Porous beams are used to properly distribute the required flow rate and are often found in many engineering applications, such as heat exchangers, burners, boilers, pipelines, beam dyeing etc. In these applications, the performance of the fluid system is closely associated with unequal distributions of the flow rate in the pipe branches. The flow occurring in the pipe branches is complicated, and there is only limited work has been reported based on the detailed flow characteristics of the pipe branches. In the present study, a simple design process of the pipe branches based on the mass and momentum equations has been used for analytical predictions. A computational fluid dynamic method has been applied to disclose the detailed flow field in the pipe branches and to validate the theoretical predictions. Further, the studies are extended to the application of beam dyeing process. The factor affecting the levelness in dyeing is predicted using many simulations.