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This paper presents a computer model for simulating dynamic responses inside an injector of an automotive fuel rail system. The injector contains a filter at the top, a coil spring in the middle, and a needle and orifices at the bottom. The equations of motion for unsteady one-dimensional flow are derived for the fluid flowing through the injector. The needle motion is described by a second order ordinary differential equation. The forces exerted on the needle include the magnetic force that controls the opening and closing of the injector and the coil spring force. To account for the loss of kinetic energy, we define two loss factors Ka and Kb. The former describes the loss of kinetic energy as fluid enters the injector through the filter at the top, and the latter depicts that as fluid is ejected into a large chamber through the passage between the needle and the needle seat and across four orifices at the bottom of the injector.