Rouse Number

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	\(\large{\frac{sec}{ft^{\frac{1}{3}}}}\)	\(\large{\frac{s}{m^{\frac{1}{3}}}}\)