Unsteady duct flow occurs when the driving pressure difference is a function of time. A special ease is the oscillating flow in a pipe under the influence of a periodic pressure difference. Transient flows can be originated by dynamic events such as the closing of a valve or the loss of power of a pump. Calculations of transient flows are more involved titan steady-state calculations, because the complete history of the system lias to be calculated from the initiation of the transient to the time of interest. The concept of the friction factor, used in steady-state flow, is generally not applicable, since there might be a time lag between the pressure gradient and the wall shear stress In turbulent flow the time-averaging procedure is not trivial, because the mean values (e.g., the mean velocities) are still time dependent. Therefore, ensemble averages have to be used; see Section 15874A.

Surveys on unsteady pipe flow liave been given by Rich (1963), Wylie and Streeter (1978), Paynter (1961), and Kalinin and Dreitser (1970).

Oscillating pipe flows liave been investigated by Uchida (1950) and Richardson and Tyler (1929) for the laminar case and Schultz-Grunow (1940) for the turbulent case.

Zielke (1968) studied the laminar transient pipe flow, whereas the turbulent case has been investigated by Brown et al. (1969), Hirose (1971), and Margolis and Brown (1975); see also Carr (1981).