Why does a shrouded propeller have a lower downstream velocity than an unshouded propeller?

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}