When a tunnel is constructed in a karst area, crystallization of the drainage pipe caused by karst water often threatens the normal operation of the tunnel. This work contributes to this field of research by proposing a functional model based on the diffusion boundary layer (DBL) theory proposed by Dreybrodt in the 1990s. The model is formed by determining the flow rate distribution of the drainage pipe in a laminar flow state and turbulent state, and then by applying Fick’s diffusion law and Skelland’s approximate formula. Then, to further verify the applicability of the functional model, a model test was carried out in the laboratory and the test results are compared to the theoretical results. The results show that the crystallization rate of karst water is mainly affected by the roughness of the pipe wall, followed by the slope of pipes. The slope can affect flow state by controlling the flow rate, which in turn affects the crystallization rate of karst water. When the slope of the drainage pipe is 3, 4, and 5%, the error between the experimental results and the theoretical calculation results is 24.7, 8.07, and 27.9%, respectively, and when the liquid level in the pipe is 7.2, 10.2, and 13.3 mm, the error is 27.9, 9.82, and 2.07%, respectively. Considering that the flow will take away the crystalline deposits on the pipe wall in the experiment, although some results have certain errors, they do not affect the overall regularity.