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When transient flow occurs in the liquid pipeline, it will result in higher water hammer pressure or negative
pressure in pipeline, thus damaging pipeline. Through the establishment of liquid pipeline transient flow mathematical
model which is solved by characteristic linear method, and by getting difference quotient equation of characteristic
equation by explicit characteristic difference method, we can obtain analytical solutions of each transient flow parameters.
After performing numerical simulation for pump start-up working condition, the result shows that the proposed model
approach in this paper is feasible.