inverse initializing model

Hi my Dear Friends,

I have a constant amount of liquid between a sphere and a flat plate in axisymmetric geometry. I want to insert some specific volume of liquid in comsol and find the height that it fills. I have V(z) = some expression for z. Now I want F-1 (V ) = z . This z is actually gap distance that I read on sphere. What can help me?
Thanks a lot in advance.
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Marjan