Q1) A ship’s double bottom tank is divided by an oiltight centre girder to form equal port and starboard tanks.
The tanks are 16 m long and have a constant plan area defined by equidistant ordinates from the centre girder to the sides of the ship of:
5.5, 5.0, 4.3, 3.5 and 2.5 metres.
At a displacement of 11164 tonne in sea water of density 1025 kg/m3, the centre of gravity is 5.733 m above the keel and both tanks are partially full of oil having a density of 900 kg/m3 to a depth of 0.75 m remains constant.
Calculate the change in effective metacentric height. (16)
Q2) For a ship of 5000 tonne displacement floating in water having a density of 1025kg/m3 , the KG is 5.19 m.
A centre double bottom tank 12.2 m in length, 6.1 m wide and 1.6 m deep is now half filled with oil of density 900 kg/m3.
A mass of 100 tonne is lifted from a quayside by means of the ship’s lifting gear.
The top of the derrick is 18 m above the keel.
The KM in the final condition is 7.5 m.
Calculate EACH of the following:
(a) the final effective metacentric height; (13)
(b) the maximum outreach of the derrick, if the angle of heel is not to exceed 5o . (3)
Q4. The hydrostatic particulars given in Table Q3 are for a ship of length 150 m when floating in water of density 1025 kg/m3.
The ship floats in water of density 1015 kg/m3 with draughts of 7.6 m aft and 6.8 m forward.
(a) The displacement;
(b) The longitudinal position of the ship’s centre of gravity.
Q6. A ship of 8000 tonne displacement has a rudder area of 22 m2. The ship has a KM of 6.7 m, KG of 6.1 m and the centre of lateral resistance is 3.8m above the keel.
The maximum rudder angle is 35oand 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 = 580 Av2 sin α
Where: A = rudder area
V = ship speed in m/s
α = rudder helm angle
Calculate EACH of the following, when the vessel is travelling at 20 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 tums in a circle of 800 m diameter. (8)
Q5. A ship has a length of 130 m and floats in the sea water of density 1025 kg/m3. A model of this ship has a length of 5 m and a wetted surface area of 6 m2. The model has a total resistance of 45 N when towed at 1.85 m/s in fresh water of density 1000 kg/ m3.
(a) Using the data below, calculate EACH of the following:
(i) the ratio of residuary resistance to total resistance for the model; (5)
(ii) the ratio of residuary resistance to total resistance for the ship at the corresponding speed. (8)
(b) State why the two ratios should be different. (3)
The frictional coefficient for the model in fresh water is 1. 694
The frictional coefficient for the ship in sea water is 1. 418
Speed in m/s with the speed index (n) for ship and model 1.825
Q6. The following data were obtained during acceptance trials for a ship of 11650 tonne displacement: ship speed 16 knots
torque delivered to the propeller 340 kNm
propeller thrust 465 kN
propeller speed 1.85 rev/s
effective power 2900 kW
propeller efficiency 67%
apparent slip ratio 0.06
transmission losses 3%
(a) the pitch of the propeller; (3)
(b) the Taylor wake fraction; (4)
(c) the real slip ratio; (1)
(d) the thrust deduction fraction; (3)
(e) the quasi-propulsive coefficient; (2)
(f) the Admiralty Coefficient based upon shaft power. (3)
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