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Q7. A ship of length 120 m displaces 11750 tonne when floating in sea water of density 1025 kg/m3. The center of gravity is 2m above the center of buoyancy and the waterplane is defined by the following equidistant half-ordinates given in Table Q1:

Calculate EACH of the following:

(a) The area of the waterplane;

(b) The position of the centroid of the waterplane from midships;

(c) The second moment of area of the waterplane about a transverse axis through the centroid;

(d) The moment to change trim one centimeter (MCT1cm).

Q2. The ‘wall sided formula’ gives an expression for righting lever (GZ) as follows:  GZ = sin θ (GM + ½ BM tan2 θ) (a) Derive an expression for the `angle of loll' of a ship which is initially unstable in still water, using the wall sided formula. (b) A box shaped vessel designed to carry timber, is 80 m long, 12 m wide and floats at a draught of 5 m in sea water of density 1025 kg/m3 with a KG of 4.815 m. A beam wind acts on the exposed area of the vessel causing it to heel to an angle of 15°. The heeling moment caused by the wind is given by the expression: Heeling moment = 0.85 A b v2 cos2 θ Nm

where:  A = exposed area = 627 m2 b = lever = 6.5 m      v = wind speed in m/s                                        θ = angle of heel in degrees.

Calculate the wind speed in knots, using the wall sided formula for GZ.

Q8. A. Describe the procedure for speed, Power and fuel consumption trials. B. An oil tanker has LBP 142m, beam 18.8m and draught 8m. It displaces 17000 tonne in seawater of 1.025 1/m3. The face pitch ratio of the propeller is 0.673 and the diameter 4.8m. The results of the speed final show that the true slip may be regarded as constant over a range of speeds of 9 to 12 knots and is 35% the wake fraction may be calculated from the equation: W=0.5Cb = 0.05. If the vessel uses 20 tonne of fuel per day at 12 knots and the consumption varies as speed. Find the consumption per day at 100 rev/min.

Q10: A. Explain the term volumetric heeling moments. B. A box barge 33m long and 5.5m wide has a light displacement and KG of 216 tonne and 2.75 m respectively. 80 tonne of machinery are put on board and in order to maintain stability 54 tonne of Ballast are at Kg 0.15m.  The final GM is 0.13 m. Calculate the Kg of the added machinery.

. Describe the effect of cavitation’s on

(i) The thrust and torque

(ii) the propeller blades.

(b) A ship of 355190 tonne displacement is 325 m long, 56m wide and floats in sea water of density 1025 kg/m3 at a draught of 22.4 m. The propeller has a diameter of 7.4 m, a pitch ratio of 0.85, and when rotating at 1.5 rev/s the real slip is 48.88% and the fuel consumption is 165 tonne per day.

The taylor wake fraction Wt=0.5Cb-0.05.

Calculate

a) The speed in knots

b) The reduced speed at which the ship should travel if the fuel consumption in a voyage is to be halved.

C) the length of the voyage if the extra time on passage is six days when travelling at the reduced speed.

d) The amount of fuel required onboard before commencing on the voyage at the reduced speed.

Q7. A. What factors influence the frictional resistance of a ship and what formula is used to calculate the resistance?

B. A ship 120m long displaces 10500 tonne and has a wetted surface area of 3000m2. At 15 knots the shaft power is 4100KW, propulsive coefficient 0.6 and 55% of the thrust is available to overcome frictional resistance; calculate the shaft power required for a similar ship 140m long at the corresponding speed.  f= 0.42 and n = 1.825

Q10. A. If resistance S V2 and S 2/3, derive the Admiralty Coefficient formula. B. A ship 160m long, 22m beam and 9.2m draught has a block coefficient of 0.765. The Pitch of the propeller is 4m and when it turns at 96 rev/min the true slip is 33%, the wake fraction 0.335 and shaft power 2900 Kw.  Calculate the Admiralty Coefficient and the shaft power at 15 knots.

Q7. A. Explain the effect on GM during the filing of a double – bottom tank

B. An oil tanker 160m long and 22m beam floats at a draught of 9m in seawater. Cw is 0.865. The midships section is in the form of a rectangle with 1.2m radius at the bilges. A midships tank 10.5m long has twin longitudinal bulkheads and contains oil of 1.4 m3/t to a depth of 11.5m. The tank is holed to the sea for the whole of its transverse section.  Find the new draught.

Q6. A. Describe the stability requirements of a ship for dry-docking.

b) A ship of 12000 tonne displacement has a rudder 15 m2 in area, whose centre is 5 m below the waterline. The metacentric height of the ship is 0.3 m and the centre of buoyancy is 3.3 m below the waterline. When travelling at 20 knots the rudder is turned through 30 degree. Find the initial angle of heel if the force Fr perpendicular to the plane of the rudder is given by:

Fr=577Av2 Sin  a N

Allow 20% for the race effect. (10)

Q6. (A) Explain the concept of dynamical stability. (6)

b) A vessel of 8000 tonne displacement has 75 tonnes of cargo on the deck. It is lifted by a derrick whose head is 10.5m above the centre of gravity of the cargo and placed in the lower hold 9m below the deck and 14m forward of its original position. Calculate the shift in the vessel's centre of gravity from its original position when the cargo is: (10)

(i) just clear of the deck

(ii) at the derrick head

(iii) in its final position.

Q10. a) Explain the concept of dynamical stability. (6)

b) A ship of length 140m, Breadth of 18.5m, draught of 8.1m and a displacement of 17,025 tonnes in sea water, has a face pitch ratio of 0.673. The diameter of the Propeller is 4.8m. The results of the speed trial show that true slip may be regarded as constant over a range of 9 to 13 knots and is 30%, w = 0.5CB-0.05. If fuel used is 20t/day at 13 knots and fuel consumption/day varies as cube of speed of ship, determine the fuel consumption, when propeller runs at 110 rpm. (10)

Q9. A ship 120 meters long at the waterline has equidistantly spaced half-ordinates commencing from forward as follows 0,3.7,5.9,7.6,7.5,4.6, and 0.1 meters respectively. Find the area of the waterplane using Simpson’s Second rule and the TPC at this draft, Water density is 1.025 t/m3. (16)