This paper presents a new approach for the computation of flow velocity in pipes arranged in parallel based on an analytic development. The estimation of the flow parameters using existing methods requires trial and error procedures. The assessment of flow velocity is of great importance in flow measurement methods and in the design of drainage networks, among others. In drainage network design, the flow is mostly of free surface type. A new method is developed to eliminate the need for trial methods, where the computation of the flow velocity becomes easy, simple, and direct with zero deviation compared to Manning equation results and other approaches such as that have been considered as the best existing solutions. This research work shows that these approaches lack accuracy and do not cover the entire range of flow surface angles: 0° ≤ θ ≤ 360°.