Hello mdurchholz
In the case of an agitator, it has weight whose center of mass is offset from the centerline of the nozzle. So, there would be a downward force P and a moment from the offset weight. There is also torsion from the rotation of the agitator. The torsion can usually be ignored. However, if it has to be included, you would need to know the horsepower (or kW) of the motor, and the speed of the agitator to calculate the torsional load.
If the agitator is mounted on a blind flange, there is no way (using WRC 107) to compute the stresses induced in the blind flange, but that does not usually pose a problem. However, the loads are transferred to the nozzle itself and would generate stresses in the vessel wall which can be analyzed using WRC 107.
I hope that helps, at least a little bit.
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Sincerely,
Ray Delaforce
CADWorx & Analysis Solutions
Hexagon PPM