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Why does a shrouded propeller have downstream velocity $V_3 = V_0 + w$, while the unshrouded propeller has a velocity $V_3 = V_0 + 2 w$?

What are the reasons of this difference?

$ \begin{align} w &= \textrm{induced velocity of the propeller}\\ V_3 &= \textrm{exit velocity}\\ V_0 &= \textrm{free stream velocity} \end{align} $

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