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Q1. A vessel of SWATH (small waterplane area twin hull) design, has the following hydrostatic particulars when floating in water of density 1025 kg/m³:

Displacement = 1390 tonne

centre of buoyancy above the keel (KB) = 2.744 m

centre of gravity above the keel (KG) = 6.37 m

The distance between the centretines of each hull is 12 m and the half breadths of each hull, measured at equal intervals along the 72 m length of waterptane, are as shown in Table Q1.

Calculate the transverse metacentric height of the vessel in the above condition. (16)

Q2. (a) Sketch and clearly label a statical stability curve for a vessel with its centre of gravity on the centretine but having a negative metacentric height when in the upright condition.  (3)

(b) The ordinates for part of a statical stability curve for a bulk carrier at a displacement of 18000 tonne are given in Table Q2.

The ship has a hold 40 m long and 30 m wide which contains bulk grain towed at a stowage rate of 1.25 m3/tonne.

During a heavy roll, the grain shifts so that the level surface is lowered by 1.5 m on one side and raised by 1.5 m on the other side.

(i) Plot the amended statical stability curve for the ship. (12)

(ii) Determine the angle of list due to the cargo shift, from the curve. (1)

Q3. A ship 150 m in length displaces 14000 tonne and floats at draughts of 6.25 m Forward and 6.6 m aft. The longitudinal metacentric height Is 165 m, the Centre of flotation is 1.8 m aft of midship  and the TPC is 22. The vessel is required to enter dock with draught of 6.5 m and a trim of 1m by stern.

Calculate EACH Of the following

(a) mass of ballast to be discharged; (6)

(b) the distance its centre of gravity from midships.  (10)

Q5. A rectangular oil barge of light displacement 300 tonne is 60 m tong and 10 m wide. The barge is divided by four transverse bulkheads into five Compartments of equal length.

When compartments 2 and 4 contain equal quantities of oil and the other compartments are empty, the barge floats at a draught of 3 m in fresh water of density 1000 kg/m³.

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

(i) curve of toads; (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 single screw vessel with a service speed of 16 knots is fitted with an unbalanced rectangular rudder 6 m deep and 3.5 m wide with an axis of rotation 0.25 m forward of the leading edge. At the maximum designed rudder angle of 350 the centre of effort is 30% of the rudder width from the leading edge.

The force on the rudder normal to the plane of the rudder is given by the

expression:

Where:

20.2 A v2 a newtons

A rudder area (m2)

v ship speed (m/s)

- rudder helm angle (degrees)

The maximum stress on the rudder stock is to be Limited to 70 MN/m².

Calculate EACH of the following:

(a) the minimum diameter of rudder stock required; (9)

(b) the percentage reduction in rudder stock diameter that would be achieved  (7)

if the rudder was designed as a balanced rudder, with the axis of rotation 0.85 m from the leading edge.

Q7. The following data refer to two geometrically similar ships:

Fig Q7 shows the results of a progressive speed trial for ship A

Calculate the shaft power required for Ship B travelling as a speed of 18.5 knots, given that the propulsive coefficient for both ship is 0.6. (16)

Note: friction coefficient to be used with speed in m/s

Q8. A vessel of 10500 tonne displacement is fitted with a propeller Of 5.5 m diameter

and pitch ratio 0.9.

During a fuel consumption trial of 6 hours duration, a steady shaft speed of 1.8 revs/sec was maintained and 7.54 tonne of fuel was consumed.

The following results were also recorded:

real Slip ratio = 0.34

Taylor wake fraction = 0.32

shaft power = 6050 kW

transmission losses = 3%

quasi-propulsive coefficient (QPC) = 0.71

propeller thrust = 680 kN

Calculate EACH of the following:

(a) the speed of the ship; (4)

(b) the apparent Slip ratio; (1)

(c) the propeller efficiency; (3)

(d) the thrust deduction fraction; (3)

(e) the fuel coefficient; (3)

(f) the specific fuel consumption.  (2)

Q9. (a) Show that the position of the centre of pressure, for a circular plane with its edge in surface, is 5/8 of the depth of the plane below the surface. (6)
(b) A circular Cross-flooding duct between port and starboard wing tanks is 400 mm in diameter and is closed by a gate valve. One tank is empty and the other has sea water of density 1025 kg/m^3' to a head of 1 m above the duct.
Calculate EACH of the following:
(i) the load on the gate valve; (4)
(ii) the position of the centre of pressure on the valve. (6)