Flow Development in the Entrance Region of Slender Converging Pipes

Abstract

This work presents an analytical investigation of the hydrodynamic entrance region in laminar flows through slender converging pipes. Extending previous analyses for straight pipes, the model radially divides the flow into a viscous wall region and a central core where both inertia and viscous effects are important. The study analyzes the impact of the inlet Reynolds number and convergence angle on the velocity profile and pressure drop. Results show that a converging geometry, which imposes a favorable pressure gradient, significantly shortens the hydrodynamic entrance length compared to a straight pipe. Analytical solutions show good agreement with numerical simulations.