Water enters through end $A$ with speed ${v_1}$ and leaves through end $B$ with speed ${v_2}$ of a cylindrical tube $AB$. The tube is always completely filled with water. In case $I$ tube is horizontal and in case $ II$ it is vertical with end $ A $ upwards and in case $ III $ it is vertical with end $B$ upwards. We have ${v_1} = {v_2}$ for
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