... ? R ? wall ? axis of ? ?2r ? rotation r g y ? A The force in the radial direction is m?2r. The force in the vertical direction is mg The slope at position (r, y) is dy/dr. dy ?2r i.e ? = ?? [1] dr g which on integration gives:- y = (?2r2/2g) + C [2] At the axis (where r = 0) and the bottom of the bowl where (say) y = yo, the liquid depth at the axis is C = yo. This can be either positive or negative (an imaginary depth). Equation [2] represents a section of the liquid surface through the axis of rotation and describes a parabola. When ?2r/g is large this approximates to the vertical whose radial position is determined by the location of an outlet weir (which self-evidently must be at a greater radial position than the inlet e.g. at ri). The hold up of fluid in the ...

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