Q1) A ship 150 m in length floats in sea water of density 1025 kg/m3 . At the load draught, the immersed sectional areas of the main body of the ship are as given in Table Q1A.
Calculate EACH of the following:
(a) the displacement; (8)
(b) the longitudinal position of the centre of buoyancy from midships. (8)
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.
(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)
Q3) A ship of length 136 m has a light displacement of 4850 tonne with the longitudinal centre of gravity 1.64 m aft of midships.
Loading now takes place as shown in Table Q3.
Using the relevant data extracted from the hydrostatic curves provided on worksheet Q3, determine the final end draughts of the vessel in sea water of density 1025 kg/m3. (16)
Q5) The hull of a box shaped vessel is 80 m long and has a structural mass of 640 tonne uniformly distributed over its length.
Machinery of mass 200 tonne extends uniformly over the middle 20 m length of the vessel.
TWO holds extending over the extreme forward and aft 20 m lengths of the vessel EACH have 340 tonnes of cargo stowed uniformly over their lengths.
(a) Using graph paper, construct curves of EACH of the following:
(i) load per metre; (8)
(ii) shearing force. (4)
(b) Calculate the value of the maximum bending moment. (4)
Q6) The force acting normal to the centreline plane of a rudder is given by the expression:
F n =15.5 A V2 α newtons
Where: A = rudder area (m2)
V = ship speed (m/s)
α = rudder helm angle(degrees)
A ship travelling at a speed of 20 knots, has a rudder configuration as shown in Fig Q6.
The centre of effort for areas A1 and A2 are 32% of the width from their respective leading edges. The rudder angle is limited to 35ofrom the ship’s centreline.
Fig Q6
(a) the diameter of rudder stock required for a maximum allowable stress of 77MN/m2; (12)
(b) the drag component of rudder force when the rudder is put hard over at full speed. (4)
Q7) A ship of length 156 m and breadth of 24 m floats at a draught of 8.25 m in sea water of density 1025 kg/m3. In this condition the block coefficient (Cb) is 0.72.
A geometrically similar model, 6 m in length, gives a total resistance of 43.55 N when tested at a speed of 1.65 m/s in fresh water of 1000 kg/m3 at a temperature of 12oC.
The following data are also available:
Ship correlation factor = 1.23
Temperature correction = ±0.43% per oC.
Wetted surface area(S) = 2.57 √∆L (m2)
Frictional coefficient for the model in water of density 1000 kg/m3 at 15oC is 1.655
Frictional coefficient for the ship in water of density 1025kg/m3 at 15oC is 1.411
Speed in m/s with index (n) for ship and model 1.825
The ship is travelling at the corresponding speed to the model in sea water of density 1025 kg/m3 at a temperature of 150C.
Calculate the effective power of the ship. (16)
Q8) The following data applies to a ship operating on a particular voyage with a propeller of 6 m diameter having a pitch ratio of 0.9.
Propeller speed = 1.85 revs/s Real slip = 33% Apparent slip = 6% Shaft power = 11000kW Specific fuel consumption = 0.205 kg/kWhr
(a) the ship speed in knots; (3)
(b) the taylor wake fraction; (3)
(c) the reduced speed at which the ship should travel in order to reduce the voyage consumption by 30%; (2)
(d) the voyage distance if the voyage takes 30 hours longer at the reduced speed; (4)
(e) the amount of fuel required for the voyage at the reduced speed. (4)
Q9) (a) Show that, the position of the centre of pressure for a triangular plane apex down, with its edge in surface, is half of the depth of the plane below the surface. (4)
(b) A bulkhead 7.5 m deep, is in the form of a trapezoid, 13 m wide at the top and 10 m wide at the bottom.
The bulkhead has sea water of density 1025 kg/m3 on one side to a depth of 5 m.
(i) the load on the bulkhead; (8)
(ii) the position of the centre of pressure. (4)
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