A U-tube contains two immiscible, incompressible liquids of densities ρ1 and ρ2, with a sharp interface between them. The heights of the columns measured from the interface to the free surfaces are h1 for the liquid of density ρ1 (left limb) and h2 for the liquid of density ρ2 (right limb).
(i) Prove that the equilibrium condition leads to the relation ρ1h1=ρ2h2.
(ii) Mercury of density 13.6×103kgm−3 is poured into the right limb until the mercury column height is 120mm. Calculate the height of a water column that can balance this mercury column under standard atmospheric conditions.
(iii) If atmospheric pressure rises to 1.05×105Pa while the mercury height remains 120mm, determine the new height of the equivalent water column. Comment briefly on whether the initial calculation in part (ii) represented gauge or absolute pressure.