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Q13. Ship of length 168 m, floating in sea water of density 1025 kg/m³, has a displacement of 30750 tonne.

The waterplane is defined by equally spaced half widths as shown in Table Q1.

The following particulars are also available:

Center of buoyancy above the keel (KB) = 4.154 m

Center of gravity above the keel (KG) = 7.865 m

Center of lateral resistance above the keel = 4.665 m

The following tanks contain slack liquid as indicated:

Rectangular fresh water tank 10 m long and 8 m wide;

Rectangular fuel oil tank, containing fuel of relative density 0.875, 10 m long and 12 m wide, divided into two equal tanks by an oil-tight longitudinal bulkhead.

Calculate the angle to which the ship will heel when turning on a circular course of 400 m Diameter at a speed of 16 knots.

Q26. The righting moment for a ship in a particular condition of loading is known to be 44000 tonne meters at a displacement of 27500 tonne when heeled to an angle of 30° from upright.

Using the cross curves of stability provided on Worksheet Q2:

(a) Determine the KG of the ship for the condition of loading;

(b) Draw, on graph paper, a curve of statical stability for the load condition;

(c) From the statical stability curve drawn in Q2 (b), determine EACH of the following:

(i) The range of stability;

(ii) The righting moment at 20° heel.

Q3. A ship of length 130 m is loaded as shown in Table Q3(a).

Table Q3(a)

The following hydrostatic data in Table Q3(b) can be assumed to have a linear relationship between the draughts shown.

Table Q3(b)

Calculate the final end draughts.   (16)

Q5) A box shaped barge of uniform construction is 80 m long , 10 m wide and has a light displacement of 720 tonne. It is divided into three compartments by two transverse watertight bulkheads so that the end compartments are of equal length. The barge is loaded to draught of 6 m in water of density 1025 kg/m³ with cargo evenly distributed over the two end compartments.

The empty midship compartment, extending the full width and depth of the barge is now bilged and the draught increases to 8 m.

(a) Determine the length of the midship compartment. (3)

(b) For the original intact condition:

(i) plot curves of mass and buoyancy distribution; (5)

(ii) determine the longitudinal still water bending moment at midships. (4)

(c) Determine the longitudinal still water bending moment at midships for the final bilged condition. (4)

Q7. A ship of length 140 m and breadth of 22 m floats at a draught of 9 m in sea water of density 1025 kg/m³. In this condition the block coefficient (G) is 0.72.

A geometrically similar model, 5 m in length, gives a total resistance of 30.85 N when tested at a speed of 1.55 m/s in fresh water of 1000 kg/m³ at a temperature of 12^oC.

The following data are also available:
Ship correlation factor 1.22
Temperature correction ±0.43% per ^oC
Frictional coefficient for the model in water of density 1000 kg/m³ at 15^oC is 1.694

Frictional coefficient for the ship in water of density 1025 kg/m³ at 15^oC is 1.415

Speed in m/s with index (n) for ship and model 1.825
Wetted surface area (S) = 2.57  m².
Calculate the effective power of the ship at the speed corresponding to the model when the ship is travelling in sea water of density 1025 kg/m³ at a temperature of 15^oC.  (16)

Q14. The following data apply to a ship travelling at 16 knots:

Propeller speed = 1.8 rev/sec

Propeller pitch ratio = 0.9

Real slip ratio = 0.33

Taylor wake fraction = 0.30

Torque delivered to the propeller = 420 kNm

Propeller thrust = 560 kN

Quasi-propulsive coefficient (QPC) = 0.70

Transmission losses = 3%

Fuel consumption per day = 24.5 tonne

Calculate EACH of the following:

(a) The apparent slip ratio;

(b) The propeller diameter;

(c) The propeller efficiency;

(d) The thrust deduction fraction;

(e) The specific fuel consumption.