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Q6. A. What is Prismatic Co-efficient (C_P). Derive the formula C_P = C_b/C_m , where  C_b= Co-efficient of fineness and C_m = midship section area co-efficient.

B. The length of a ship is 18 times the draught. while the breadth is 2.1 times the draught. At the load water plane, the water plane area co-efficient is 0.83 and the difference between the TPC in sea water and the TPC in fresh water is 0.7. Determine the length of the ship and the TPC in fresh water.

Q10. (a). Explain the various efficiencies associated with propeller and shafting arrangement.

(b) A propeller 6m diameter has a pitch ratio of 0.9, BAR 0.48 and, when turning at 110 rev/min, has a real slip of 25% and wake faction 0.30. If the propeller delivers a thrust of 300 KN and the propeller efficiency is 0.65. Calculate:

i. Blade area;

ii Ship speed;

iii. Thrust power;

iv Shaft power

v. Torque.

Q8. With the aid of sketches:
a. Explain various lines plan.
b. The half -breadths of waterplane of a ship of 120m length ad 15m breadth are given below:

Calculate i) Water plane area ii) TPC in salt water iii) Cw iv) LCF from Mid-ship

Q9. At a draught of 1.0 m in sea water of density 1025 kg/M3 the displacement of a ship is 900 tonne and the height of the centre of buoyancy above the keel (KB) is O.6m. Values of tonne per centimetre immersion (TPC) in sea water for a range of draughts are given in Table Q1.

(a) Calculate EACH of the following for a draught of 6. Om in sea water:

(î) the displacement; (ii) the height of the centre of buoyancy above the keel (KB).

(b) At a draught of 6.0 m, the height of the longitudinal metacentre above the keel (KML) is 128m and the second moment of area of the waterplane about a transverse axis through midships is 996 728 m4. The centre of flotation is aft of midships.

Calculate the distance of the centre of flotation (LCF) from midships.

Q10. A ship 120m long displaces 12000 tonne. The following data are available from trial results:

V (knots) 10  11  12  13  14  15
sp (kw) 880  1155  1520  2010  2670  3600
(a) Draw the curve of admiralty coefficients on a base of speed

(b) Estimate the shaft power required for a similar ship 140m long at 14 knots.

Q9. A. Explain what is meant by: i. Wave making resistance; ii. Frictional resistance; iii. Eddy-making resistance B. When a ship is 800 nautical miles from port, its speed is reduced by 20%, thereby reducing the daily fuel consumption by 42 tonne and arriving in port with 50 tonne on board. If the fuel consumption in t/h is given by the expression (0.136+0.001 V3) where V is the speed in knots, estimate: (i) The reduced consumption per day; (ii) The amount of fuel on board when the speed was reduced; (iii) The percentage decrease in consumption for the latter part of the voyage; (iv) The percentage increases in time for this latter period.

Q6. Explain why the bilging of empty double-bottom or deep tanks below the waterline leads to an increase in GM. B. A ship of 10,000 tonnes displacement has GM=0.5 metres. The period of roll in still water is 20 seconds. Find the new period of roll if a mass of 50 tonnes is discharged from a position 14 metres above the centre of gravity.

Q8. A. List the factors that determine the starting torque of the three-phase induction motor. How does this torque generally compare with the value of the rated torque?

B. A three phase induction motor is wound for four poles and is supplied from a 50 Hz system. Calculate.

i. The synchronous speed;

ii. The speed of the rotor when the slip is 4 per cent;

iii. The motor frequency when the speed of the rotor is 600 r.p.m

Q4. A. Explain why the GM must remain positive until the critical instant at which the ship takes the blocks overall. B. A Ship of 5000 tonnes displacement enters a dry dock trimmed 0.45m by the stern. KM=7.5m., KG=6.0m. MCTC=120 tonnes-m.  The centre of flotation is 60m. Frome aft. Find the effective metacentric height at the critical instant before the ship takes the blocks overall, assuming that the transverse metacentre rises 0.075m.

Q7. A 3-phase slip ring induction motor gives a reading of 60V across the slip rings on open circuit, when at rest with normal stator voltage supplied. the motor is star connected and has an impedance of 0.6 + j6 ohms/phase. find the rotor current and its power factor when the machine is 1. At standstill with slip-rings joined to a star connected starter with a phase impedance of 5+j4 ohm 2. Running normally with a 4% slip.

Q7.A. Explain how to distinguish between list and loll and describe how to return the ship to the upright in each case.

b) A ship of 12000 tonne displacement has a rudder 15 m2 in area, whose centre is 5 m below the waterline. The metacentric height of the ship is 0.3 m and the centre of buoyancy is 3.3 m below the waterline. When travelling at 20 knots the rudder is turned through 30 degree. Find the initial angle of heel if the force Fr perpendicular to the plane of the rudder is given by:

Fr=577Av2 Sin  a N

Allow 20% for the race effect. (10)

Q7. a) Describe the stability requirements of a ship for dry-docking. (6)

B. An oil tanker 160m long and 22m beam floats at a draught of 9m in seawater. Cw is 0.865. The midships section is in the form of a rectangle with 1.2m radius at the bilges. A midships tank 10.5m long has twin longitudinal bulkheads and contains oil of 1.4 m3/t to a depth of 11.5m. The tank is holed to the sea for the whole of its transverse section.  Find the new draught. (10)