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Q1) A ship of length 140 m displaces 13492 tonne when floating in sea water of density 1025kg/m³ .

The centre of gravity is 4.0 m above the centre of buoyancy an the waterplane is defined by the following equidistant half-ordinates given in Table Q1:

Calculate EACH of the following:

(a) the area of the waterplane; (3)

(b) the position of the centroid of the waterplane from midships; (3)

(c) the second moment of area of the waterplane about a transverse axis through the centroid; (5)

(d) the moment to change trim one centimetre (MCT 1cm). (5)

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

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)

Q4)  A ship of displacement 14000 tonne has a length 130 m, breadth 17 m, and even keel draught of 6.11 m in sea water of density 1025kg/m³ .

The area of the waterplane is 1600 m² and the second moment of area of the waterplane about a transverse axis through midships 1.25 x 106 m⁴ with the LCF at midships.

The ship has a full depth empty recatangular compartment having length 13 m and breadth 11 m.

The centre of the compartment is on the centreline of the ship 30 m forward of midships.

Calculate the end draughts after the compartment is bilged. (16)

Note: For the purposes of calculating the MCT 1cm it can be assumed that GML = BML

Q5) A rectangular oil barge of light displacement 640 tonne is 80 m long and 12 m wide.

The barge is divided by four transverse bulkheads into five compartments of equal length.

When compartments 2 and 4 contain equal quanities of oil and the other compartments are empty, the barge floats at a draught of 4 m in fresh water of density 1000 kg/m³ .

(a) Draw EACH of the following curves on a base of barge length:

(i) curve of loads; (4)

(ii) curve of shearing forces; (4)

(iii)  curve of bending moments; (5)

(b) State the magnitude and position of the maximum bending moment. (3)

Q6) (a) With the aid of an outline sketch explain EACH of the following:

(i) unbalanced rudder; (2)

(ii) semi-balanced rudder; (2)

(iii) balanced rudder. (2)

(b) State the principal advantage of fiiting a balanced rudder. (1)

(c) A ship travelling at full speed has its rudder put hard over to port, where it is held until the ship completes a full turning circle.

Describe, with the aid of a sketch, how the ship will heel from the upright condition during the manoeuvre. Illustrate the moments produced by the forces acting on the ship and the rudder. (9)

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)

Q9) An end bulkhead of an upper hopper tank is shown in Fig Q9.

The tank is tested by filling with fresh water of density 1000kg/m² through a filling pipe to a head of 2.5 m above the upper deck.

Calculate EACH of the following:

(a) the load on the bulkhead; (8)

(b) the distance to the centre of pressure from the upper deck. (8)