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# Reynolds

Evaluates the Reynolds number of given parameters.
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Contents

C++

## Reynolds

 doubleReynolds( double diameter double velocity double density double viscosity )[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
•  is the characteristic length [m]
•  is the average velocity of the flow [m/s],
•  is the weight density [] and
•  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).

### References

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

### 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.

### Authors

Lucian Bentea (July 2006)
##### Source Code

Source code is available when you agree to a GP Licence or buy a Commercial Licence.

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