This paper aims to contribute to the ongoing research on tree-shaped flow structures. First, it briefly traces the progress made on constructal tree-shaped flow networks. Then, the paper focuses on tree pattern of tubes connecting the centre and the rim of a circular area. It shows that the physical description underlying the classical Darcy-Forchheimer-Ergun equation may provide a legitimate correlation for this kind of flow structure. The porosity, hydraulic permeability and the inertial factor of the flow structure are also presented.