Transient phenomena, especially water hammer, are among the fundamental challenges in fluid transmission systems, causing damage to water distribution networks due to severe pressure fluctuations. In this research, transient flow behavior was modeled by simultaneously considering viscoelasticity and unsteady friction. Given the effectiveness of the Kelvin–Voigt model for plastic pipes, this model was implemented in MATLAB and calibrated with experimental data. The innovation is an optimization framework based on the genetic algorithm for simultaneous calibration of viscoelastic parameters, including coefficients θ and α, creep compliance (J), retardation time (τ), wave speed (a), and the number of spring–dashpot elements. Results showed that the model achieves low RMSE values (0.2320 and 0.4315 for flow rates of 1.06 and 2 L/s), confirming high accuracy in reproducing transient flow behavior. Increasing α and J improved agreement between numerical and experimental results. Parameter interaction analysis determined optimal θ and element number as 0.8 and 2 units, respectively. The retardation time exhibited significant sensitivity to flow rate, rising from 0.454 to 0.959 seconds when the flow rate increased from 1.06 to 2 L/s. Finally, accurate determination of cycle time and optimal selection of spring–dashpot elements were found to play a decisive role in enhancing both accuracy and reliability of transient flow modeling.