Approximate Analysis of Unsteady Laminar Flow

Computations of unsteady laminar flows in pipies usually require lengthy calculations due to the complications presented by the exact solutions. In this paper, an alternative approach to the solutions of unsteady laminar flows in pipies is offerd. An approximation to the friction coefficient is made. It is shown that expressing the friction coefficient in terms of the instantaneous Reynolds number results in an approximation for which the error involved is relatively small when compared with available exact solutions. The concept of an average friction coefficient is developed, and its relations to a frequency Reynolds number and to the mean value of the ascillating pressure difference ratio is obtained. By the use of the average friction coefficient, unsteady laminar pipe flow computations can be done in a manner very similar to the steady flow computations.