Rouse number formula |
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\( P \;=\; \dfrac{ w_s }{ \beta \cdot k \cdot u* }\) (Rouse Number) \( w_s \;=\; P \cdot \beta \cdot k \cdot u* \) \( \beta \;=\; \dfrac{ w_s }{ P \cdot k \cdot u* }\) \( k \;=\; \dfrac{ w_s }{ P \cdot \beta \cdot u* }\) \( u* \;=\; \dfrac{ w_s }{ P \cdot \beta \cdot k }\) |
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| Symbol | English | Metric |
| \( P \) = Rouse Number | \(dimensionless\) | \(dimensionless\) |
| \( w_s \) = Sediment Fall Velocity | \(ft \;/\; sec\) | \(m \;/\; s\) |
| \( \beta \) (Greek symbol beta) = Constant that Correlates Eddy Viscosity to Eddy Diffusivity (1) | \(dimensionless\) | \(dimensionless\) |
| \( k \) = Von Karman Constant (0.40) | \(dimensionless\) | \(dimensionless\) |
| \( u* \) = Shear Velocity | \(sec \;/\; ft^{\frac{1}{3}} \) | \(s \;/\; m^{\frac{1}{3}} \) |
Rouse number, abbreviated as P or Z, a dimensionless number, is used in fluid dynamics and engineering to characterize the relative importance of buoyancy forces to viscous forces in a fluid flow. The Rouse number is typically used in the context of fluid flows that involve particles or substances suspended in the fluid, such as sediment particles in water or solid particles in a gas. It helps determine whether buoyancy or viscous forces dominate the behavior of these suspended particles.
Rouse Number Interpretation
- Low Rouse Number (Ro < 1) - Turbulent mixing dominates over settling, meaning sediment particles are well-distributed throughout the water column. This typically occurs with fine particles (silt or clay) or in highly turbulent flows.
- Rouse Number (1 < Ro < 2.5) - A transitional regime where both settling and mixing play significant roles, resulting in a graded concentration profile (higher near the bed, decreasing upward).
- High Rouse Number (Ro > 2.5) - Settling dominates over turbulent mixing, so sediment tends to concentrate near the bed. This is common with coarser particles (sand or gravel) or in less turbulent flows.
The Rouse number is particularly important in environmental engineering and sediment transport studies, where it helps predict the behavior of particles in rivers, lakes, oceans, and other natural bodies of water. It's a valuable tool for understanding how sediment particles are transported, settle, or remain suspended in a fluid under various conditions.
