What is Reynolds number and why is it significant in fluid mechanics?

Reynolds number (Re) is a dimensionless quantity that represents the ratio of inertial forces to viscous forces in a fluid flow. It is calculated as Re = ρVD/μ or Re = VD/ν, where ρ is density, V is velocity, D is characteristic length, μ is dynamic viscosity, and ν is kinematic viscosity. Reynolds number is significant because it predicts whether flow will be laminar (Re < 2300 for pipe flow) or turbulent (Re > 4000), which affects pressure drop, heat transfer, and mixing characteristics.