The pulsating viscous flow superposed on the steady laminar motion of incompressible fluid in a circular pipe

Summary An exact solution of pulsating laminar flow superposed on the steady motion in a circular pipe is presented under the assumption of parallel flow to the axis of pipe. Total mass of flow on time average is found to be identified with that given byHagen-Poiseuille's low calculated on the steady component of pressure gradient. The phase lag of velocity variation from that of pressure gradient increases from zero in the steady motion to 90° in the pulsation of infinite frequency. Integration of work for changing kinetic energy of fluid through one period is vanished, while that of dissipation of energy by internal friction remains finite and excess amount caused by the components of periodic motion is added to the components of steady flow.It is found that the given rate of mass flow is attained in pulsating motion by giving the same amount of average gradient of pressure as in steady flow, but that excess works to the steady case are necessary for maintenance of this motion.

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Zusammenfassung Eine exakte Lösung der pulsierenden laminaren Strömung in einem Kreisrohr wird angegeben mit der Annahme, dass die Richtung dem Geschwindigkeitsvektor der Rohrachse parallel ist. Die Durchflussmenge stimmt überein mit der aus der stationären Druckgefällekomponente gerechneten Menge. Für die Erhaltung der Bewegung dagegen ist die der Dissipation entsprechende Extraarbeit notwendig. Die Quantität dieser Arbeit hängt ab von den Frequenzen der Stromschwingungen.