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Q8. A ship 102 m long floats at a draught of 6 m and in this condition the immersed cross sectional areas and water plane areas are as given in Tables Q1 (A) and Q1(B).

The equivalent base area (Ab) is required because of the fineness of the bottom shell.

Calculate EACH of the following:

(a) The equivalent base area value Ab;

(b) The longitudinal position of the center of buoyancy from midships;

(c) The vertical position of the center of buoyancy above the base.

Q2) A vessel has a depth of 12 m and a displacement of 10000 tonne when the metacentric height is 1.5 m and height to the metacentre (KM) is 7.8 m.

Two adjacent rectangular bunkers, extending over the full depth of the vessel, each 10 m long and 8 m wide, are situated either side of the centreline.

Each bunker is effectively full of fuel oil of density 900 kg/m³.

Fuel is consumed from one bunker until a maximum angle of list of 3^o is caused.

Calculate the maximum mass of fuel initially consumed before switching to the other bunker. (16)

Note: KM can be assumed constant

Q3. The following particulars apply to a ship of 125 m length when floating in water of density 1025 kg/m³ at an even keel draught of 6.425 m.

Displacement = 10850 tonne

Centre of gravity above the keel (KG) = 6.69 m

Centre of buoyancy above the keel (KB) = 3.57 m

Water plane area = 1756 m²

Centre of floatation from midship (LCF) = 2.5 m aft

Second moment of area of the waterplane about a transverse axis through midships = 1.526  10 6 m⁴

(a) Calculate the moment to change trim by 1 cm (MCT _1cm) (4)

(b) The ship in the above condition now undergoes the following changes of loading.

50 tonne added with its LCG 27.5 m forward of midships.

230 tonne removed with its LCG 2 m aft of midships

120 tonne moved 46 m aft.

Calculate EACH of the following for the new condition:

(i) The new end draughts of the ship; (9)

(ii) The longitudinal position at which a mass of 188 tonne should be added to restore the ship to an even keel draught. (3)

Q3. A box barge of 40 m length has a hull mass of 320 tonne evenly distributed over its length.

Bulkheads located 2 m from the barge ends form peak tanks that remain empty.

The remainder of the barge length is divided by two transverse bulkheads into three holds of equal length.

A total of 960 tonne is loaded, one quarter of which is placed in the middle hold, the remainder being equally distributed over the two outer holds.

Draw, using graph paper, EACH of the following on a base of barge length:

(a) curves of weight and buoyancy per meter;

(b) Curve of loads;

(c) Curve of shearing forces;

(d) Curve of bending moments.

Q7. A ship 135 m long displaces 13500 tonne. The shaft power required to maintain a speed of 16 knots is 5984 kW, and the propulsive coefficient based upon shaft power is 0.65.

Wetted surface area = 2.6 √∆L

Propulsive coefficient = ep/sp

Values of the Froude friction coefficient for Froude’s Formula are given in Fig Q5, with speed in m/s and speed index (n) = 1.825

Calculate the shaft power for a geometrically similar ship which has a displacement of 18520 tonne and which has the same propulsive coefficient as the smaller ship, and is run at the corresponding speed.

Q9. A vessel of 9250 tonne displacement is fitted with a propeller of 6.0 m diameter and pitch ratio 0.85.

During a fuel consumption trial of 8 hours duration, a steady shaft speed of 1.75 rev/sec was maintained and 9.76 tonne of fuel was consumed.

The following results were also recorded:

real slip ratio = 0.33

Taylor wake fraction = 0.31

shaft power = 5950 kW

transmission losses = 3%

quasi-propulsive coefficient (QPC) = 0.71

propeller thrust = 645 kN

Calculate EACH of the following:

(a) the speed of the ship;

(b) the apparent slip ratio;

(c) the propeller efficiency;

(d) the thrust deduction fraction;

(e) the fuel coefficient;

(f) the specific fuel consumption.