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Q4. a) Explain the significance of the root-mean-square value of an alternating current or voltage waveform. Define the form factor of such a waveform. (6)

b) A total load of 8000 kW at 0.8 power factor is supplied by two alternators in parallel. One alternator supplies 6000 kW at 0.9 power factor. Find the KVA rating of the other alternator and the power factor. (10)

Q6. (a). Explain the significance of the root- mean- square value of an alternating current or voltage waveform; Define the form factor of such a wave form.

(b). A total load of 8000 kW at 0.8 power factor is supplied by two alternators in parallel. One alternator supplies 6000 kW at 0.9 power factor. Find the kVA rating of the other alternator and the power factor.

Q7. With reference to A.C Distribution system:

A. Define power factor and explain the effects of low power factor.

B. 72 KVA transformer supplies a heating and lighting load of 12 KW at unity power factor and a motor load of 70 kVA at 0.766 (lagging) power factor; Calculate the minimum rating of the power-factor improvement capacitors which must be connected in the circuit the ensure that the transformer does not become overloaded.

Q6. For the network shown in Fig.Q1 calculate each of the following: (a) The current drawn from each battery; (b) The potential difference across the 40Ωresistor and across the 50Ωresistor; (c) The power dissipated in the 60Ωresistor.

Q9.  A. Explain how the voltage regulation of a transformer is defined. Is this quantity large or small for the iron-core transformer? Explain B. A single-phase transformer has 480 turns on the primary and 90 turns on the secondary. The mean length of the flux path in the core is 1.8m and the joints are equivalent to an air gap of 0.1mm. The value of the magnetic field strength for 1.1T in the core is 400 A/m, the corresponding core loss is 1.7W/Kg at 50Hz and the density of the core is 7800 Kg/m3

Q7. A. Derive an expression for the e.m.f induced in an a.c. generator. B. A 3000 KVA, 6 pole alternators runs at 1000 r.p.m in parallel with other machines on 3300 V bus-bars. The synchronous reactance is 25%. Calculate the synchronizing power for one mechanical degree of displacement and the corresponding synchronizing torque.

Q8. A ship 160m long and 8700 tonne displacement floats at a waterline with

While floating at this waterline, the ship develops a list of 10° due to instability. Calculate the negative metacentric height when the vessel is upright in this condition

Q7. A. Describe stability requirement for dry-docking. B. A ship of 8000 tonne displacement, 110m long, floats in sea water of 1.024t/m3 at draughts of 6m forward and 6.3 m aft. The TPC is 16, LCB 0.6 m aft of midships, LCF 3m aft of midships and MCT1cm 65 tonne m, the vessel now moves into fresh water of 1.000t/m3. Calculate the distance a mass of 50 tonne must be moved to bring the vessel to an even keel and determine the final draught.

Q6. The following data applies to a ship operating on a particular voyage with a propeller of 6 m diameter having a pitch ratio of 0.95:

Propeller speed = 1.8 revs/s

Real slip = 34%

Apparent slip = 7%

Shaft power = 10000 kW

Specific fuel consumption = 0.22 kg/kW-hr

Calculate EACH of the following:

(a) The ship speed in knots;

(b) The Taylor wake fraction;

(c) The reduced speed at which the ship should travel in order to halve the voyage consumption;

(d) The voyage distance if the voyage takes 3 days longer at the reduced speed;

(e) The amount of fuel required for the voyage at the reduced speed.

Q1. A RO-RO ferry of length 80 m has a displacement of 3800 tonne in sea water of density 1025 kg/m3 with BM = 3.4 m. The breadth of the ship at the waterline, between sections 3 and 7 is constant at 13 m. To increase stability, sponsons, 1.8 m deep and of constant plan area are to be fitted as shown in Fig Q1.

The sponsons extend over the midships length between sections 3 and 7, with sponson widths as shown in Table Q1.

For the new condition, there is no change in draught and the load waterline is at mid-depth of the sponson. Calculate the increase in BM due to the sponsons.

Q6. A. What factors influence the frictional resistance of a ship and what formula is used to calculate the resistance? B. A ship of 12000 tonne displacement has a rudder 15m2 in area, whose centre is 5m below the waterline.  The metacentric height of the ship is 0.3m and the centre of buoyancy is 3.3m below the waterline.  When travelling at 20 knots the rudder is turned through 30 .  Find the initial angle of heel if the force Fn perpendicular to the plane of the rudder is given by:  Fn=577 Av2 sin  N, Allow 20% for the race effect.

Q6. A propeller has a pitch of 4.57m. At 100rev/min the real slip is 20 percent and wake speed is I knot.  Calculate the apparent slip percentage