An eigenfunction solution of entry flow in a semi-infinite pipe at low Reynolds numbers

The developing flow in a semi-infinite pipe is solved for by an eigenfunction method. The results are applicable to zero and low Reynolds number flows. The eigenfunction method yields a solution which accurately predicts overshoots in the axial velocity for small axial positions. Results are presented for both uniform and non-uniform inlet conditions. The latter condition has important implications for numerical simulations of the developing flow problem.