  The KATRIN experiment aims to measure the effective mass of the electron
antineutrino from the analysis of electron spectra stemming from the beta-decay
of molecular tritium with a sensitivity of 200 meV. Therefore, a daily
throughput of about 40 g of gaseous tritium is circulated in a windowless
source section. An accurate description of the gas flow through this section is
of fundamental importance for the neutrino mass measurement as it significantly
influences the generation and transport of beta-decay electrons through the
experimental setup. In this paper we present a comprehensive model consisting
of calculations of rarefied gas flow through the different components of the
source section ranging from viscous to free molecular flow. By connecting these
simulations with a number of experimentally determined operational parameters
the gas model can be refreshed regularly according to the measured operating
conditions. In this work, measurement and modelling uncertainties are
quantified with regard to their implications for the neutrino mass measurement.
We find that the systematic uncertainties related to the description of gas
flow are represented by $\Delta m_{\nu}^2=(-3.06\pm 0.24)\cdot10^{-3}$ eV$^2$,
and that the gas model is ready to be used in the analysis of upcoming KATRIN
data.
