The Reynolds number (Re) is a dimensionless quantity that predicts flow patterns in different fluid flow situations. It represents the ratio of inertial forces to viscous forces and determines whether flow is laminar, transitional, or turbulent.
| Flow Regime | Reynolds Number | Characteristics | Examples |
|---|---|---|---|
| Laminar | Re < 2300 | Smooth, orderly, predictable | Honey flow, capillary tubes |
| Transitional | 2300 < Re < 4000 | Unstable, intermittent | Water in medium pipes |
| Turbulent | Re > 4000 | Chaotic, mixing, efficient | River flow, high-speed pipes |
Laminar flow is characterized by smooth, parallel fluid layers with no disruption between them. Viscous forces dominate, and flow is highly predictable. Common in low velocities, small diameters, or high-viscosity fluids.
| Application | Re Range | Regime | Significance |
|---|---|---|---|
| Blood Flow | Re ~ 1000-2000 | Laminar | Reduces energy loss |
| Capillary Tubes | Re ~ 100-500 | Laminar | Predictable behavior |
| Oil Pipelines | Re ~ 500-1500 | Laminar | High viscosity flow |
Turbulent flow is characterized by chaotic, irregular fluid motion with mixing and eddy formation. Inertial forces dominate, and flow is highly efficient for heat and mass transfer. Common in high velocities, large diameters, or low-viscosity fluids.
| Application | Re Range | Regime | Significance |
|---|---|---|---|
| Water Supply | Re ~ 10,000-100,000 | Turbulent | High flow rate |
| Aircraft Wings | Re ~ 10⁶ - 10⁷ | Turbulent | Boundary layer control |
| Heat Exchangers | Re ~ 5,000-50,000 | Turbulent | Enhanced heat transfer |