We present a search for outflows towards 51 submillimetre cores in Perseus. With consistently derived outflow properties from a large homogeneous dataset within one molecular cloud we can investigate further the mass dependence and time evolution of protostellar mass loss. Of the 51 cores, 37 show broad linewings indicative of molecular outflows. In 13 cases, the linewings could be due to confusion with neighbouring flows but 9 of those sources also have near-infrared detections confirming their protostellar nature. The total fraction of protostars in our sample is 65%. All but four outflow detections are confirmed as protostellar by Spitzer IR detections and only one Spitzer source has no outflow, showing that outflow maps at this sensitivity are equally good at identifying protostars as Spitzer. Outflow momentum flux correlates both with source luminosity and with core mass but there is considerable scatter even within this one cloud despite the homogeneous dataset. We fail to confirm the result of Bontemps et al. (1996) that Class I sources show lower momentum fluxes on average than Class 0 sources, with a KS test showing a significant probability that the momentum fluxes for both Class 0s and Class Is are drawn from the same distribution. We find that outflow power may not show a simple decline between the Class 0 to Class I stages. Our sample includes low momentum flux, low-luminosity Class 0 sources, possibly at a very early evolutionary stage. If the only mass loss from the core were due to outflows, cores would last for 10^5-10^8 years, longer than current estimates of 1.5-4 x 10^5 years for the mean lifetime for the embedded phase. Additional mechanisms for removing mass from protostellar cores may be necessary.
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