its surface. This process, known as vortex shedding, produces a repeating pattern of swirling eddies downstream. Engineers first documented this phenomenon in the nineteenth century while studying air passing cylindrical chimneys and liquid moving around bridge piers. In the twentieth century, physicist Theodore von Kármán described why the vortices arrange themselves into a staggered pattern now called a Kármán vortex street. This regular shedding can induce oscillating forces on the body, potentially leading to vibrations or even structural failure if the frequency coincides with a natural resonance. For this reason, scientists carefully evaluate vortex shedding when designing towers, offshore risers, aircraft landing gear, and similar components exposed to moving fluids.
The shedding frequency depends primarily on three factors: the flow velocity, the object’s characteristic width (such as diameter for a cylinder), and the Strouhal number. The Strouhal number expresses the nondimensional ratio between the shedding frequency , the body width , and the flow velocity . For many common situations, stays nearly constant, making it convenient to solve for the unknown frequency once the other quantities are known. Circular cylinders in air or water at moderate Reynolds numbers typically exhibit around 0.2. Other shapes or conditions may have higher or lower values, as shown in the table below.
| Geometry | Typical Strouhal Number |
|---|---|
| Circular Cylinder | 0.18–0.22 |
| Square Prism | 0.12–0.15 |
| Triangular Prism | 0.13–0.18 |
| Flat Plate (edge-on) | 0.14–0.17 |
Rearranging the Strouhal relation gives . This means the shedding frequency grows linearly with the flow speed and decreases as the object gets wider. If the Strouhal number remains constant, a doubling of velocity doubles the frequency, while doubling the diameter halves it. In reality, may vary slightly with the Reynolds number, surface roughness, or turbulence level, but the above expression usually offers a useful first approximation.
Enter your measured or desired flow velocity in meters per second along with the object’s characteristic width. Cylinders use their outer diameter, while non-circular objects often use the width perpendicular to the flow. Supply an estimated Strouhal number for your geometry. Many engineering handbooks include typical values, or you may derive it from experiments. When you click the Compute Frequency button, the script multiplies the velocity by the Strouhal number and divides by the width to produce the shedding frequency in hertz. The tool also offers a one-click copy button so you can paste the result into a report or spreadsheet.
Suppose wind moves at 10 m/s past a cylindrical mast 0.5 m in diameter. Taking a typical of 0.2 yields ≡ 4 Hz. Such a periodic force might shake the mast if its natural frequency lies near 4 Hz. Designers could change the diameter, add strakes, or alter the cross section to shift and avoid resonance. In practice, dynamic analysis accounts for structural damping and stiffness to confirm safety. Even if frequencies do not match perfectly, oscillations can still produce fatigue over time.
Vortex shedding is not solely the enemy of engineers. Researchers exploit it to measure flow speed with vortex flow meters: as vortices shed from a bluff body inside a pipe, sensors detect the alternating pressure and derive the velocity. Some musical instruments like the aeolian harp produce sound by the same mechanism when wind passes over strings. Even the hum from a phone cable in a breeze owes its origin to vortex shedding. By understanding the conditions that create and suppress these vortices, we can design quieter cars, stable chimneys, and accurate instrumentation.
The Strouhal number remains fairly constant for a given shape only within a certain Reynolds number range. At very low or high Reynolds numbers, laminar or turbulent effects may alter vortex formation, causing to drift. Surface roughness also influences shedding behavior by promoting early boundary layer separation. If your application involves extreme conditions or unusual geometries, consult experimental data or computational fluid dynamics models. Nonetheless, the simple formula presented here offers quick insights for many practical cases.
Across history, vortex-induced vibrations have both intrigued and frustrated engineers. In the early twentieth century, collapsed smokestacks led to the recognition that steady winds could cause oscillations. During World War II, the Tacoma Narrows Bridge famously twisted itself apart due in part to wind-induced vibration, though torsional flutter also played a role. Modern architects account for these lessons in tall buildings by incorporating tuned mass dampers or aerodynamic modifications. By entering different velocities and diameters into this calculator, you can appreciate how seemingly subtle changes shift the shedding frequency away from resonant danger zones.
From skyscrapers and radio towers to submarine periscopes, many structures extend into a flowing fluid. Predicting the vibrations they may experience is essential for durability and safety. This calculator lets you quickly estimate the frequencies involved so you can plan wind tunnel experiments or adjust dimensions early in the design process. Because all the mathematics runs directly in your browser with no data transmitted elsewhere, you can use the tool offline or incorporate it into teaching materials. Whether you are an engineering student exploring fluid dynamics or a seasoned professional double-checking a design, the ability to compute vortex shedding frequency in seconds provides peace of mind.
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