# Reynolds_number¶

plasmapy.formulary.Reynolds_number(rho: Unit("kg / m3"), U: Unit("m / s"), L: Unit("m"), mu: Unit("kg / (m s)")) -> Unit(dimensionless)

The Reynolds Number is a dimensionless quantity that is used to predict flow patterns in fluids. The Reynolds Number is defined as the ratio of inertial forces to viscous forces. A low Reynolds Number describes smooth, laminar flow while a high Reynolds Number describes rough, turbulent flow.

$Re = \frac{\rho U L }{\mu}$

Aliases: Re_

Parameters: rho (Quantity) – The density of the plasma. U (Quantity) – The flow velocity of the plasma. L (Quantity) – The characteristic length scale. mu (Quantity) – The dynamic viscosity of the plasma. ~astropy.units.UnitsWarning – If units are not provided, SI units are assumed. TypeError – The U is not a Quantity and cannot be converted into a ~astropy.units.Quantity. UnitConversionError – If the U is not in appropriate units. RelativityError – If the velocity U is greater than the speed of light.

Examples

>>> import astropy.units as u
>>> rho = 1000 * u.kg / u.m ** 3
>>> U = 10 * u.m / u.s
>>> L = 1 * u.m
>>> mu = 8.9e-4 * u.kg / (u.m * u.s)
>>> Reynolds_number(rho, U, L, mu)
<Quantity 11235955.05617978>
>>> rho = 1490 * u.kg / u.m ** 3
>>> U = 0.1 * u.m / u.s
>>> L = 0.05 * u.m
>>> mu = 10 * u.kg / (u.m * u.s)
>>> Reynolds_number(rho, U, L, mu)
<Quantity 0.745>

Returns: Re – Dimensionless quantity. Quantity