What is the Reynolds number formula for flow in a pipe?

• A. Re = μ /(ρ v D)
• B. Re = ρ v D / μ
• C. Re = p/γ
• D. Re = ρ v^2 / μ

Answer: (B)

In pipe flow, Reynolds number shows how dominant inertial forces are compared with viscous forces, helping indicate whether the flow will be laminar or turbulent. Use the pipe diameter as the characteristic length and the average flow velocity as the characteristic speed. The standard form is Re = ρ v D / μ, with ρ the fluid density, v the average velocity, D the pipe diameter, and μ the dynamic viscosity. It can also be written as Re = v D / ν, where ν = μ/ρ is the kinematic viscosity. The other expressions aren't dimensionless or don't represent this balance of forces (for example, p/γ is a pressure-related ratio, and ρ v^2/μ mixes momentum flux with viscosity).