Q1. A ship of length 160 m displaces 22862 tonnes when floating at a draught of 8.526 m in sea water density 1025 kg/m3.
The waterplane area is defined by half breadths as given in Table Q1.
The following tanks are partially full of liquid as indicated:
ONE rectangular tank 10.2 m long and 6 m wide, containing fresh water of density 1000 kg/m3.
ONE rectangular tank 7.4 m long and 5 m wide containing oil fuel of density 890 kg/m3.
When a mass of 20 tonne is moved a distance of 22 m across the deck, a deflection of 71 mm is recorded on a pendulum of 9.2 m length.
The height of the centre of buoyancy above the keel (KB) may be determined using Morrish’s formula as given below:
KB =[5/6×d]-[∇/3×Aw ]
Calculate the KG of the ship in the above condition. (16)
Q3. The hydrostatic particulars given in Table Q3 are for a ship of length 160 m when floating in water of density 1025 kg/m3.
The ship floats in water of density 1010 kg/m3 with draughts of 7.8 m forward and 8.6 m aft.
Calculate EACH of the following:
(i) the displacement; (8)
(ii) the longitudinal position of ship’s centre of gravity. (8)
Q4. A box shaped vessel is 100 m long, 12 m wide and floats at an even keel draught of 5 m in water of density 1025 kg/m3 with a KG of 3.98 m.
A full width empty compartment at the forward end of the vessel is 10 m long and has a watertight flat 2.8 m above the keel.
This end compartment is now bilged below the flat only.
Calculate the new end draughts of the vessel. (16)
Note: The KB in the bilged condition may be taken as half the new mean draught.
Q5. A box barge of 88 m length, 12 m breadth and 6 m depth has a hull mass of 600 tonne evenly distributed throughout its length.
Bulkheads located 4 m from the barge ends, form peak tanks which may be used for ballast.
The remainder of the barge length is divided by 4 transverse bulkheads into 5 holds of equal length.
The holds are full of bulk cargo having a stowage rate 1.6 m3/tonne.
The peak tanks are empty.
(a) Calculate the midship bending moment during discharge when both end holds are half empty. (8)
(b) The midship bending moment is to be restricted to a maximum of 50 MNm (Sagging) during unloading.
Calculate the minimum depth of sea water ballast of density 1025 kg/m3, which must be added to the peak tanks to allow complete discharge of the end holds. (8)
Q6. The force acting normal to the plane of a rudder is given by the expression:
Fn = 20.17 Av2α newtons Where: A= rudder area (m2) v = ship speed (m/s) α = rudder angle (degrees
A manoeuvrability specification for a ship that requires a constant transverse rudder force of 75 kN is generated when the angle of helm is 35o with the ship travelling at a speed of 5 knots.
(a) Determine suitable dimensions for a rectangular rudder having a depth to width ratio of 1.6. (6)
(b) The rudder stock is designed to have a diameter of 320 mm with the allowable shear stress in the material limited to 70 MN/m2 at its service speed of 15 knots.
At the maximum helm angle of 35o the centre of effort is 34% of the rudder width from the leading edge of the rudder.
Calculate the distance of the axis of rotation from the leading edge of the rudder so that the stock is not overstressed at the service speed. (10)
Q7. A ship of length 160 m, breadth 28 m and a block coefficient of 0.7, floats at a draught of 12 m in sea water of density 1025 kg/m3.
A geometrically similar model 8 m in length, when tested at a speed of 1.6 m/s in fresh water of density 1000 kg/m3 gives a total resistance of 82 N.
appendage allowance = 6 %
weather allowance = 14 %
quasi-propulsive coefficient (QPC) = 0,71
Calculate the service delivered power for the ship at the corresponding speed to that of the model. (16)
Note:
The frictional coefficient for the model in fresh water is 1.69
The frictional coefficient for the ship in sea water is 1.42
Speed is in m/s with index n = 1.825
Wetted surface area (m2) = 2.6 √∆L
Q8. A ship of 25120 tonne displacement has a length of 140 m, breadth of 25 m and floats at a draught of 10 m when in sea water of density of 1025 kg/m3.
The ship’s propeller has a diameter of 6 m with a pitch ratio of 0.85. When the propeller is operating at 1.85 rev/s, the real slip is 32 % and the thrust power is 6200 kW.
The thrust power is reduced to 5000 kW and the real slip is increased to 34 %.
Assuming that the thrust power is proportional to (speed of advance)3, calculate EACH of the following for the reduced power:
(a) ship speed; (11)
(b) the propeller speed of rotation; (3)
(c) the apparent slip. (2)
Note: Wake fraction= 0.5 Cb – 0.05
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