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Q15. A ship 160 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;

(b) The longitudinal position of the center of buoyancy from midships.

Q2) A ship of 10000 tonne displacement floats in sea water of density 1025 kg/m³ at a draught of 6 m.

A rectangluar tank 10 m long and 8 m wide is partially full of oil fuel having a density of 900 kg/m³.

In this condition, the KG of the ship is 6.25 m.

Other hydrostatic data for the above condition are:

Centre of buoyancy above the keel (KB) = 3.325 m

Transverse metacentre above the centre of buoyancy (BM) = 4.865 m

Tonnes per centimetre immersion (TPC)  =  20.5

Calculate the change in effective metacentric height when a rectangular tank 12 m long 10 m wide and 6 m deep, with its base 1 m above the keel, is filled to depth of 5 m with sea water ballast. (16)

Note : Assume the ship to be wall-sided over the affected range of draught

Q4. A box shaped vessel 100 m long and 10 m wide floats at an even keel draught of 4 m in sea water of density 1025 kg/m³ with a KG of 5 m.

A full width, empty compartment has its after bulkhead 20 m forward of midships and its forward bulkhead 30 m forward of midships.

Calculate the end draughts of the vessel if this compartment is bilged. (16)

Q5. A uniformly constructed box shaped vessel of length 80 m and breadth 12 m has an even keel draught of 2 m when floating in the light condition in sea water of density 1025 kg/m³. The vessel has five holds of equal length and is to be loaded with 7000 tonne of cargo, with equal quantities in each of the centre and end holds, and the balance equally distributed in No.2 and No.4 holds.  The cargo in all holds will be trimmed level.

Calculate EACH of the following:

(a) The maximum amount to be loaded in the centre and end holds in order that a maximum hogging bending moment amidships of 4000 tm will not be exceeded.  (10)

(b) The resulting shear force at each of the bulkheads. (6)

Q7) The following values of effective power (naked hull) refer to a ship which is to have a service speed of 16.25 knots.

The following data also apply:

Appendage allowance  = 7%

Weather allowance  = 14%

Quasi propulsive coefficient  =0.71%

Transmission losses  =3%

Engine mechancial efficiency =86%

Ratio of service indicated power to installed machinery indicated power = 0.9.

Determine EACH of the following:

(a) the indicated power of the engine to be installed; (8)

(b) the speed obtained if all the available power of the engine is used:

(i) when the ship is running on acceptance trial in calm conditions; (4)

(ii) when operating under actual service conditions. (4)

Q8. A model propeller of 0.3 m diameter and 0.25 m pitch is tested in fresh water of density 1000 kg/m³. At a speed of advance of 1.8 m/s and a rotational speed of 10.0 revs/s, the shaft torque is 12 Nm  and  the thrust developed is 260 N.

A geometrically similar ship’s propeller 5.4 m in diameter, is operating in sea water of density 1025 kg/m³ at corresponding linear and rotational speeds.

(a) For the ship’s propeller, calculate EACH of the following:

(i) Revolution per second. (1)

(ii) Speed of advance. (1)

(iii) Real slip. (3)

(iv) Delivery power. (3)

(v) Efficiency; (4)

(vi) Calculate the hull efficiency when the propeller is operating on a vessel at a Taylor wake fraction of 0.26 and a thrust deduction fraction of 0.22. (4)

Note: For geometrically similar propellers of corresponding speeds it can be assumed:

Linear speed is proportional to (diameter)^1/2

Rotational speed is proportional to (diameter)^-1/2

Thrust is proportional to (diameter)³

Torque is proportional to (diameter)⁴.

Q4) With reference to the inclining experiment:

(a) state the purpose of the experiment and when the experiment should be performed during the life of a ship; (2)

(b) explain the procedure immediately prior to the experiment; (4)

(c) describe the procedure for the experiment; (4)

(d) list SIX precautions to ensure acceptable accuracy of results. (6)