# Rouse Number

Written by Jerry Ratzlaff 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

 $$\large{ P = \frac{ w_s }{ \beta \; k \; u* } }$$

### Where:

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