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Q1) At a draught of 1.2 m in sea water of density 1025 kg/m³ the displacement of a ship is 1100 tonne and the height of the centre of buoyancy above the keel (KB) is 0.72 m.

Values of tonne per centimetre immersion (TPC) in sea water, for a range of draughts, are given in Table Q1.

(a) Calculate EACH of the following for a draught of 7.2 m in sea water:

(i)The displacement; (4)

(ii) The height of the centre of buoyancy above the keel (KB). (6)

(b) At a draught of 7.2 m, the height of the longitudinal metacentre above the keel (KML) is 135 m and the second moment of area of the waterplane about a transverse axis through midships is 1289670 m⁴. The centre of floatation is aft of midships.

Calculate the distance of the centre of floatation (LCF) from midships. (6)

Q5) A box shaped barge of uniform construction is 80 m long , 10 m wide and has a light displacement of 720 tonne. It is divided into three compartments by two transverse watertight bulkheads so that the end compartments are of equal length. The barge is loaded to draught of 6 m in water of density 1025 kg/m³ with cargo evenly distributed over the two end compartments.

The empty midship compartment, extending the full width and depth of the barge is now bilged and the draught increases to 8 m.

(a) Determine the length of the midship compartment. (3)

(b) For the original intact condition:

(i) plot curves of mass and buoyancy distribution; (5)

(ii) determine the longitudinal still water bending moment at midships. (4)

(c) Determine the longitudinal still water bending moment at midships for the final bilged condition. (4)

Q6) A ship of 10000 tonne displacement has a rudder area of 25 m². The ship has a KM of 6.9 m, KG of 6.3 m and the centre of lateral resistance is 3.9 m above the keel.

The maximum rudder angle is 35 degrees, and the centroid of the rudder is 2.3 m above the keel.  The force generated normal to the plane of the rudder is given by:

F=590 A v²  sin⁡α  (N)

where, A=rudder area ( m²)

v=ship speed (m⁄s)

α-rudder helm angle ( degrees)

Calculate EACH of the following, when the vessel is travelling at 22 knots.

(a) the angle and direction of heel due to the rudder force only, if it is put hard over to port; (8)

(b) the angle and direction of heel due to the combination of centrifugal force and rudder force when the rudder is hard over to port and the vessel turns in a circle of 800 m diameter. (8)

Q7) A ship of length 150 m and breadth 19 m floats at a draught of 8.5 m in sea water of density 1025 kg/m³. In this condition the block coefficient ( C_b) is 0.69.

At a speed of 16 knots the following data applies:

delivered power = 6800 kW

quasi propulsive coefficient (QPC) = 0.71

correlation factor (SCF) = 1.20

Wetted surface area (S) = 2.57√∆L  ( m²)

Calculate the pull required to tow a similar model of length 5 m at the corresponding speed in fresh water of density 1000 kg/m³.  (16)

Note: The frictional coefficient for the model in fresh water of density 1000 kg/m³ is 1.694

The frictional coefficient for the ship in sea water of density 1025 kg/m³ is 1.413

Speed in m/s with the speed index (n) for ship and model 1.825

Q8). The ship data in table Q8 have been derived from the results of model experiment.

Table Q8

Using the data in table Q8, determine EACH of the following:

(a) The ship speed when the propeller is absorbing 5250 kW delivered power;   (10)

(b) The propeller speed ( rev/s) given that the propeller has a diameter of 5 m with a pitch ratio of 0.9 and is operating at a real slip of 32 %. (6)

Q9) A ballast tank watertight bulkhead 5.0 m deep is stiffened by vertical angle bar stiffeners, 250 mm x 75 mm x12 mm thick, spaced 610 mm apart.

The ends of the stiffeners in contact with the tank top are welded all around as shown in Fig Q9 and the thickness of the weld is 6 mm.

The bulkhead has sea water of density 1025 kg/m³ on one side to a depth of 4.5 m.

Calculate the shear stress in the weld. (16)