Reynolds number

The Reynolds number is also a dimensionless ratio, relating the effect of viscosity to inertia, used to determine whether fluid flow is laminar or turbulent (Chow 1959). The Reynolds number relates inertial forces to viscous forces and was derived by a nineteenth century English scientist, Osborne Reynolds, for use in wind tunnel experiments.

Inertia is represented in equation 6 by the product of velocity and hydraulic radius, divided by the kinematic viscosity of water, with units of length squared per time. For turbulent flow Re>2000, for laminar, Re<500, and values between these limits are identified as transitional.

where:
V = velocity (ft/s)
R = hydraulic radius (ft)
ν = kinematic viscosity (ft²/s)

For use in sediment transport analysis, the Reynolds number has been formulated to apply at the watersediment boundary. In this case, the velocity is local to the boundary and termed shear velocity (V*). Also, the length term is not the hydraulic radius, but roughness height, or the diameter of particles (D) forming the boundary. This boundary Reynolds number has also been called the bed Reynolds number or shear Reynolds number.

where:
V_* = boundary shear velocity (ft/s)
D = particle diameter
ν = kinematic viscosity (ft²/s)

Because streamflow is almost exclusively turbulent, the Reynolds number is not needed as a flag of turbulence. The Reynolds number has value for sedimentation analyses in that drag coefficients have been empirically related to Reynolds number. Another important use in sedimentation involves incipient motion of sediment particles. Studies have related the bed Reynolds number to critical shear stress (the initiation point of sediment movement). Through the Shields diagram, for example, one can determine critical shear, given a bed Reynolds number. Additional information on this topic is provided in NEH654.13.