We investigate the fine structure of the sunspot penumbra by means of a model that allows for a flux tube in horizontal pressure balance with the magnetic background atmosphere in which it is embedded. We apply this model to spectropolarimetric observations of two neutral iron lines at 1.56 μm and invert several radial cuts in the penumbra of the same sunspot at two different heliocentric angles. In the inner part of the penumbra we find hot flux tubes that are somewhat inclined to the horizontal. They become gradually more horizontal and cooler with increasing radial distance. This is accompanied by an increase in the velocity of the plasma and a decrease of the gas pressure difference between flux tube and the background component. At large radial distances the flow speed exceeds the critical speed and evidence is found for the formation of a shock front. These results are in good agreement with simulations of the penumbral fine structure and provide strong support for the siphon flow as the physical mechanism driving the Evershed flow.