A printer comprising: an inkjet printhead having a plurality of ink inlets, a plurality of ink outlets and an array of nozzles; a plurality of ink chambers, each ink chamber having an outlet port connected to a corresponding ink inlet via a respective upstream ink conduit; a single air pump having a pump outlet communicating with a headspace in each ink chamber, the pump being configured to positively pressurize each headspace during a printhead priming operation; and a plurality of downstream ink conduits, each downstream ink conduit being connected to a corresponding ink outlet, and each downstream ink conduit communicating with a pump inlet of the pump.