How to design/build the electronic part of a hybrid (liquid + electronic) multi tube manometer
Mercury (Hg shown in picture in question) is 62 times less conductive than silver (the best ambient conductor) but you can still induce significant eddy currents in it so, for each tube, encircle with a coil (a solenoid). With no mercury present the inductance will be (say) high and progressively, as mercury rises in the tube, the inductance will lower due to eddy currents in the liquid conducting metal.

Use the TI inductance measurement chip: -





Even salty water could be measured using this method I reckon.