ENGR217 2017 Q A1 (ENGR5002)

ENGR217 2017 Q A1Past paperOld spec ENGR2172:125 marks30 min

Answer ALL parts (a) - (c).

Formulas you may need

Buoyancy / displacement: $F_B = \rho_{sw} g V$ , so $V = M/\rho_{sw}$ (on the formula sheet)
Relative density: $RD = \rho/\rho_w$ (on the formula sheet)
Second moment of a rectangular free surface about its own fore-and-aft centreline: $i = \dfrac{l b^3}{12}$ (on the formula sheet, shape table)
Free-surface effect (virtual rise of G): $\Delta GM = \dfrac{\rho_{liq} \sum i}{\rho_{sw} V}$ (learn this)
Stability criterion: stable if $GM > 0$ (M above G) (learn this)

(a)
A car ferry of displacement 12500 tonne carries oil fuel in 8 tanks each 8 m long and 4 m broad, the tanks arranged with their long dimension in the fore and aft directions. The specific gravity of the oil is 0.87, and the density of the sea water in which the ship is floating is $1090\ \mathrm{kg/m^3}$ . By how much is the metacentric height of the ship reduced by the oil contained in the tanks and is this serious?
i per tank =m^4
GM reduction (8 tanks) =mm
[10]
(b)
The car deck on the above car ferry is approximately rectangular, 20 m wide by 150 m long, and the metacentric height in roll is 0.94 m. If sea water of density $1090\ \mathrm{kg/m^3}$ is accidentally taken into the car deck, in quantity sufficient to cover the deck even when the boat heels, will the vessel become stable or unstable?
V displaced =m^3
GM reduction =m
GM effective =m
[10]
(c)
If on the above car ferry, the car deck is divided down the middle, into two areas each of 150 m x 10 m, would the vessel still be unstable if one of these areas took in water?
GM reduction (one half) =m
GM effective =m
[5]