Radial loading on multistage pump

What do you mean by "concentric casing"?

By "concentric casing" i mean radial clearance between impeller and housing is constant; no tongues, cutwaters, etc.

Think of an ESP or water-injection pump like sulzer makes.

OK - I think you are referring to what I would call a "side channel pump". Is this the type?

If so, the radial forces will be low and for most purposes can be ignored. (Static radial load is the mass of the rotor). The star type impeller has many blades and the casing is circular and concentric to the shaft. The liquid ring formed will have equal radial thrust in all directions. There must be some unbalanced radial forces as the liquid moves between the areas created by the impeller blades and the side channels but I can not imagine that these would be significant.

As these pumps are fundamentally self-priming, even at start up the water remaining in the pump casing almost instantly creates a water ring which again is concentric, so radial forces should be minimal.

The greatest radial forces will be created if the shaft is not concentric to the casings, which can happen with these pumps after many overhauls.