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ENGR5002 / Week 1
Week 1 Exercise 2Exercise sheetCurrent spec2:28 min

Week 1 Exercises, Exercise 2 (Multiple Fluid Hydrostatics)

The U-tube shown in the figure contains oil in the left leg, water in both legs, and a trapped air bubble.

The following heights are given:

  • Oil column: h1=0.75h_1 = 0.75 m
  • Air pocket: h2=0.15h_2 = 0.15 m
  • Water column in the left leg: h3=0.30h_3 = 0.30 m
  • Water column in the right leg: h4=0.90h_4 = 0.90 m
  • The horizontal distance between the two legs is 0.60 m.

Using the hydrostatic balance, determine the relative density of the oil.

Data: ρw=1000 kg/m3\rho_w = 1000\ \mathrm{kg/m^3}; g=9.81 m/s2g = 9.81\ \mathrm{m/s^2}; pa=101.3 kPap_a = 101.3\ \mathrm{kPa}.

U-tube, both ends open: left leg oil (h1) over an air pocket (h2) over water (h3); right leg water (h4). h3 and h4 are measured from the bottom of the tube.
U-tube, both ends open: left leg oil (h1) over an air pocket (h2) over water (h3); right leg water (h4). h3 and h4 are measured from the bottom of the tube.
Formulas you may need
  • Pressure at depth: p(z)=p(z=0)+ρgzp(z) = p(z=0) + \rho g z (on the formula sheet)
  • Relative density: RD=ρρwRD = \dfrac{\rho}{\rho_w} (on the formula sheet)
  • Equal pressure at equal level in one continuous static fluid (learn this; it is the basis of every manometer)