COMPUTER EXTENDED SERIES SOLUTION FOR UNSTEADY-FLOW IN A CONTRACTING OR EXPANDING PIPE

Unsteady flow in a semi-infinite contracting or expanding pipe is rein vestigated using long series analysis. The proposed series method is u seful in analysing the problem for a moderately large constant alpha ( alpha = aa/nu, where a = a(t), the radius of the pipe is a function of time, a(t) is the velocity of the wall, and nu is kinematic viscosity ). For positive values of alpha (expansion of the pipe) accuracy of th e series representing shear stress and pressure gradient is increased from alpha = 2.89 to alpha = 6.0 by extracting the singularity followe d by completion of the series. For negative values of alpha (contracti on of the pipe), we revert the series which results into the increase of the region of validity of the transposed series from alpha = -25.0 to alpha = -2.89. Later we use Pade approximants for summing them. Als o, the asymptotic solution for large values of alpha is obtained and i t agrees closely with pure numerical values of sheer stress at the wal l and pressure gradient.