The aim of this study is to show the influence of the effect of water hammer at the level junctions and valves on the values of the pressure and velocity for the fluid and the axial velocity and stress for the piping on the exact solution of the FSI four-equation model of two filling pipes system by using two methods, the first is the analytical method and the second is the computational fluid dynamics (CFD) method. The application of the conservation laws of the mass, momentum, and energy for a flow transient in driving, leads us to a system of differential equations to partial derivatives of the hyperbolic type. This equation system takes into account counts the two fluid-pipe interaction, the pipe velocity, as well as mechanical vibrations at the junctions or valves. The exact solution of the FSI four-equation model by a Tijsseling model (Tijsseling, 2009) [1]. The resolution of this system of equations is done by the method of characteristics coupled with finite differences. The proposed model was tested by a comparison with the results of Ahmadi et al. (Ahmad and Ali, 2008) [2] validated with those of Heinsbroek.

本研究的目的是展示液位接头和阀门处的水锤效应对流体压力和速度值以及管道轴向速度和应力值对 FSI 4 精确解的影响。 -使用两种方法建立两个填充管道系统的方程模型，第一种是解析方法，第二种是计算流体动力学（CFD）方法。将质量、动量和能量守恒定律应用于驱动中的流动瞬变，将我们引向双曲线型偏导数的微分方程组。该方程系统考虑了两个流体-管道相互作用、管道速度以及接头或阀门处的机械振动。Tijsseling 模型对 FSI 四方程模型的精确解 (Tijsseling, 2009) [1]。该方程组的求解是通过特征结合有限差分的方法完成的。通过与 Ahmadi 等人的结果进行比较来测试所提出的模型。(Ahmad 和 Ali, 2008) [2] 与 Heinsbroek 的验证。