In the previous problem, if 15.0 cm of water and spirit each are further poured into the respective arms of the tube, what is the difference in the levels of mercury in the two arms? (Specific gravity of mercury = 13.6)
Given:
Height of the spirit column (h1) = 12.5 + 15 = 27.5 cm
Height of the water column (h2) = 10 + 15 = 25 cm
Density of spirit (ρ1) = 1 gm/cc
Density of spirit (ρ2) = 0.8 gm/cc
Density of mercury (ρ) = 13.6 gm/cc
Mercury rises because of the differences in pressure exerted by the columns of water and spirit.
Pressure due to height h of mercury column = ρgh
= (13.6gm/cc) × (980 cm/s) × (h cm)
Differences in pressures due to water and spirit = ρ1gh1-ρ2gh2
= (1 × 980 × 25)-(0.8 × 980 × 27.5)
= 2940 gm/cm2s
Pressure due to height h of mercury = Differences in pressures due to water and spirit
13.6 × 980 × h = 2940
h = 0.2205 cm
Difference in the levels of mercury in two columns is 0.2205.