An apparatus for supplying an enteral or parenteral fluid to a patient is a cooperative assembly of a rotary peristaltic pump and a fluid delivery set. The peristaltic pump has (a) a housing and (b) a peristaltic rotor projecting from the housing on a rotatable drive shaft. The housing has first and second receptacles for retaining and supporting the fluid delivery set. The fluid delivery set has (a) a drip chamber, or sight chamber, (b) a plurality of lengths or segments of flexible tubing, and (c) fluid connection elements therefor. The fluid delivery set defines a fluid pathway from a supply container of the enteral or parenteral fluid to a connector element adapted to be connected to a device for introducing the fluid into the patient. Preferably the fluid delivery set has a tension responsive pinch valve to prevent bolus feeding in the event that the fluid delivery set becomes displaced from the pump housing.