A device for delivering fluid, such as insulin for example, to a patient. The device includes a flow path having an exit port assembly adapted to connect to a transcutaneous patient access tool, and a reservoir connected to the exit port assembly. The device also includes a flow restriction system having an air removal filter communicating with the flow path and allowing air to exit the flow path and preventing fluid from exiting the flow path, and a flow restrictor positioned within the flow path between the air removal filter and the exit port assembly. Among other features and advantages, the flow restriction system of the present invention allows the flow path of the fluid delivery device to be purged of air, or “primed” prior to operation, such that desired volumes of fluid can be accurately delivered by the device.