Define Reynolds number and explain its role in determining flow regime in hydraulics.

Define Reynolds number and explain its role in determining flow regime in hydraulics.

• A. Re = μ v D / ρ; indicates boundary layer thickness.
• B. Re = ρ v / μ; indicates scale of turbulence.
• C. Re = ρ v D / μ; indicates laminar vs turbulent and informs friction factors.
• D. Re = v / (D μ); indicates pressure drop.

Answer: (C)

Reynolds number is a dimensionless quantity that compares inertial forces to viscous forces in a fluid flow. In a pipe with a characteristic diameter D and velocity v, using density ρ and dynamic viscosity μ, it’s Re = ρ v D / μ. This value tells you whether the flow will be smooth and orderly (laminar) or chaotic and mixed (turbulent). It also guides which friction-factor correlations to use when calculating head losses: in laminar pipe flow the friction factor is f = 64 / Re, so head loss scales predictably with velocity; in turbulent flow the friction factor depends on Re and the pipe’s roughness (via charts or empirical correlations like the Moody chart). Since Re = vD/ν (where ν = μ/ρ), the same idea holds with kinematic viscosity, just another way to express the balance between inertia and viscosity.

Reynolds number is a dimensionless quantity that compares inertial forces to viscous forces in a fluid flow. In a pipe with a characteristic diameter D and velocity v, using density ρ and dynamic viscosity μ, it’s Re = ρ v D / μ. This value tells you whether the flow will be smooth and orderly (laminar) or chaotic and mixed (turbulent). It also guides which friction-factor correlations to use when calculating head losses: in laminar pipe flow the friction factor is f = 64 / Re, so head loss scales predictably with velocity; in turbulent flow the friction factor depends on Re and the pipe’s roughness (via charts or empirical correlations like the Moody chart). Since Re = vD/ν (where ν = μ/ρ), the same idea holds with kinematic viscosity, just another way to express the balance between inertia and viscosity.