In the BHR71 region, two low-mass protostars drive two distinguishable outflows. They constitute an ideal laboratory to investigate the effects of shock chemistry and the mechanisms that led to their formation. We aim to define the morphology of the warm gas component of the BHR 71 outflow and at modelling its shocked component. We present the first far infrared Herschel images of the BHR71 outflow in the CO(14-13), H$_2$O (2$_{21}$-1$_{10}$), H$_2$O (2$_{12}$-1$_{01}$) and [OI] 145 $mu$m, lines, revealing the presence of several knots of warm, shocked gas associated with fast outflowing gas. In two of these knots we performed a detailed study of the physical conditions by comparing a large set of transitions from several molecules to a grid of shock models. Herschel lines ratios in the outflow knots are quite similar, showing that the excitation conditions of the fast moving gas do not change significantly within the first $sim$ 0.068 pc of the outflow, apart at the extremity of the southern blue-shifted lobe that is expanding outside the molecular cloud. Rotational diagram, spectral line profile and LVG analysis of the CO lines in knot A show the presence of two gas components: one extended, cold ($Tsim$80 K) and dense ($n$(H$_2$) = 3$times$10$^5$-4$times$10$^6$ cm$^{-3}$) and another compact (18 arcsec), warm ($T$ = 1700-2200 K) with slightly lower density ($n$(H$_2$) = (2-6)$times$10$^4$ cm$^{-3}$). In the two brightest knots (where we performed shock modelling) we found that H$_2$ and CO are well fitted with non-stationary (young) shocks. These models, however, significantly underestimate the observed fluxes of [OI] and OH lines, but are not too far off those of H$_2$O, calling for an additional, possibly dissociative, J-type shock component. Our modelling indirectly suggests that an additional shock component exists, possibly a remnant of the primary jet
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