Transient flow is a common phenomenon in the nuclear facility pipeline system, such as essential service water system (SEC) and nuclear chemical system. Transient flow can cause a large fluctuation of fluid pressure in the pipeline, which poses a threat to the normal operation of the system and instrument equipment, and is accompanied by the vibration and noise. In the paper, the basic governing equations and Brunone unsteady friction model are established and solved numerically by method of characteristics. For the pipeline system with surge chamber, the energy analysis method is used to study the variation law and mechanism during the transient flow. The results show that: (1) the internal energy of the downstream pipe fluctuates obviously, including high frequency and low frequency. The internal energy of the upstream pipe contains only low-frequency oscillations, and its curve is smoother. The high frequency corresponds to the wave frequency of the water hammer, and the low frequency corresponds to the wave frequency of the surge chamber. (2) when the valve is closed, the fluid oscillates only between the upstream pipe and the surge chamber. The period and fluctuation direction of the surge chamber kinetic energy are the same as that of the upstream pipe, and they decay rapidly under the frictional dissipation. However, the surge chamber kinetic energy is always less than that of the upstream pipe. (3) The internal energy and kinetic energy of the transient process decay quickly, and the decay function can be determined by a power function. The research results provide guidance for energy analysis of transient flow phenomena in nuclear facility pipeline system.