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Q12. A vessel of 10000 tonne displacement floats in sea water of density 1025 kg/m³.

A wing deep tank on the vessel is 16 m long, 8 m deep and has a constant plan area formed by the transverse end bulkheads and a longitudinal bulkhead, parallel to and 4 m from the centerline of the ship. The equally spaced transverse ordinates defining the plan area are as follows:

4.00, 3.80, 3.50, 3.00 and 2.50 meters.

The base of the tank is 2.0 m above the keel.

With the deep tank full of oil of density 900 kg/m³, the ship floats upright with a metacentric height of 0.725 m.

Half of the oil in the deep tank is now removed.

Calculate EACH of the following, assuming the KM remains constant at 5.125 m:

(a) The final effective metacentric height;

(b) The final angle of heel.

Q13. A coastal tanker has a breadth of 16 m and in the lightship condition, has a displacement of 2600 tonne and a KG of 3.34 m.

The vessel is now loaded as indicated in Table Q2.

The following tanks are partially full with liquid as follows:

One rectangular slop tank 10 m long and 8 m wide, containing fresh water of density 1000 kg/m³ with oil of density 900 kg/m³ floating on top;

Four full width rectangular tanks, carrying crude oil of density 952 kg/m³, each 20 m long with centerline oil-tight bulkheads.

In this condition, when floating in sea water of density 1025 kg/m³ the height of the transverse metacenter above the keel (KM) is 5.286 m.

(a) Calculate the effective metacentric height in the loaded condition.

(b) (i) Using Worksheet Q2, draw the curve of statical stability for the loaded condition.

(ii) From the curve drawn in Q2 (b) (i), determine the range of stability

Q3) A ship of 125 m length has the following particulars when floating in sea water of density 1025 kg/m³ .

Displacement  = 11923 tonne

Draught aft  = 7.244 m

Draught forward  = 6.844 m

Longitundinal metacentric height (GML)  = 130 m

Longitudinal centre of floating (LCF)  = 2.5 m aft of midships

Tonne per centimetre immersion (TPC)   = 18.5

TWO tanks, EACH contanining a substantial quantity of water ballast, are situated with their centres of gravity 50 m aft of midships and 25 m forward of midships respectively.

The vessel is required to enter dock with a draught aft of 7.0 m and a trim of 0.6 m by the stern.

Calculate the mass of ballast to be removed from each tank. (16)

Q6. The force acting normal to the plane of a rudder is given by the expression:

Fn = 20.2 A V² a newtons

Where :         A = rudder area (m²)

V = ship speed (m/s)

a = rudder angle (degrees)

A manoeuvrability specification for a ship that requires a transverse rudder force of 92 kN is generated when the angle of helm is 35^o with the ship travelling at 5 knots.

(a) Determine suitable dimensions for a rectangular rudder having an aspect ratio (depth to width ratio) of 1.5.  (6)

(b) The rudder stock is designed to have a diameter of 360 mm with the allowable shear stress in the material limited to 70 MN/m² at its service speed of 16 knots. At the maximum helm angle of 35^o, the centre of effort is 35% of the rudder width from the leading edge of the rudder.

Calculate the maximum 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 140 m long has a total displacement of 21750 tonne in sea water of density 1025 kg/m³. To maintain a speed of 16.5 knots in the above condition on trials, a shaft power of 7800 kW is required.

SCF for trial condition = 1.08

SCF for service condition = 1.24

Quasi-propulsive coefficient (QPC) = 0.69

Transmission losses = 3%

Wetted surface area (m2) = 2.57

Using the information given above, calculate the shaft power required in service for a geometrically similar ship of 26750 tonne load displacement operating at the corresponding speed. (16)

Note: The frictional coefficient for the 21750 tonne ship in sea water is 1.415

The frictional coefficient for the 26750 tonne ship in sea water is 1.413

Speed is in m/s and speed index n = 1.825.

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 C_b – 0.05