mathematical modeling of the flow in a pipeline with a leak

pipeline leaks can lead to excessive economical loss as well as posing environmental hazards. mathematical modeling of the flow in a pipeline with a leak can be used to evaluate the loss caused by a leak and provide a guide for pipeline operation as well as an aid for leak detection. the mathematical expressions describing the flow in a pipeline with a leak have been formulated. a new approach based on the analogy between pipeline and electric circuit has been proposed to solve these equations. in this approach, an equivalent circuit with a certain structure has been used to simulate the leaking pipeline and the flow characteristics of the pipeline end have been treated with approximation. the mathematical model of the pipeline with a leak has been developed with the solution of the equations. the model was verified by using an experimental gas pipeline and a real oil pipeline. the simulated results agreed well with the experimental recordings confirmed the accuracy of the models and the validity and efficiency of the proposed approach.