Developing oscillatory flow in a circular pipe: a new solution.

The problem of oscillatory flow in a circular pipe was analyzed by Atabek and associates more than two decades ago. Their formulas for velocity and pressure distributions in developing pipe flows under oscillatory conditions have been often cited. However, the application of these formulas for flow field computations requires a rather complex procedure involving plotting of a set of curves and predetermination of the phase angles. This paper presents a method using the imaginary argument of the Bessel function to solve the Navier-Stokes equations. A different set of solution formulas are obtained. A comparison of the formulas obtained in this paper with those of Atabek shows that the former is considerably simpler and more convenient to use in flow computations. Numerical results computed using this paper's formulas are consistent with Atabek's and with the experimental measurements.