Reynolds Number Calculator
Reynolds Number Calculator computes the Reynolds number to predict laminar or turbulent flow in fluids.
Formulas Used in Reynolds Number Calculator
The Reynolds number (\\(Re\\)) is a dimensionless quantity that predicts whether fluid flow is laminar, transitional, or turbulent based on the ratio of inertial to viscous forces:
Variables:
- \\(\rho\\): Fluid density (kg/m³), mass per unit volume of the fluid.
- \\(v\\): Fluid velocity (m/s), average velocity of the fluid flow.
- \\(D\\): Characteristic length (m), typically the pipe diameter for internal flow.
- \\(\mu\\): Dynamic viscosity (Pa·s or kg/(m·s)), measure of the fluid’s resistance to shear.
- \\(\nu\\): Kinematic viscosity (\\(\nu = \mu / \rho\\), m²/s), ratio of dynamic viscosity to density.
Flow Regimes (for circular pipes):
- Laminar: \\(Re < 2300\\), smooth, orderly flow with parallel streamlines.
- Transitional: \\(2300 \leq Re \leq 4000\\), mixed behavior with intermittent turbulence.
- Turbulent: \\(Re > 4000\\), chaotic flow with eddies and vortices.
Illustration
The diagram below illustrates laminar flow (smooth, parallel streamlines) and turbulent flow (chaotic, swirling patterns) in a pipe, influenced by the Reynolds number:
Example Calculation
Example: Water (\\(\rho = 1000 \, \text{kg/m}^3\\), \\(\nu = 1.004 \times 10^{-6} \, \text{m}^2/\text{s}\\)) flows at \\(v = 1.7 \, \text{m/s}\\) through a pipe with diameter \\(D = 0.025 \, \text{m}\\). Calculate \\(Re\\):
Since \\(Re > 4000\\), the flow is turbulent.