The objective of this note is to reexamine the static behavior of a 2-D channel conveying fluid, when the wall tension becomes small or zero at some point along the channel. In addition to the shear stress exerted by the fluid flow, we take into account restoring forces acting on the wall, such as the bending moment, the transverse shearing force, etc., which have often been neglected in the equation of equilibrium of the tube wall. Numerical results show that zero wall tension does not mean nonexistence of steady solutions. When the wall tension becomes small, it is important to derive the equation of equilibrium by taking into account those terms which have been neglected in comparison with strong effect of the wall tension in physiological vessels.

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