Reynolds Number for Pipe Flow
Reynolds Number for Pipe Flow
The Reynolds number is the single most important dimensionless group in pipe hydraulics: it predicts whether flow is smooth (laminar) or chaotic (turbulent), which in turn sets the friction factor and the heat-transfer behaviour.
For a circular pipe Re = ρvD/μ, where ρ is density, v the mean velocity, D the diameter and μ the dynamic viscosity.
Inputs
Water at about 20 °C flowing in a 50 mm pipe.
rho := 998 kg/m^3=998 kg/m^3
v := 2 m/s=2 m/s
D := 50 mm=50 mm
mu := 0.001 Pa·s=1e-03 kg/m/s
Reynolds number
Re := rho·v·D/mu=99800
Results
As a guide, Re below about 2300 is laminar, above about 4000 is fully turbulent, and the band between is transitional. The value computed here is well into the turbulent regime, which is typical of practical water-distribution velocities and means the Colebrook/Moody friction factor applies.
Assumptions & limitations
- Newtonian fluid, fully developed flow in a round pipe.
- Mean (bulk) velocity used; properties at the bulk temperature.
- Use the hydraulic diameter for non-circular ducts.