In laminar flow, friction head loss is proportional to which?

In laminar flow, friction head loss is proportional to which?

• A. Velocity squared
• B. Velocity
• C. Both
• D. Neither

Answer: (B)

In laminar flow the viscous forces dominate, and the friction head loss follows a linear relationship with velocity. The Darcy–Weisbach form for head loss is h_f = f (L/D) (V^2 / 2g). In laminar flow, the friction factor is f = 64/Re, where Re = ρVD/μ. Substituting gives h_f = (64/Re) (L/D) (V^2 / 2g) = (64 μ / (ρ V D)) (L/D) (V^2 / 2g). The V^2 term is divided by V, leaving h_f ∝ V. So the head loss increases directly with velocity in laminar flow. In contrast, for turbulent flow the head loss is proportional to V^2.

In laminar flow the viscous forces dominate, and the friction head loss follows a linear relationship with velocity. The Darcy–Weisbach form for head loss is h_f = f (L/D) (V^2 / 2g). In laminar flow, the friction factor is f = 64/Re, where Re = ρVD/μ. Substituting gives h_f = (64/Re) (L/D) (V^2 / 2g) = (64 μ / (ρ V D)) (L/D) (V^2 / 2g). The V^2 term is divided by V, leaving h_f ∝ V. So the head loss increases directly with velocity in laminar flow. In contrast, for turbulent flow the head loss is proportional to V^2.