Which factors influence the Darcy-Weisbach friction factor?

Which factors influence the Darcy-Weisbach friction factor?

• A. Only viscosity and temperature.
• B. Only velocity.
• C. Density and cross-sectional area.
• D. Reynolds number and surface roughness.

Answer: (D)

The factor in the Darcy-Weisbach equation that represents friction losses responds to how the flow behaves in the pipe and how rough the pipe surface is. In laminar flow, the friction factor is inversely proportional to the Reynolds number (f = 64/Re), so Re fully controls f in that regime. In turbulent flow, the friction factor depends on both the Reynolds number and the pipe’s roughness, and is often described by charts where f varies with Re and the relative roughness ε/D. In smooth pipes, f decreases with increasing Re, but once roughness dominates (the fully rough regime), f becomes largely set by the roughness itself and changes little with Re. Because Re captures the combined effects of viscosity (through μ), density (through ρ), velocity, and diameter, and surface roughness captures the pipe’s roughness, the two direct factors determining the Darcy-Weisbach friction factor are the Reynolds number and the surface roughness. The other choices list quantities that influence Re or are less directly tied to friction losses on their own, so they don’t define f as precisely.

The factor in the Darcy-Weisbach equation that represents friction losses responds to how the flow behaves in the pipe and how rough the pipe surface is. In laminar flow, the friction factor is inversely proportional to the Reynolds number (f = 64/Re), so Re fully controls f in that regime. In turbulent flow, the friction factor depends on both the Reynolds number and the pipe’s roughness, and is often described by charts where f varies with Re and the relative roughness ε/D. In smooth pipes, f decreases with increasing Re, but once roughness dominates (the fully rough regime), f becomes largely set by the roughness itself and changes little with Re.

Because Re captures the combined effects of viscosity (through μ), density (through ρ), velocity, and diameter, and surface roughness captures the pipe’s roughness, the two direct factors determining the Darcy-Weisbach friction factor are the Reynolds number and the surface roughness. The other choices list quantities that influence Re or are less directly tied to friction losses on their own, so they don’t define f as precisely.