Reynold Number Water Flow Pipes

Overview

Engineering reference data for Reynold Number Water Flow Pipes in fluid mechanics.

Key Formulas

Reynolds Number

$Re = \frac{\rho v D}{\mu}$

Ratio of inertial to viscous forces — determines flow regime.

Bernoulli's Equation

$P + \frac{1}{2}\rho v^2 + \rho g h = \text{const}$

Conservation of energy for steady, inviscid, incompressible flow.

Continuity Equation

$A_1 v_1 = A_2 v_2$

Conservation of mass for incompressible flow.

Darcy-Weisbach

$\Delta P = f \frac{L}{D} \frac{\rho v^2}{2}$

Pressure drop due to friction in a pipe.

Variables

Symbol	Description	Unit
$Re$	Reynolds number	—
$\rho$	Fluid density	kg/m³
$v$	Flow velocity	m/s
$D$	Characteristic dimension	m
$\mu$	Dynamic viscosity	Pa·s
$P$	Pressure	Pa
$f$	Darcy friction factor	—

Flow Regime Classification

The Reynolds number determines the flow regime in pipes:

• Laminar flow: $Re < 2300$
• Transient (transition) flow: $2300 < Re < 4000$
• Turbulent flow: $Re > 4000$

Reynolds Number for Water Flow in Pipes

The table below shows Reynolds numbers for one liter of water at approximately 20°C (68°F) flowing through pipes of different dimensions.

Viscosity Correction for Temperature

The kinematic viscosity of water varies with temperature, affecting the Reynolds number. Use the correction factor relative to the 20°C baseline values:

Temperature	Kinematic Viscosity (m²/s)	Correction Factor
0°C	$1.787 \times 10^{-6}$	$\times 0.56$
20°C	$1.004 \times 10^{-6}$	$\times 1.00$ (baseline)
100°C	$0.29 \times 10^{-6}$	$\times 3.46$

To calculate the correction factor for any temperature:

$\text{Correction Factor} = \frac{\nu_{20°C}}{\nu_T} = \frac{1.004 \times 10^{-6}}{\nu_T}$

where $\nu_T$ is the kinematic viscosity at temperature $T$.

Interactive Charts

References

• Original Source