The hydrodynamical heart of an ink-jet printer is the print head, in which a large number of miniature valveless pumps are integrated. Each pump, when actuated electrically, delivers exactly one droplet of a specified flight direction, speed and size (drop-on-demand: DOD). In studies of the behaviour of miniature pumps only one pump is usually considered. The issue discussed in this paper is: do size and velocity of a droplet depend on the design of the print head? To answer this question we modelled the print head as a number of identical Helmholtz resonators, all connected to a main supply channel. The main supply channel was connected to the ink reservoir through a hose pillar and was also modelled as a Helmholtz resonator. The behaviour of such a manifold of Helmholtz resonators was analysed in both the frequency and the time domain. The paper concerns the hydro-acoustics and hydrodynamics of piezoelectrically activated ink-jet print heads.