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ENGR5002 / Week 1
Week 1 Exercise 9Exercise sheetCurrent spec2:115 min

Week 1 Exercises, Exercise 9 (Force on a Panel Between Two Fluids)

A vertical rectangular plate AB (total area A=2 m2A = 2\ \mathrm{m^2}) separates water and glycerine. Specific weights: γw=9.81 kN m−3\gamma_w = 9.81\ \mathrm{kN\,m^{-3}}, γg=12.36 kN m−3\gamma_g = 12.36\ \mathrm{kN\,m^{-3}}.

Geometry (refer to the figure):

  • The water-free surface is 2.0 m higher than the glycerine free surface.
  • Point A on the plate is 1.0 m below the water free surface
  • Point B is 3.0 m below the water free surface
  • Hence the plate height between A and B is 2.0 m
  • The bottom is 6.0 m below the water free surface, and the glycerine depth is 4.0 m.

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

Vertical plate AB between water (left) and glycerine (right): h1 = 2 m (water surface to glycerine surface), h2 = 1 m (glycerine surface to A), h3 = 2 m (A to B), h4 = 1 m (B to bottom).
Vertical plate AB between water (left) and glycerine (right): h1 = 2 m (water surface to glycerine surface), h2 = 1 m (glycerine surface to A), h3 = 2 m (A to B), h4 = 1 m (B to bottom).
Formulas you may need
  • Hydrostatic force on a plane surface: F=ρgzCGA=γzCGAF = \rho g z_{CG} A = \gamma z_{CG} A (on the formula sheet)
  • Centre of pressure (vertical plate, l=zl = z): zCP=zCG+IGAzCGz_{CP} = z_{CG} + \dfrac{I_G}{A z_{CG}} (on the formula sheet)
  • Rectangle: IG=bh312I_G = \dfrac{b h^3}{12} (on the formula sheet, shape table)
  • Resultant of two parallel forces: Fnetznet=F1z1−F2z2F_{net} z_{net} = F_1 z_1 - F_2 z_2 (learn this)
  1. (a)
    Calculate the net hydrostatic force on the panel.
  2. (b)
    Determine the depth of the centre of pressure from the free surface of water.
  3. (c)
    Determine the distance of centre of pressure from the centroid.