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ENGR5002 / Week 1
Week 1 Exercise 3Exercise sheetCurrent spec2:210 min

Week 1 Exercises, Exercise 3 (Aquarium Porthole)

An aquarium has a circular porthole of diameter D=1.0D = 1.0 m mounted on a sloping wall inclined at an angle θ=60∘\theta = 60^\circ to the horizontal. The centroid of the porthole is located at a depth of zCG=1.5z_{CG} = 1.5 m below the free surface of water. The density of water is ρ=1000 kg/m3\rho = 1000\ \mathrm{kg/m^3}.

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}; D=1.0D = 1.0 m; zCG=1.5z_{CG} = 1.5 m; θ=60∘\theta = 60^\circ.

Aquarium wall sloping at 60 deg to the horizontal with a 1.0 m diameter porthole, centroid 1.5 m below the free surface.
Aquarium wall sloping at 60 deg to the horizontal with a 1.0 m diameter porthole, centroid 1.5 m below the free surface.
Formulas you may need
  • Hydrostatic force on a plane surface: F=pCGA=ρgzCGAF = p_{CG} A = \rho g z_{CG} A (on the formula sheet)
  • Centre of pressure along the plane: lCP=lCG+IGA lCGl_{CP} = l_{CG} + \dfrac{I_G}{A\, l_{CG}} (on the formula sheet)
  • Circle: A=πd24A = \dfrac{\pi d^2}{4}, IG=πd464I_G = \dfrac{\pi d^4}{64} (on the formula sheet, shape table)
  • Slant distance and depth: z=lsin⁡θz = l \sin\theta (learn this)
  1. (a)
    Compute the resultant hydrostatic force acting on the porthole.
  2. (b)
    Determine the location of the centre of pressure below the free surface.