Apparatus and methods of dispensing fluid intravenously to a subject, and of flushing a line of an intravenous fluid administration apparatus, are provided. The apparatus may include a reservoir pump configured to operate in fluid communication with an upstream source of a first fluid and a downstream pressure-operated valve. The apparatus may also include a port connector configured to operate in fluid communication with at least the pressure-operated valve. The reservoir pump may also be configured to, during operation, automatically refill itself with the first fluid from the first upstream source. The downstream pressure-operated valve may be configured to operate in fluid communication with the reservoir pump and a second fluid source upstream of the pressure-operated valve, and to, during operation, dispense the first fluid to tubing downstream of the pressure-operated valve based on a pressure condition within the pressure-operated valve exceeding a threshold pressure.