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Evaluates the Reynolds number of given parameters.
Controller: CodeCogs




doubleviscosity )[inline]
Dynamic Viscosity
  • Water (@20C) = 0.001002 Pa s
  • Motor oil = 0.250 Pa s
  • Honey = 2-10 Pa a
  • Blood = 0.003-0.004 Pa s
  • Air = 0.00001827 Pa s

Reynolds number, named after Osborne Reynolds who proposed it in 1883, is the ratio of inertial forces to viscous forces in a fluid. It can be used to determine whether a flow within a pipe or around an object will be laminar, turbulent or within the so-called critical zone. The formula for this dimensionless measure is: where
  • D is the characteristic length [m]
  • v is the average velocity of the flow [m/s],
  • \rho is the weight density [kg/m^3] and
  • \mu is the dynamic (or absolute) viscosity of the fluid [Pa s].

Where the viscosity is high, i.e. syrup, the flow is normally laminar.

Pipe Flow

For fluid going through pipe the Reynolds values are
  • Re < 2300 for laminar flow
  • Re = 2300 to 4000 for flow is unpredictable (often called the "critical zone")
  • Re > 4000 for turbulent flow

Object In Fluid

  • Re < 0.1 for laminar flow
  • Re > 0.1 for turbulent flow

Example 1

#include <stdio.h>
#include <codecogs/engineering/fluids/reynolds.h>
int main()
  double Re = Engineering::Fluids::Reynolds(5, 10, 23, 0.45345);
  printf("Re = %.13lf\n", Re);
  if (Re < 2000) printf("Laminar flow.\n");
  else if (Re > 4000) printf("Turbulent flow.\n");
  else printf("Unpredictable flow (critical zone).\n");
  return 0;


Re = 2536.1120299922814
Unpredictable flow (critical zone).


The Engineering Division, Crane Co., "Flow of fluids through valves, fittings, and pipe", Chicago, 1957


diametercharacteristic length [m]
velocitymean velocity of flow [m/s]
densityweight density of fluid (kg/m^3)
viscositydynamic viscosity of fluid (Pa s)


The Reynolds number corresponding to the given parameters.


Lucian Bentea (July 2006)
Source Code

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