Final Form of Void Fraction Equation

Substituting the shear stresses, Tg i and from Eqs.(13.C.ll) and (13.C.18) into the force balance equation, Eq. (13.C.4), and simplifying, we obtain an implicit expression relating void fraction to known quantities such as cyclone diameter, gas and liquid mass flow rates, gas and liquid densities and viscosities, and the acceleration of gravity  

Equation (29) must be solved iteratively for the void fraction, , as a function of the independent quantities  

Once is known for a given set of local conditions, it is then possible to compute the liquid phase fraction (1 — e), the film thickness, t, the film and gas phase velocities, vi and and the slip velocity, VsUp. 

Knowing and the cyclone diameter, D, the film thickness, t, for any value of can now be computed. 

An estimate of the residence time of the liquid film over cyclone height H can be obtained by dividing its helical path length, H/ sin a, by the film velocity 

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