CodeCogs

Evaluates the Reynolds number of given parameters.

Interface

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

#include <codecogs/engineering/fluid_mechanics/fundamentals/reynolds.h>

using namespace Engineering::Fluid_Mechanics::Fundamentals;

inline double Reynolds(double diameter, double velocity, double density, double viscosity)

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:

$\mathrm{R}_e = \frac{D\;v\;\rho}{\mu}$

(1)

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;
}

Output

Re = 2536.1120299922814
Unpredictable flow (critical zone).

Parameters

diameter

characteristic length [m]

velocity

mean velocity of flow [m/s]

density

weight density of fluid (kg/m^3)

viscosity

dynamic viscosity of fluid (Pa s)

Returns

The Reynolds number corresponding to the given parameters.

References

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

Interactive Calculator

diameter

velocity

density

viscosity

Result –