Two very large open tanks A & F both contain the same liquid. A horizontal pipe BCD, having a small constriction at C, leads out of the bottom of tank A, and a vertical pipe E containing air opens into the constriction at C and dips into the liquid in tank F. Assume streamline flow and no viscosity. If the cross section area at C is one-half that at D, and if D is at distance $h_1$ below the level of the liquid in A, the height $h_2$ will liquid rise in pipe E. The relation between $h_1$ and $h_2$ given as $h_2=k{h}_1,$ if ‘k’ is positive integer, then the value of k is______.
[Neglect changes in atmospheric pressure with elevation. In the containers there is atmosphere above the water surface and D is also open to atmosphere.]