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ENGR5002 / Week 1
Week 1 Exercise 7Exercise sheetCurrent spec2:210 min

Week 1 Exercises, Exercise 7 (Hydrostatics with Multiple Fluids)

A connected vessel contains water and air at T=20∘CT = 20^\circ\mathrm{C}. The compartment on the left-hand side is opened to the atmosphere p0=101,325p_0 = 101{,}325 Pa.

Geometric data (see figure):

  • Left bay: air space height above the left free surface h1=0.40h_1 = 0.40 m; water depth below that free surface h2=0.60h_2 = 0.60 m.
  • Middle bay: the free surface (point BB) lies h3=0.30h_3 = 0.30 m below the top;
  • Right bay: distance from the bottom to the intermediate level is h6=0.20h_6 = 0.20 m.
  • The water level difference between the central and the right bay is h4=0.50h_4 = 0.50 m

Determine the pressure at points B, C and D.

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

Three bays joined at the bottom: left bay open (surface A), middle bay sealed with surface B, right bay sealed with C at the top and D at the bottom.
Three bays joined at the bottom: left bay open (surface A), middle bay sealed with surface B, right bay sealed with C at the top and D at the bottom.
Formulas you may need
  • Pressure at depth: p(z)=p(z=0)+ρgzp(z) = p(z=0) + \rho g z (on the formula sheet)
  • Same pressure at the same level in one continuous static fluid (learn this)
  • Pressure in a small trapped gas volume is uniform (ρairgh\rho_{air} g h negligible) (learn this)