The Fanning friction factor is usually a function of which two dimensionless parameters?

The Fanning friction factor is usually a function of which two dimensionless parameters?

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

Answer: (D)

In pipe flow, the friction factor measures how much head loss is caused by shear at the wall, and it changes with the flow regime and the surface texture. For turbulent flow, it isn’t a fixed value but a function of two key dimensionless groups: the Reynolds number, which compares inertial to viscous forces, and the relative roughness, the pipe wall roughness ε/D. As Re increases, the flow becomes more inertial and turbulent, altering the friction factor; as relative roughness grows, rough wall features interact with the boundary layer to increase friction, especially at higher Re. The Fanning friction factor is simply a quarter of the Darcy friction factor, so it inherits this same dependence on Re and ε/D. The other pairs involve heat transfer or mass transfer descriptors (Prandtl, Nusselt; Schmidt, Péclet) or compressibility effects (Mach), which aren’t the primary governing factors for friction in typical pipe flow.

In pipe flow, the friction factor measures how much head loss is caused by shear at the wall, and it changes with the flow regime and the surface texture. For turbulent flow, it isn’t a fixed value but a function of two key dimensionless groups: the Reynolds number, which compares inertial to viscous forces, and the relative roughness, the pipe wall roughness ε/D. As Re increases, the flow becomes more inertial and turbulent, altering the friction factor; as relative roughness grows, rough wall features interact with the boundary layer to increase friction, especially at higher Re. The Fanning friction factor is simply a quarter of the Darcy friction factor, so it inherits this same dependence on Re and ε/D. The other pairs involve heat transfer or mass transfer descriptors (Prandtl, Nusselt; Schmidt, Péclet) or compressibility effects (Mach), which aren’t the primary governing factors for friction in typical pipe flow.