design solution needed

Frank Pita

What curve of a centrifugal impeller blade wil produce the greatest exit velocity from the rotor for incom- pressible fluids? If the design constraint limits the vane's surface to be parallel with the rotational axis, this will produce one result. If however the width of the vane also tapers radially, other solutions are possible! Curvature in three dimensions or a helical pitch is also a consideration. The application will be for a device within which liquid circulates as in a liquid ring compressor - but for a different purpose. Not being skilled in the art, I'm looking for an idealized optimal solution mathematically described. I know this is a horrific problem in fluid dynamics, but surely something close to an answer must have been found. Any and all advice is welcome. Thank you.