New fluid velocity expression in an extensible semi-circular pipe conveying fluid

A new expression for fluid velocity is presented for a fluid-conveying semi-circular pipe with an extensible centreline. The proposed fluid velocity expression is obtained from the material derivative, while the previous velocity expressions are from Love's kinematical relations. In order to show that the new fluid velocity expression is more reasonable than the previous velocity expressions, the equations of in-plane motion derived with the new expression are compared to the equations derived with the previous expressions. Furthermore, the equilibrium positions, natural frequencies and mode shapes obtained with both the new and previous expressions are analysed and discussed.