Roshko number

In fluid mechanics, the Roshko number (Ro) is a dimensionless number describing oscillating flow mechanisms. It is named after the American Professor of Aeronautics Anatol Roshko. It is defined as

R o = f L 2 ν = S t R e R o = 0.212 R e − 4.5 valid over [ 50 <= Re < 200] R o = 0.212 R e − 2.7 valid over [200 <= Re < 2000] S t = f L U , R e = U L ν

where

St is the dimensionless Strouhal number;

Re is the Reynolds number;

U is mean stream velocity;

f is the frequency of vortex shedding;

L is the characteristic length (for example hydraulic diameter);

ν is the kinematic viscosity of the fluid.

Note: Linear relation between Ro# and Re# from Roshko's Caltech Thesis (figures 9-10); tested in air [over range Re=50 to Re=2000]

The kinematic viscosity of air at 15 °C is 1.48×10⁻⁵ m²/s. at 20 °C, the kinematic viscosity is 1.525×10⁻⁵ m²/s. at 25 °C, the kinematic viscosity is 1.57×10⁻⁵ m²/s.