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

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

• A. Re = μ v D / ρ
• B. Re = ρ v / μ
• C. Re = ρ v D / μ
• D. Re = P v / μ

Answer: (C)

Reynolds number is a dimensionless quantity that compares the inertial forces to the viscous forces in a flowing fluid. For pipe or duct flow, it is defined as Re = ρ v D / μ, where ρ is the fluid density, v is the average flow velocity, D is a characteristic length (the pipe diameter), and μ is the dynamic viscosity. This ratio tells you how the flow will behave. When inertial effects dominate (high Re), the flow tends to become turbulent, with chaotic eddies and mixing. When viscous effects dominate (low Re), the flow stays smooth and orderly, or laminar. In practical terms, there are transition ranges (for example, in pipes, flow is typically laminar at Re below about 2000 and becomes turbulent above around 4000, with a transition region in between). The form Re = ρ v D / μ is the standard expression for incorporating density, velocity, and a characteristic length against viscosity to predict flow regime. Other forms that omit a key variable or replace it with something like pressure do not capture the balance between inertia and viscosity that drives the transition between laminar and turbulent flow.

Reynolds number is a dimensionless quantity that compares the inertial forces to the viscous forces in a flowing fluid. For pipe or duct flow, it is defined as Re = ρ v D / μ, where ρ is the fluid density, v is the average flow velocity, D is a characteristic length (the pipe diameter), and μ is the dynamic viscosity.

This ratio tells you how the flow will behave. When inertial effects dominate (high Re), the flow tends to become turbulent, with chaotic eddies and mixing. When viscous effects dominate (low Re), the flow stays smooth and orderly, or laminar. In practical terms, there are transition ranges (for example, in pipes, flow is typically laminar at Re below about 2000 and becomes turbulent above around 4000, with a transition region in between).

The form Re = ρ v D / μ is the standard expression for incorporating density, velocity, and a characteristic length against viscosity to predict flow regime. Other forms that omit a key variable or replace it with something like pressure do not capture the balance between inertia and viscosity that drives the transition between laminar and turbulent flow.