For the various tuning as well as ignition campaigns, targets on the National Ignition Facility (NIF) need to be filled with gases, typically with the different isotopes of H2 and He. Fill tubes that supply the two small chambers in the target, the capsule and the hohlraum, are microcapillaries that are only tens of microns in diameter and present significant impedance to flow. Knowledge of the exact pressures and gas compositions in the capsule and the hohlraum is critical for fielding targets on NIF. This requires modeling of the gas flow through the capillary tubes, at both room temperature and cryogenic temperatures. We present results from a comprehensive model and its experimental verification for a range of conditions such as temperature and pressure.