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
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Low Roshko Number - Indicates low oscillation frequency relative to the viscous effects. The flow might be more stable, with less pronounced vortex shedding or oscillatory behavior. This could happen in highly viscous fluids or at low Reynolds numbers (laminar flow), where viscosity damps out oscillations.
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High Roshko Number - Suggests a high frequency of oscillation relative to viscous effects. Typically occurs in flows with higher Reynolds numbers (transitional or turbulent regimes), where inertial forces dominate and vortex shedding becomes significant. Common in scenarios like flow past a cylinder or sphere, where a wake forms with regular vortex patterns (e.g., a Kármán vortex street).
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 | \(dimensionless\) | \(dimensionless\) |
| \( f \) = Frequency of Vortex Shedding | \(dimensionless\) | \(dimensionless\) |
| \( l_c \) = Characteristic Length | \(in\) | \(mm\) |
| \( \nu \) (Greek symbol nu) = Kinematic Viscosity | \(ft^2\;/\;sec\) | \(m^2\;/\;s\) |
