| Abstract: | The problem of the stability of a viscous laminar liquid flow with a liquid free surface in an inclined duct is theoretically
considered. Since the dependence of the flow rate on the free-surface height is not monotonic (the highest flow rate in a
cylindrical duct is observed at H*=1.7R), primary attention is given to the region H>H*. It is proved that there is aw region of instability: for an arbitrarity low Reynolds number, there is a free-surface level
above which the flow becomes unstable against one-dimensional disturbances. When the height of the liquid layer is close to
the vertical dimension of the duct, the one-dimensional disturbances propagate mainly upstream (for moderate Reynolds numbers).
Hence it follows that there is not steady regime of liquid flow from a fully filled duct with an open end.
Kutateladze Institute of Thermal Physics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from
Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 3, pp. 90–96, May–June, 1999. |
