Reynolds_number

plasmapy.formulary.dimensionless.Reynolds_number(

rho: Annotated[Quantity, Unit('kg / m3')],

U: Annotated[Quantity, Unit('m / s')],

L: Annotated[Quantity, Unit('m')],

mu: Annotated[Quantity, Unit('kg / (m s)')],

) → Annotated[Quantity, Unit(dimensionless)]

Compute the Reynolds number.

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.

\[Re = \frac{ρ U L}{μ}\]

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.

Returns:

Re – Dimensionless quantity.

Return type:

Quantity

Raises:

• TypeError – If U is not a Quantity and cannot be converted into a Quantity.

• UnitConversionError – If U is not in appropriate units.

• RelativityError – If U is greater than the speed of light.

Warns:

UnitsWarning – If units are not provided, SI units are assumed.

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>