A system and method of accurately pumping a fluid using tubing of variable inner diameter and material is disclosed. The disclosed pump comprises a pumping mechanism configured to compress and release a portion of a flexible tube to cause fluid to flow along the flexible tube, a gauging apparatus, and a vacuum apparatus. The gauging apparatus is configured to determine the inner diameter of the flexible tube, which value is used in calibrating the pumping rate of the pump. The vacuum apparatus is configured to reduce the ambient pressure in a volume surrounding the portion of the flexible tube, thereby causing the flexible tube to fully expand to its original outside diameter when the flexible tube is released by the pumping mechanism.