U-tube: water 30 cm, liquid 1.5 g/cm³

The left arm of a U-tube holds water to a height of 30 cm, and the right arm holds another liquid of density 1.5 g/cm³ (water density 1.0 g/cm³). At rest, how high is the liquid column in the right arm, and what is the height difference between the two liquid surfaces?

Step-by-step

1. ρ_water·h_water = ρ_oil·h_oil (equal pressure at the same level)
   In connected vessels the same liquid has equal pressure at the same level
2. h_oil = ρ_water·h_water/ρ_oil = 1×30/1.5 = 20
   The lower the density, the taller the column needed to balance
3. Δh = |h_oil − h_water| = 10 cm
   Height difference between the two liquid levels

Why it works

At rest the two columns produce the same pressure at the bottom of the tube, so ρ_water × h_water = ρ_liquid × h_liquid. A denser liquid needs a shorter column, and the height difference is the gap between the two column heights.

Common mistakes

• Multiplying 30 by 1.5 and getting 45 cm instead of dividing.
• Reporting the right-hand height as the height difference.

Related

u-tube-two-liquids-level-difference buoyancy-float u-tube-water-oil-height-difference