Roshko Number formula |
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\( Ro \;=\; St \cdot Re \;=\; \dfrac{ f \cdot l_c^2 }{ \nu }\) (Roshko Number) \( f \;=\; \dfrac{ Ro \cdot \nu }{ l_c^2 }\) \( l_c \;=\; \sqrt{ \dfrac{ Ro \cdot \nu }{ f } }\) \( \nu \;=\; \dfrac{ f \cdot l_c^2 }{ Ro }\) |
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| Symbol | English | Metric |
| \( Ro \) = Roshko Number | \(dimensionless\) | \(dimensionless\) |
| \( St \) = Strouhal Number | \(dimensionless\) | \(dimensionless\) |
| \( Re \) = Reynolds Number | \(dimensionless\) | \(dimensionless\) |
| \( f \) = Vortex Shedding Frequency | \(dimensionless\) | \(dimensionless\) |
| \( l_c \) = Characteristic Length | \(in\) | \(mm\) |
| \( \nu \) (Greek symbol nu) = Kinematic Viscosity | \(ft^2\;/\;sec\) | \(m^2\;/\;s\) |
Roshko number, abbreviated as Ro, a dimensionless number, is used in fluid mechanics that describes oscillating flow mechanisms, particularly in the context of vortex shedding. It’s named after Anatol Roshko, an aeronautics professor who studied turbulent wakes and vortex streets. The Roshko number is essentially a way to relate the frequency of oscillations in a flow to the fluid’s properties and the geometry of the system.
Roshko Number Interpretation
The Roshko number is often interpreted in the context of the Reynolds number (Re) and Strouhal number (St), since \(Ro = St \cdot Re\) . These relationships allow it to serve as a bridge between flow velocity, viscosity, and oscillatory behavior.
Vortex Shedding Frequency - It quantifies how frequently vortices are shed from the bluff body, which is critical in applications like aerodynamics, hydrodynamics, and structural engineering, where periodic forces can induce vibrations (in bridges or cables).
Flow Regime - The Roshko number, often used alongside the Reynolds number (\(Re = \frac{U\cdot D }{v }\), where U is the free stream velocity), helps categorize the flow regime-laminar, transitional, or turbulent-based on the shedding characteristics.
Scaling - It allows comparison of vortex shedding phenomena across different scales and fluid properties by normalizing the frequency with respect to the body's size and the fluid's viscosity.
Roshko Number Applications
Engineering Design - The Roshko number is used to predict vortex-induced vibrations (VIV) in structures like chimneys, bridges, and offshore risers, helping engineers design to avoid resonance.
Aerodynamics - It aids in understanding drag and lift fluctuations on objects like aircraft components or wind turbine blades.
Fluid-Structure Interaction - In applications involving oscillating flows, the Roshko number helps model the interaction between the fluid and the structure.
