Which dimensionless number is used to determine whether pipe flow is laminar or turbulent?

Which dimensionless number is used to determine whether pipe flow is laminar or turbulent?

• A. Mach number
• B. Prandtl number
• C. Reynolds number
• D. Nusselt number

Answer: (C)

The main idea is that whether pipe flow is laminar or turbulent is governed by the balance between inertial forces and viscous forces in the fluid. The Reynolds number captures that balance: Re = density × velocity × diameter divided by viscosity (or velocity × diameter divided by kinematic viscosity). When viscous forces dominate (low Re), the flow stays smooth and layered—laminar. When inertial forces dominate (high Re), disturbances are amplified and the flow becomes chaotic—turbulent. In typical fully developed pipe flow, laminar behavior occurs at Re roughly below 2000, turbulent behavior above about 4000, with a transition region in between that depends on surface roughness and flow disturbances. Other dimensionless numbers don’t indicate the flow regime. Mach number concerns compressibility and speed relative to sound; Prandtl number relates momentum and thermal diffusivity for heat transfer, not the onset of turbulence; Nusselt number is a heat-transfer metric. So Reynolds number is the appropriate measure to classify laminar versus turbulent pipe flow.

The main idea is that whether pipe flow is laminar or turbulent is governed by the balance between inertial forces and viscous forces in the fluid. The Reynolds number captures that balance: Re = density × velocity × diameter divided by viscosity (or velocity × diameter divided by kinematic viscosity). When viscous forces dominate (low Re), the flow stays smooth and layered—laminar. When inertial forces dominate (high Re), disturbances are amplified and the flow becomes chaotic—turbulent. In typical fully developed pipe flow, laminar behavior occurs at Re roughly below 2000, turbulent behavior above about 4000, with a transition region in between that depends on surface roughness and flow disturbances.

Other dimensionless numbers don’t indicate the flow regime. Mach number concerns compressibility and speed relative to sound; Prandtl number relates momentum and thermal diffusivity for heat transfer, not the onset of turbulence; Nusselt number is a heat-transfer metric. So Reynolds number is the appropriate measure to classify laminar versus turbulent pipe flow.