Turbulent Pipe Flow Transition

Hagen-Poiseuille laminar flow transitions to turbulence above Re ≈ 2300. The velocity profile, friction factor, and pressure drop change dramatically at the transition.

Velocity Profile & Moody-like Diagram

Flow Parameters

Re = ρUD/μ
f_lam = 64/Re
f_turb ≈ 0.316 Re^(-1/4)
(Blasius, 1913)

Flow Quantities

Re1000
Friction factor f---
U_max / U_avg---
ΔP / L (rel)---
Boundary layer δ---
Profile shapes:
Laminar: u(r) = 2U(1−r²/R²) (parabolic)
Turbulent: u(r) ≈ U(1−r/R)^(1/n)
n ≈ 7 (1/7-power law)
Transition: Re 2300–4000 (hysteretic)