By wider do you mean the petals of WS-15 being longer than WS-10? If so I don't think that indicate WS-15 having a larger diameter.
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The petals of WS-10 without the induction channel look longer than ordinary WS-10 too, in the same effect as WS-15.
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WS-15 probably uses conventional CD nozzle unlike the WS-10 which has an induction + CD nozzle. The outer petals of WS-10 is shorter because it is designed to converge less than the convergence section of a usual CD nozzle. The inner petals of WS-10 and the induced air in between all works for the purpose, so the demand for the outer petals' change of cross-section is less.