Abstract: The characteristic equation and the eigenfunctions of the supported beam are derived. Using the characteristic equation derived, the effect of the spring constants on the eigenvalues of the beam is discussed. The analytical expressions of critical flow velocity of the supported pipes, which may be used in the analysis of the dynamic behavior of the system, are obtained using the eigenfunctions derived for beam with the same end conditions. The effect of some parameters of the system on the values of critical flow velocity is discussed according to the analytical expressions derived. The results obtained show that the effect of the spring constants on the value of critical flow velocity is very great if their dimensionless values are taken in region 0-50, whereas the value of critical flow velocity is very little affected by the values of spring constants when the dimen-sionless values are greater than 50. Generally, as the gravity, tension and spring constants increase the value of critical flow velocity increase also.

Key words: Critical veloc-ity Stability, Supported pipes conveying fluid