This study investigates transient flow behavior and the sensitivity of key hydraulic parameters in the Al-Hashimiyah water transmission pipeline under steady and unsteady flow conditions. Steady-state analysis yielded a flow velocity of 5.66 m/s, a Reynolds number of 1.18 × 10⁶, and a Darcy-Weisbach friction factor of 0.008, with total head losses remaining below the allowable 70 m limit. A hybrid numerical model integrating the Method of Characteristics and Method of Integration (MOC–MOI) was developed and validated to simulate transient events, including sudden valve closures and pump shutdowns. Transient analysis indicated peak surge pressures of 205.13 m at a discharge of 0.34 m³/s, exceeding the safe operating range, while lower discharges (0.111 m³/s) limited surge pressures to 65.56 m. Pump failures induced severe pressure drops, with fluctuations reaching 95.9% of the initial head, generating negative pressures that risk cavitation. A surge tank (12 m diameter, 15 m height, 1,700 m³ volume) positioned 70 m downstream of the pumping station reduced peak pressures by 24.6%. Sensitivity analysis revealed that increasing pipe diameter from 0.24 m to 0.35 m reduced surge pressures from 191.21 m to 122.32 m, while higher friction (0.003–0.012) decreased surges from 187.40 m to 149.80 m. These findings confirm that the MOC–MOI model reliably predicts transient hydraulic behavior and provides an effective tool for design optimization, risk assessment, and operational planning in water transmission pipelines.