START-UP FLOW IN A PIPE FOLLOWING THE SUDDEN IMPOSITION OF A CONSTANT FLOW RATE

The transient flow in a long pipe following the sudden imposition of a constant flow rate is considered. An exact analytical solution of the axisymmetric Navier-Stokes equations in terms of an infinite series of Bessel functions is derived. Time-dependent velocity profiles, as well as time histories of the axial pressure-gradient and the wall-friction, are presented. It is observed that the start-up time required to reach steady state is significantly shorter than if the start-up flow results from a suddenly imposed constant pressure gradient. The “Annular Jet Effect” observed experimentally by Kataoka et al. (1975) is not exhibited by the present solution.