Conservative formulation of unsteady pipe-flow model for water in its liquid form

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We consider flows in a pipe system. The problem relating to the pipe system usually occurs in real life as well as in the laboratory, such as in the distillation process. This unsteady problem can be modeled into a hyperbolic system of partial differential equations. Our goal is to propose the use of a conservative finite-volume numerical method for solving the unsteady pipe-flow model. We obtain that the method is able to solve the pipe-flow problem successfully.