The friction coefficient of a fully developed laminar reciprocating flow in a circular pipe

Pressure drops in a fully developed laminar incompressible reciprocating pipe flow have been investigated analytically and experimentally. An exact analytical solution for the instantaneous and cycle-averaged friction coefficients of a fully developed laminar reciprocating flow has been obtained. It was found that, although the dimensionless axial velocity profiles of a fully developed flow depend only on the kinetic Reynolds number, the friction coefficients depend not only on the kinetic Reynolds number but also the dimensionless oscillation amplitude of fluid. Experiments have been carried out to measure the pressure drops of a laminar reciprocating flow at downstream of a long pipe at various frequencies and fluid displacements. Comparisons are made for the time-resolved and the cycle-averaged friction coefficients between the analytical solution and experimental data. It is shown that the analytical solution is in good agreement with measurements.