Water flows into end A of a cylindrical tube AB at a speed v_1 and...

By the equation of continuity for an incompressible fluid, the volume flow rate remains constant throughout the tube.

$A_1 v_1 = A_2 v_2$

Since the tube is cylindrical, its cross-sectional area is uniform, so $A_1 = A_2$.

Therefore, $v_1 = v_2$.

This relation depends only on the conservation of mass and the incompressibility of water, and is independent of the orientation of the tube.

Thus, $v_1 = v_2$ is valid for each case.