When velocities in the piping systems change rapidly, spectacular accidents occur, due to transient-state pressures where the elastic properties of the pipe and liquid must be considered. This hydraulic transient is commonly known as water hammer. A conventional widely-used technique for analyzing this phenomenon is the Method Of Characteristic (MOC), in which, by introducing the characteristic lines, two ordinary differential equations, in lieu of the governing partial differential equations, are produced. In the undisturbed form of the equations, the energy dissipation is evaluated by the steady or quasi-steady approximation. But, there is experimental and theoretical evidence which shows that the velocity profiles in unsteady-flow conditions have greater gradients and, thus, greater shear stresses, than corresponding values in steady-flow. Moreover, the numerical integration of the friction-loss is based on the values at the previous time step. This paper employs the External Energy Dissipator, Karney's method, to apply the boundary conditions in a network. To investigate the effect of the unsteady friction formula, the cross characteristic mesh, based on the Vitkovsky formulation, is completely derived and incorporated in the network. At last, the effect of the weighting term in the integration of the friction-loss term is examined. The paper shows that if the maximum head rise were to be practically considered, it would not need the unsteady friction term to be taken into account. Moreover, the weighting integration constant has the slightest effect on the text network.