A paradox of non-monotonicity in stability of pipes conveying fluid

The paradoxical result of the non-monotonous relationship between the critical speed of the fluid that is conveyed in the elastic pipe, and the mass ratio was reported first some four decades ago. Since then this result was reproduced in numerous books and articles. In this study the paradox is revisited. It appears that it is a numerical artifact; instead of non-monotonicity there are jumps.