The paper presents a simple transfer function model of a diffusive flow system represented by a narrow pipe with longitudinal mixing. This new model is composed of three coupled transfer functions describing the dynamics of flow, delay and diffusion, respectively. Unlike previous models, the contributions of delay and diffusion are kept separate and both depend on the hydraulic submodel. As a result, good delay approximation is achieved even with a very low-order model. The model development is justified by experimental evidence through a laboratory setup, used to obtain experimental data and perform model testing. To determine the ＇best＇ model order, the model structure is assessed from the parameter redundancy point of view and parameter calibration results are presented before model calibration.