Reynolds Number
Reynolds number, abbreviated as Re, a dimensionless number, measures the ratio of inertial forces (forces that remain at rest or in uniform motion) to viscosity forces (the resistance to flow).
Reynolds Number Range
Laminar flow = up to Re = 2300
Transition flow = 2300 < Re < 4000
Turbulent flow = Re > 4000
Reynolds number formulas |
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\(\large{ Re = \frac{ \rho \; v \; l_c }{ \mu } }\) \(\large{ Re = \frac{ v \; l_c }{ \nu } }\) \(\large{ Re = \frac{ U \; l_c }{ \mu } }\) \(\large{ Re = \frac{ \bar {v} \; d \; \rho}{ \mu } }\) \(\large{ Re = \frac{ \bar {v} \; d }{ \nu } }\) \(\large{ Re = \frac{ 4 \; Q }{ \pi \; d \; \bar {v} } }\) |
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| Symbol | English | Metric |
| \(\large{ Re }\) = Reynolds number | \(\large{ dimensionless }\) | |
| \(\large{ \bar {v} }\) = average velocity | \(\large{ \frac{ft}{sec} }\) | \(\large{ \frac{m}{s} }\) |
| \(\large{ l_c }\) = characteristic length or diameter of fluid flow | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ U }\) = characteristic velocity | \(\large{ \frac{ft}{sec} }\) | \(\large{ \frac{m}{s} }\) |
| \(\large{ \rho }\) (Greek symbol rho) = density of fluid | \(\large{ \frac{lbm}{ft^3} }\) | \(\large{ \frac{kg}{m^3} }\) |
| \(\large{ \mu }\) (Greek symbol mu) = dynamic viscosity | \(\large{\frac{lbf-sec}{ft^2}}\) | \(\large{ Pa-s }\) |
| \(\large{ \nu }\) (Greek symbol nu) = kinematic viscosity | \(\large{ \frac{in^2}{sec} }\) | \(\large{ \frac{mm^2}{s} }\) |
| \(\large{ \pi }\) = Pi | \(\large{3.141 592 653 ...}\) | |
| \(\large{ d }\) = pipe inside diameter | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ v }\) = velocity of fluid | \(\large{ \frac{ft}{sec} }\) | \(\large{ \frac{m}{s} }\) |
| \(\large{ Q }\) = volumetric flow rate | \(\large{\frac{ft^3}{sec}}\) | \(\large{\frac{m^3}{s}}\) |
Tags: Flow Equations Viscosity Equations Orifice and Nozzle Equations