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