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ENGR5002 / Week 1
ENGR217 2025 Q A2Past paperOld spec ENGR2172:225 marks30 min

ENGR217 Summer 2025 Q A2[VALID] official answers

Answer all parts (a) - (d).

[Figure summary, not printed: a rectangle 11.6 m wide and 6.6 m deep, its top edge at the free water surface, with a triangle of the same base and 3.6 m depth below it.]

Figure A2-1: the rectangle (11.6 m x 6.6 m) and triangle (3.6 m deep) forming the end of a water tank.
Figure A2-1: the rectangle (11.6 m x 6.6 m) and triangle (3.6 m deep) forming the end of a water tank.
Formulas you may need
  • Rectangle: A=bhA = bh, centroid h/2h/2 from the top, IG=bh312I_G = \dfrac{bh^3}{12} (on the formula sheet)
  • Triangle: A=12bhA = \tfrac{1}{2}bh, centroid h/3h/3 from the base, IG=bh336I_G = \dfrac{bh^3}{36} (on the formula sheet)
  • Composite centroid: yˉ=∑Aiyi∑Ai\bar y = \dfrac{\sum A_i y_i}{\sum A_i} (learn this)
  • Parallel axis theorem: I=IG+Ad2I = I_G + A d^2 (learn this)
  • Hydrostatic force on a plane: F=ρgzCGAF = \rho g z_{CG} A (on the formula sheet)
  • Centre of pressure: lCP=lCG+IGA lCGl_{CP} = l_{CG} + \dfrac{I_G}{A\,l_{CG}} (on the formula sheet)
  1. (a)
    Find the depths y1y_1 and y2y_2, to the centroids C1C_1 and C2C_2 of the rectangle and triangle shown in Figure A2-1 below, and then find the depth yy to the centroid C of the whole figure.
    [5]Third
  2. (b)
    The plane figure shown in Figure A2-1 forms the vertical end of the water tank. What is the magnitude of the force exerted on the plane by the water?
    [5]Third
  3. (c)
    Find the second moment of area of the Figure A2-1 about the horizontal axis O-O through the centroid C. (Hint: use parallel axis theorem in both the triangle and the rectangle).
    [10]
  4. (d)
    Finally find the position of the centre of pressure P of the complete Figure A2-1.
    [5]