The paper proposes an extension to the original water flow algorithm used for the text line segmentation in a document image. This extension is called a parametric water flow algorithm. The original algorithm assumes that the hypothetical water flows to the barrier representing objects. After that barrier, the hypothetical water creates different pathways under few specified angles creating labeled wetted and unwetted regions. The direction of the hypothetical water is from left to right side and vice versa. Hence, the final labeled wetted and unwetted image regions are created as their unions. The unwetted regions are used to segment text lines in a document image. The extension of the original water flow algorithm establishes the so-called water flow function, which is responsible for the unwetted region's creation. The proposed linear water flow function is exchanged with its parametric function counterpart. The basic, linear and parametric water flow algorithms are tested and evaluated under different synthetic and handwritten text samples. The experiments show promising results in the area of text line segmentation.