# 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

\(\large{ P = \frac{ w_s }{ \beta \; k \; u* } }\) |

### Where:

\(\large{ P }\) = Rouse number

\(\large{ w_s }\) = sediment fall velocity

\(\large{ \beta }\) (Greek symbol beta) = constant that correlates eddy viscosity to eddy diffusivity (1)

\(\large{ k }\) = von Karman constant (0.40)

\(\large{ u* }\) = shear velocity