Estimate the Reynolds number for a pipe given ρ=1000 kg/m^3, V=2 m/s, D=0.25 m, and μ=1.0×10^-6 Pa·s, and state the flow regime.

• A. Re ≈ 5.0×10^3; Laminar
• B. Re ≈ 5.0×10^5; Turbulent
• C. Re ≈ 5.0×10^6; Turbulent
• D. Re ≈ 5.0×10^4; Transitional

Answer: (B)

Reynolds number tells you whether inertial forces dominate over viscous forces in pipe flow. It’s calculated as Re = ρ V D / μ.

Plugging in the values: ρ = 1000 kg/m^3, V = 2 m/s, D = 0.25 m, μ = 1.0×10^-6 Pa·s gives

Re = (1000)(2)(0.25) / (1.0×10^-6) = 500 / 1.0×10^-6 = 5×10^8.

A Reynolds number this large is far above the typical threshold for transition to turbulence (about 4000). So the flow is turbulent.

Note: the numbers in the answer choices correspond to a different viscosity (about 1×10^-3 Pa·s would give Re ≈ 5×10^5), but with the provided μ the correct conclusion is that the flow is turbulent.