windpowerlib.density.rho_barometric

windpowerlib.density.rho_barometric(pressure, pressure_height, hub_height, T_hub)[source]

Calculates the density of air at hub height using the barometric height equation.

This fuction is carried out when the parameter rho_model of an instance of the Modelchain class is ‘barometric’.

Parameters:
  • pressure (pandas.Series or array) – Pressure in Pa.
  • pressure_height (float) – Height in m for which the parameter pressure applies.
  • hub_height (float) – Hub height of wind turbine in m.
  • T_hub (pandas.Series or array) – Temperature at hub height in K.
Returns:

Density of air at hub height in kg/m³.
Return type:

pandas.Series

Notes

The following equation is used [1], [2] :

\rho_{hub}=\left(p/100-\left(h_{hub}-h_{p,data}\right) \cdot\frac{1}{8}\right)\cdot \frac{\rho_0 T_0\cdot 100}{p_0 T_{hub}}

with:
T: temperature [K], h: height [m], \rho: density [kg/m³], p: pressure [Pa]

h_{p,data} is the height of the measurement or model data for pressure, p_0 the ambient air pressure, \rho_0 the ambient density of air, T_0 the ambient temperature and T_{hub} the temperature at hub height.

Assumptions:

  • Pressure gradient of -1/8 hPa/m

References

[1]Hau, E.: “Windkraftanlagen - Grundlagen, Technik, Einsatz, Wirtschaftlichkeit”. 4. Auflage, Springer-Verlag, 2008, p. 560
[2]Deutscher Wetterdienst: http://www.dwd.de/DE/service/lexikon/begriffe/D/Druckgradient_pdf.pdf?__blob=publicationFile&v=4