The Darcy-Weisbach formula, used in the majority of mathematic models for calculating the head losses in the unsteady motion of water does not simulate with sufficient accuracy the damping of flow and pressure in the water hammer phenomenon. Taking into account the dynamic structure of water column motion in a pressurized pipe, for a compressible fluid, as well as the energy losses in the elastic walls of the pipe, we present for the calculation of the flow and pressure oscillation damping a formula based on the structural (hysteretic) friction forces [6, 13]. In the case of elastic bodies the structural damping forces are proportional to the elastic forces, but a quarter of a period phase out. By putting into practice the presented formula a good agreement between computations and experimental measurements is achieved.