The rapid prototyping industry is growing dramatically because of its high potential to reduce product design and prototyping cycles. One of the recent technologies in this field is 3D printing using conventional ink jet technology. In order to maximize the capability of this process, it is required to understand the operating mechanism and drop formation process. The current work focuses on the mechanism of a piezoelectric cylindrical actuator and the hydrodynamic characteristics inside a print head in order to achieve more realistic boundary conditions for the numerical simulation of the drop formation process. Linearised Navier-Stokes equations for Newtonian fluid flow are solved analytically for the pump section with a constant radius and for the nozzle section with a tapering angle. Results from the developed solutions are input to Flow 3D and it is observed that analytical pressure histories show better agreement with numerical results than axial velocity histories. The presented analytic model can be used for fully further drop formation simulation as an upstream pressure boundary within an acceptable tolerance.