# Water Flow in Tubes - Reynolds Number

## Clean cold waterflow in pipes and the Reynolds number

Turbulent or laminar flow is determined by the dimensionless **Reynolds Number **which is important when analyzing fluid flow where there is a substantial velocity gradient (i.e. shear). The Reynolds number indicates the relative significance of the viscous effect compared to the inertia effect and the number is proportional to the inertial force divided by the viscous force.

- Reynold's Number - a definition

The flow is

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

Reynolds Number for one liter of water at approximately *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 1 liter/min | 835 | 550 | 420 | 280 | 210 | 140 | 105 | 85 | 70 | 46 |

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

Note that the water viscosity varies with temperature.

- the kinematic viscosity 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*