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Formulated are simple models for the flow in liquid film, formed by impinging jet, and a two-phase downward flow in pipe. The models are based on simplified equations of mass, momentum and energy. The solutions of such conservation equations may have regular points belonging to one integral curve only as well as turning points can be found amongst them, which refer to extreme values in the appropriate co-ordinate system. The solutions can also have singular points belonging to none or more than one integral curve. Both the turning and singular points have a clear physical meaning. They could be linked to critical flow conditions in the pipe flow or to the so-called hydraulic jump. Analogy existing between critical conditions in the pipe and the flow of liquid films formed by the liquid jet have been shown in the paper.
Formulated are simple models for the flow in liquid film, formed by impinging jet, and a two-phase downward flow in pipe. The models are based on simplified equations of mass, momentum and energy. The solutions of such conservation equations may have regular points belonging to one integral curve only as well as turning points can be found amongst them, which refer to extreme values in the appropriate co-ordinate system. The solutions can also have singular points belong to none or more than one integral curve. Both the turning and singular points have a clear physical meaning. They could be linked to critical flow conditions in the pipe flow or to the so-called hydraulic jump. been shown in the paper