The difference between the initial energy and the ending energy of the hydrodynamics system reflects the head loss of the hydraulic system directly.Based on the structurepreserving idea,the symmetric form with the spatial symplectic structure,the energy flux conservation law and the momentum flux conservation law were deduced firstly.And then,the Euler Box scheme as well as its discrete spatial symplectic structure for the symmetric form were constructed to simulated the steadystate solution of the WBK equation.In the numerical experiments,the structurepreserving properties of the Euler Box scheme were verified.In addition,the total energies for the WBK system in the steady state with different relative diffusion coefficients were studied in detail,which will provide a reference for calculating the head loss in a hydraulic system.