The Reynolds number of a fluid is a dimensionless constant which allows you to determine whether the flow of a fluid is laminar or turbulent. It represents the ratio of inertial forces to viscous forces in the fluid.

$latex R_e = \frac{inertial forces}{viscous forces}&s=2$

The equation is:

$latex R_e = \frac{D_ev}{\upsilon}&s=2$

*Where:*

* D _{e} = Hydraulic Diameter (ft or m)*

*v = velocity of the fluid (ft/s or m/s)*

*υ = kinematic viscosity of the fluid (ft*

^{2}/s or m^{2}/s)The Reynolds number allows one to determine whether the flow is laminar, turbulent, or within the transition zone between the two.

- Laminar: Less than 2100
- Transition: 2100 to 4000
- Turbulent: Greater than 4000

Laminar flow is flow in a straight line, i.e. If all of the particles are moving parallel, it is perfectly laminar.

## If the absolute viscosity is known

If you know the absolute, instead of the kinematic, viscosity of the fluid, you can revise the Reynolds equation to accomodate:

$latex R_e = \frac{D_ev\rho}{\upsilon \mu}&s=2$

This is a simple conversion from the kinematic viscosity equation:

$latex \upsilon = \frac{\mu}{\rho}&s=2$

## If the mass flow rate is known

Sometimes you might know the mass flow rate per unit area, *G = ρv*. In this case, the Reynolds number equation can also be modified to accomodate:

$latex R_e = \frac{D_eG}{\mu}&s=2$

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