# Water Flow in Tubes - Reynolds Number

## Reynolds Number in pipes transporting clean cold water

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Turbulent or laminar flow is determined by the dimensionless **Reynolds Number.**

The Reynolds number is important in analyzing any type of flow when there is substantial velocity gradient (i.e., shear.) It indicates the relative significance of the viscous effect compared to the inertia effect. The Reynolds number is proportional to inertial force divided by viscous force.

- Reynold's Number A definition of the Reynold's Number .

The flow is

**laminar**when*Re < 2300***transient**when*2300 < Re < 4000***turbulent**when*4000 < Re*

The table below shows Reynolds Number for one liter of water at aprox. 20^{o}C (68^{o}F) flowing through pipes of different dimensions:

Pipe Size | ||||||||||

(inches) | 1 | 1 1/2 | 2 | 3 | 4 | 6 | 8 | 10 | 12 | 18 |

(mm) | 25 | 40 | 50 | 75 | 100 | 150 | 200 | 250 | 300 | 450 |

Reynolds number with one (1) liter/min | 835 | 550 | 420 | 280 | 210 | 140 | 105 | 85 | 70 | 46 |

Reynolds number with one (1) gal/min | 3180 | 2090 | 1600 | 1060 | 780 | 570 | 400 | 320 | 265 | 175 |

Note that viscosity of water varies with temperature.

- the kinematic visosity of water at
*20*- used to calculate the table above - is^{o}C*1.004·10*^{-6}m^{2}/s - at
*0*the kinematic viscosity is^{o}C*1.787·10*- the Reynolds values in the table above must be multiplicated with^{-6}m^{2}/s*1.004 / 1.787 = 0.56* - at
*100*the kinematic viscosity is^{o}C*0.29·10*- the values in the table above must be multiplicated with^{-6}m^{2}/s*1.004 / 0.29 = 3.46*

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