ENGR271 2026 Q1Past paperCurrent spec2:230 marks36 min

ENGR271 Summer 2026 Q1[VALID]

An open vertical tank contains two immiscible liquids: an oil floating on a water layer. The tank bottom is taken as the elevation z=0z = 0 m. The water layer is 1.0 m deep (density of water ρw=1000 kg m−3\rho_w = 1000\ \mathrm{kg\,m^{-3}}). Above the water there is a layer of oil of 1.0 m depth. The relative density of the oil with respect to water is RDoil=0.8RD_{oil} = 0.8. The tank is open to the atmosphere, so the free surface is at atmospheric pressure. Take the atmospheric pressure as patm=101 300p_{atm} = 101\,300 Pa and g=9.81 m s−2g = 9.81\ \mathrm{m\,s^{-2}}.

Two vertical, transparent tubes (piezometers) are connected to the tank, as shown in Fig. Q1-1 (see the paper). One piezometer is connected to the tank wall at an elevation of z=1.5z = 1.5 m above the bottom, and the other at an elevation of z=0.5z = 0.5 m.

Figure Q1-1: water-oil tank with piezometers connected at elevations 0.5 m and 1.5 m.
Figure Q1-1: water-oil tank with piezometers connected at elevations 0.5 m and 1.5 m.
Formulas you may need
  • Relative density: RD=ρAρwRD = \dfrac{\rho_A}{\rho_w} (on the formula sheet)
  • Pressure at depth: p(z)=p0+ρgzp(z) = p_0 + \rho g z (zz = depth below the free surface) (on the formula sheet)
  • Gauge pressure: pg=p−patmp_g = p - p_{atm} (on the formula sheet)
  • Pressure continuous across a static fluid-fluid interface; layer by layer p=ptop+ρghp = p_{top} + \rho g h (learn this)
  • Piezometer: open column of height HH above the tapping, p=patm+ρgHp = p_{atm} + \rho g H (learn this; it is the pressure-at-depth formula read backwards)
  1. (a)
    Calculate the absolute pressure and the gauge pressure at point A.
    [10]
  2. (b)
    Under hydrostatic conditions, what condition must hold for the pressure at the interface between the two immiscible fluids (oil and water)?
    [5]
  3. (c)
    Determine the elevation z1z_1 reached by the liquid surface in point C. Consider that there is only oil in the tube. The figure is not to scale and piezometer levels are not indicative. Determine z1z_1 and justify your calculation using hydrostatic principles.
    [5]
  4. (d)
    Determine the elevation z2z_2 reached by the liquid surface in point D. Consider that there is only water in the tube. Determine z2z_2 and justify your calculation using hydrostatic principles.
    [10]