Two identical rectangular tanks are connected by a small tube at the bottom. In the left tank contains liquid of density $$d_1 = 800\text{ kg/m}^3$$ to a height $$h_1 = 30\text{ cm}$$. The right tank contains liquid of density $$d_2 = 1600\text{ kg/m}^3$$, to a height $$h_2 = 20\text{ cm}$$. The two liquids don't mix. a) Find the heights of the respective columns, if a small tube connects them at the bottom. b) Where should a horizontal tube be connected, without causing any flow between the tanks?
[image]

PLACEHOLDER ANSWER - the question has two parts. a) The bottom pressures are proportional to $$800 \times 30 = 24000$$ (left) and $$1600 \times 20 = 32000$$ (right), so the denser liquid flows into the bottom of the left tank. If a height $$x$$ of it moves across, $$800 \times 30 + 1600x = 1600(20 - x)$$, giving $$x = 2.5\text{ cm}$$; the left tank then has 2.5 cm of the dense liquid under 30 cm of the light liquid (32.5 cm in all), and the right tank has 17.5 cm of the dense liquid. b) In the original state the pressures are equal at a height $$y$$ above the bottom where $$800(30 - y) = 1600(20 - y)$$, i.e. $$y = 10\text{ cm}$$, so a horizontal tube there causes no flow.