A bend or any another pipe component disturbs solids transport in pipes. Longitudinal pressure profiles downstream of such a component may show a stationary transient harmonic wave, as revealed by a recent settling slurry laboratory experiment. Therefore the fundamental transient response of the two-layer model for fully stratified flow is investigated as a first approach. A linear stability analysis of the sliding bed configuration is conducted. No stationary transient harmonic waves are found in this analysis, but adaptation lengths for exponential recovery are quantified. An example calculation is given for a 0.1 m diameter pipeline. Also consequences for long stretches of pipe line emerged. A so far undiscovered exclusion zone is found in the I-V diagram. This exclusion zone is situated adjacent to the deposit limit velocity locus curve. This simplified physical system reveals that flow velocities should be taken about 10% greater than the calculated maximum deposit limit velocity for stable converging flow.