A U-tube manometer is partially filled with water (density 1.00×103kgm−3). An unknown, immiscible liquid is then carefully poured into the right arm until a column of the unknown liquid of height 0.080m rests above the water in that arm. After equilibrium is reestablished, the water level in the left arm stands 0.015m higher than the water–unknown interface in the right arm. Both open ends of the U-tube are exposed to atmospheric pressure.
(a) Derive an expression for the density of the unknown liquid in terms of the measured height differences and the density of water.
(b) Calculate the numerical value of the unknown liquid’s density.
(c) If the unknown liquid were completely removed and replaced by a column of oil of density 8.50×102kgm−3 occupying the same 0.080m height, determine the new difference in water levels between the two arms when equilibrium is reached.