THE MOTION OF A VISCOUS-FLUID IN A PIPE OF FINITE LENGTH

A solution is obtained of a linearized, initial-boundary-value problem of the unsteady motion of a viscous fluid in a cylindrical pipe of circular cross-section with a horizontal axis, under the assumption that the pressure at one end of the pipe is constant, and at the other end a device is set up which changes the flow rate of the fluid. It is shown that, depending on the relations between the defining parameters of the problem, the solution tends asymptotically either to a periodic solution, or to one of the two stable steady-state solutions. These results are obtained using methods similar to those developed in [1-3], where the unsteady motions of ground waters during the irrigation were considered, taking into account the evaporation from the regions between the channels. It was assumed there that the irrigation, which was carried out at a constant rate, was switched on and off depending on the level of ground waters in the inspection well.