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ENGR5002 / Week 1
Week 1 Exercise 8Exercise sheetCurrent spec2:28 min

Week 1 Exercises, Exercise 8 (A differential manometer)

A differential U-tube manometer filled with mercury (RDHg=13.6RD_{Hg} = 13.6) is connected to a pipe carrying oil (RDoil=0.91RD_{oil} = 0.91).

  • Point A is located just upstream of the orifice.
  • Point B is located just downstream of the orifice.
  • The vertical distance between the mercury levels is 10 cm.

Calculate the pressure difference between points A and B.

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

Pipe with an orifice; tappings at A (upstream) and B (downstream) lead through oil-filled loops to a mercury U-tube; mercury levels differ by 10 cm, lower on the A side; y unknown.
Pipe with an orifice; tappings at A (upstream) and B (downstream) lead through oil-filled loops to a mercury U-tube; mercury levels differ by 10 cm, lower on the A side; y unknown.
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=ρ/ρwRD = \rho/\rho_w (on the formula sheet)
  • Differential manometer: pA−pB=(ρm−ρ)g Δhp_A - p_B = (\rho_m - \rho) g\,\Delta h for A and B at the same level (learn this; derive it)