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ENGR5002 / Week 1
Week 1 Exercise 10Exercise sheetCurrent spec2:28 min

Week 1 Exercises, Exercise 10 (hydrometer; printed title "Force on a Panel Between Two Fluids")

A hydrometer weighs W=0.0216W = 0.0216 N and has a cylindrical stem of diameter d=2.80d = 2.80 mm. When floating in water, its reference immersion depth (measured along the stem) is hw=12.0h_w = 12.0 mm. When placed in an unknown liquid, the immersion depth increases by Δh=6.5\Delta h = 6.5 mm.

Calculate the density of the unknown liquid.

Data: ρw=1000 kg/m3\rho_w = 1000\ \mathrm{kg/m^3}; g=9.81 m/s2g = 9.81\ \mathrm{m/s^2}.

Hydrometer (bulb plus thin stem) floating in water (left) and, deeper by Delta h, in the unknown liquid (right).
Hydrometer (bulb plus thin stem) floating in water (left) and, deeper by Delta h, in the unknown liquid (right).
Formulas you may need
  • Buoyancy force: FB=ρgVdisplacedF_B = \rho g V_{displaced} (on the formula sheet)
  • Gravity force: Fg=mgF_g = m g (here WW is given) (on the formula sheet)
  • Floating equilibrium FB=WF_B = W in each liquid (learn this)