Rouse Number

on . Posted in Dimensionless Numbers

Rouse number, abbreviated as P or Z, a dimensionless number, used in fluid dynamics showing how a concentration of suspended sediment will be transported in a flowing fluid.


Rouse number formula

\(\large{ P = \frac{ w_s }{ \beta \; k \; u* }  }\) 
Symbol English Metric
\(\large{ P }\) = Rouse number \(\large{dimensionless}\)
\(\large{ w_s }\) = sediment fall velocity \(\large{\frac{ft}{sec}}\) \(\large{\frac{m}{s}}\)
\(\large{ \beta }\)  (Greek symbol beta) = constant that correlates eddy viscosity to eddy diffusivity  (1) \(\large{dimensionless}\)
\(\large{ k }\) = von Karman constant  (0.40) \(\large{dimensionless}\)
\(\large{ u* }\) = shear velocity \(\large{\frac{sec}{ft^{\frac{1}{3}}}}\) \(\large{\frac{s}{m^{\frac{1}{3}}}}\)


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Tags: Flow Equations Fluid Equations