The Fanning friction factor in pipe flow is a function of Reynolds number and relative roughness. Which option expresses this correctly?

The Fanning friction factor in pipe flow is a function of Reynolds number and relative roughness. Which option expresses this correctly?

• A. Mach number and Reynolds number
• B. Schmidt number and Peclet number
• C. Reynolds number and relative roughness
• D. Prandtl number and Nusselt number

Answer: (C)

The main idea is that the Fanning friction factor in pipe flow is governed by how strongly inertial effects compare to viscous effects and by how rough the pipe wall is relative to its diameter. Reynolds number captures the inertial versus viscous balance and determines the flow regime (laminar or turbulent). Relative roughness, epsilon over D, characterizes how pipe roughness influences momentum transfer near the wall, which becomes important in turbulent flow and can even dominate the friction factor in the fully rough regime. Other pairings mix in concepts from heat or mass transfer or compressibility, which aren’t what set the wall shear resistance in typical pipe flow.

The main idea is that the Fanning friction factor in pipe flow is governed by how strongly inertial effects compare to viscous effects and by how rough the pipe wall is relative to its diameter. Reynolds number captures the inertial versus viscous balance and determines the flow regime (laminar or turbulent). Relative roughness, epsilon over D, characterizes how pipe roughness influences momentum transfer near the wall, which becomes important in turbulent flow and can even dominate the friction factor in the fully rough regime. Other pairings mix in concepts from heat or mass transfer or compressibility, which aren’t what set the wall shear resistance in typical pipe flow.