Taking into account the relaxation properties of the fluid, a hyperbolic equation of motion is obtained that describes the change in velocity under conditions of nonlocal equilibrium, that is, taking into account the effect of unsteadiness of the flow on the magnitude of the friction force. Studies of its exact analytical solution have shown that taking into account the nonstationarity of tangential stresses leads to results that differ significantly from the solutions of the classical hyperbolic equation obtained by using the values of velocity, density, tangential stresses, and pressure averaged over the flow cross section (the hypothesis of quasi-stationarity). Comparison of the obtained solution with experimental data, as well as with the results of theoretical studies of other authors (I.A. Charny), obtained from the solution of the Navier - Stokes equations (equations for local quantities), showed their satisfactory agreement. Consequently, studies based on the theory of quasi-stationarity can be used only after comparing them with the results obtained taking into account the nonstationarity of tangential stresses (friction force) or with experimental data, that is, only after determining the range of the degree of nonstationarity in which it can be used.