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Q1. The end bulkhead of the wing tank of an oil tanker has the following widths at 3 m intervals, commencing from the deck are 6.0, 6.0 5.3, 3.6 and 0.6 m. The tank is full of oil of density 800 kg/m³. Calculate EACH of the following:

(a) the load on the bulkhead; (8)

(b) the position of the centre of pressure. (8)

Q2. A ship of 4000 tonne displacement floats at a mean draught of 6 m in sea water of density 1025 kg/m³ but is unstable and has an angle of loll.

Hydrostatic particulars for the ship in the upright condition at the above displacement are as follows:

Centre of buoyancy above the keel (KB) = 3.225 m

Height of transverse metacentre above the keel (KM) = 5.865 m

Tonne per centimetre immersion (TPC) = 8.0

To achieve a satisfactory stable condition with a metacentric height of 350 mm, a load of 480 tonne at a Kg of 2.5 m is added to the ship on the centreline.

Calculate, for the original unstable condition, EACH of the following:

(a) the height of the original centre of gravity above the keel (KG); (12)

(b) the angle of loll. (4)

Note: The vessel may be considered ‘wall-sided’ between the limits of draught,

hence: GZ = sin θ (GM + ½ BM tan² θ)

Q4. A ship of displacement 14000 tonne has a length 130 m, breadth 17 m, and even keel draught of 6.11 m in sea water of density 1025 kg/m³. The area of the waterplane is 1600 m² and the second moment of area of the waterplane about a transverse axis through midships is 1.25 × 106 m4 with the LCF at midships.

The ship has a full depth empty rectangular compartment of length 13 m and breadth 11 m. The centre of the compartment is on the centreline of the ship 30 m forward of midships.

Calculate the end draughts after the compartment is bilged.  (16)

Note: For the purposes of calculating the MCT1cm it can be assumed that GML = BML

Q5. A uniformly constructed box shaped vessel of length 60 m and breadth 10 m has an even keel draught of 2 m when floating in the light condition in sea water of density 1025 kg/m³.

The vessel has five holds of equal length and is to be loaded with 4000 tonne of cargo, with equal quantities in each of the centre and end holds, and the balance equally distributed in No.2 and No.4 holds.

The cargo in all holds will be trimmed level.

Calculate EACH of the following:

(a) the maximum amount to be loaded in the centre and end holds in order that a maximum hogging bending moment amidships of 3000 tm will not be exceeded; (10)

(b) the resulting shear force at EACH of the bulkheads.  (6)

Q7. A ship consumes an average of 60 tonne of fuel per day on main engines at a speed of 16 knots. The fuel consumption for auxiliary purposes is 8 tonne per day.

When 1000 nautical miles from port it is found that only 160 tonne of fuel remains on board and this will be insufficient to reach port at the normal speed.

Determine the speed at which the ship should travel to complete the voyage with 20 tonne of fuel remaining.  (16)

Note: A graphical solution is recommended.

Q8. (a) The residuary resistance of a 1/25 scale model of a ship is 7.65 N when tested at 1.75 m/s in fresh water of density 1000 kg/m³. The frictional resistance of the ship at 15 knots in sea water of density 1025 kg/m³ is 185 kN.

Frictional resistance can be assumed to vary with speed to the power 1.825. Calculate the effective power (naked) for the ship at the speed corresponding to the model test.  (8)

(b) The following additional data apply to the ship operating in service at the corresponding speed as calculated in Q6(a), with a propeller having a pitch of 4.75 m.

Appendage and weather allowance = 23%

Quasi-propulsive coefficient (QPC) = 0.71

Propeller speed = 1.9 revs/sec

Taylor wake fraction = 0.33

Propeller thrust = 640 kN

Calculate EACH of the following:

(i) the torque delivered to the propeller; (3)

(ii) the propeller efficiency; (3)

(iii) the real slip ratio.  (2)