Abstract: A wave tracking method (WTM) for hydraulic transients in a pump-pipe system is derived to solve the equations of water hammer and its bridging in the water column separation case; similarities and differences between this method and the Eulerian fixed-grid method of characteristic (MOC) are compared and discussed in theory, solving procedure, and calculation accuracy. Calculations in two study cases show that theories of the two methods are the same fundamentally but WTM directly calculates the pressure wave (plus head differences in the initial value). WTM calculations are completely consistent with MOC when friction loss is not considered, indicating our equations, boundary conditions, and bridging method for the system with column separation are effective and satisfactory. Even in the cases of friction loss considered, a difference less than 0.3% is revealed between the two methods that share virtually the same accuracy. This slight difference is caused by the treatment of the friction loss term. And both share the same max and min values of transient parameters for water column separating and bridging. For a large-scale pipeline or pipe network system, WTM can directly calculate its hydraulic transients from the boundary conditions, with no need of the numerical algorithms as adopted by MOC, thus enjoying a higher computational efficiency.

Key words: water hammer in pump stations, water column separation and bridge, wave tracking method, wave conservation law, boundary conditions