Dimensionless numbers

linerate.equations.dimensionless.compute_reynolds_number(wind_speed, conductor_diameter, kinematic_viscosity_of_air)

Compute the Reynolds number using the conductor diameter as characteristic length scale.

Defined in the text on page 25 of [1] and equation (2c) on page 10 in [2].

The Reynolds number is a dimensionless quantity that can be used to assess if a stream is likely to be turbulent or not. It is given by

\[\text{Re} = \frac{v L}{\nu},\]

where \(v\) is the flow velocity, \(L\) is a characteristic length (in our case, the conductor diameter) and \(\nu\) is the kinematic viscosity.

Parameters:

• wind_speed (Annotated[float | float64 | ndarray[Any, dtype[float64]], 'm/s']) – \(v~\left[\text{m}~\text{s}^{-1}\right]\). The wind speed.

• conductor_diameter (Annotated[float | float64 | ndarray[Any, dtype[float64]], 'm']) – \(D~\left[\text{m}\right]\). Outer diameter of the conductor.

• kinematic_viscosity_of_air (Annotated[float | float64 | ndarray[Any, dtype[float64]], 'm²/s']) – \(\nu_f~\left[\text{m}^2~\text{s}^{-1}\right]\). The kinematic viscosity of air.

Returns:

\(\text{Re}\). The Reynolds number.

Return type:

Union[float, float64, ndarray[Any, dtype[float64]]]

linerate.equations.dimensionless.compute_grashof_number(conductor_diameter, surface_temperature, air_temperature, kinematic_viscosity_of_air, coefficient_of_gravity=9.807)

Compute the Grashof number.

Defined in the nomenclature on page 7 of [1] and on page 5 of [4].

The Grashof number is a dimensionless quantity that can be used to assess the degree of free and forced convective heat transfer.

Parameters:

• conductor_diameter (Annotated[float | float64 | ndarray[Any, dtype[float64]], 'm']) – \(D~\left[\text{m}\right]\). Outer diameter of the conductor.

• surface_temperature (Annotated[float | float64 | ndarray[Any, dtype[float64]], '°C']) – \(T_s~\left[^\circ\text{C}\right]\). The conductor surface temperature.

• air_temperature (Annotated[float | float64 | ndarray[Any, dtype[float64]], '°C']) – \(T_a~\left[^\circ\text{C}\right]\). The ambient air temperature.

• kinematic_viscosity_of_air (Annotated[float | float64 | ndarray[Any, dtype[float64]], 'm²/s']) – \(\nu_f~\left[\text{m}^2~\text{s}^{-1}\right]\). The kinematic viscosity of air.

• coefficient_of_gravity (Annotated[float | float64 | ndarray[Any, dtype[float64]], 'm/s²']) – \(g~\left[\text{m}~\text{s}^{-2}\right]\). The graviatational constant, optional (default=9.807).

Returns:

\(\text{Gr}\). The Grashof number.

Return type:

Union[float, float64, ndarray[Any, dtype[float64]]]

linerate.equations.dimensionless.compute_prandtl_number(thermal_conductivity_of_air, dynamic_viscosity_of_air, specific_heat_capacity_of_air)

Compute the Prandtl number.

Defined in the nomenclature on page 8 of [1].

The Prandtl number measures the ratio between viscosity and thermal diffusivity for a fluid.

Parameters:

• thermal_conductivity_of_air (Annotated[float | float64 | ndarray[Any, dtype[float64]], 'W/(m K)']) – \(\lambda_f~\left[\text{W}~\text{m}^{-1}~\text{K}^{-1}\right]\). The thermal conductivity of air at the given temperature.

• dynamic_viscosity_of_air (Annotated[float | float64 | ndarray[Any, dtype[float64]], 'kg/(m s)']) – \(\mu_f~\left[\text{kg}~\text{m}^{-1}~\text{s}^{-1}\right]\). The dynamic viscosity of air.

• specific_heat_capacity_of_air (Annotated[float | float64 | ndarray[Any, dtype[float64]], 'J/(kg K)']) – \(\text{J}~\left[\text{kg}^{-1}~\text{K}^{-1}\right]\). The specific heat capacity of air.

Returns:

\(\text{Pr}\). The Prandtl number.

Return type:

Union[float, float64, ndarray[Any, dtype[float64]]]

linerate.equations.dimensionless.compute_conductor_roughness(conductor_diameter, outer_layer_strand_diameter)

Compute the surface roughness of the conductor.

Defined in the text on page 25 of [1] and on page 6 of [4].

Parameters:

• conductor_diameter (Annotated[float | float64 | ndarray[Any, dtype[float64]], 'm']) – \(D~\left[\text{m}\right]\). Outer diameter of the conductor.

• outer_layer_strand_diameter (Annotated[float | float64 | ndarray[Any, dtype[float64]], 'm']) – \(d~\left[\text{m}\right]\). The diameter of the strands in the outer layer of the conductor.

Returns:

\(\text{Rs}\). The roughness number

Return type:

Union[float, float64, ndarray[Any, dtype[float64]]]