What is the friction factor for laminar flow in a circular pipe and the Reynolds number criterion?

• A. f = 0.316 / Re^0.25; Re = ρ v D / μ.
• B. f = 1 / Re; Re = ρ v D / μ.
• C. f = 64 / Re for Re < ~2100; Re = ρ v D / μ.
• D. f = 0.2; Re = ρ v D^2 / μ.

Answer: (C)

In laminar flow through a circular pipe, the friction factor in the Darcy–Weisbach relation is simple: it equals 64 divided by the Reynolds number. The Reynolds number uses the average velocity, pipe diameter, fluid density, and dynamic viscosity: Re = ρ v D / μ. The laminar regime is typically defined as Re less than about 2100, within which the relation f = 64 / Re holds. This comes from solving the flow for a fully developed, steady, laminar profile (Poiseuille-like flow) and linking the pressure drop to the viscous stresses.

So the best choice states f = 64 / Re for Re < ~2100, with Re defined as Re = ρ v D / μ. This contrasts with other formulas that apply to turbulent flow or that use an incorrect Re definition (for example, Re = ρ v D / μ is the correct form; using D^2 or a constant f like 0.2 does not describe laminar pipe flow).