QUESTION

1. A rectangular double bottom tank is 20 m long. 12 m wide and 1.5 m deep, and is
full of sea water having a density of 1.025 tonne/m3 .
Calculate the pressure in kN/m2 and the load in MN on the top and bottom of the
tank if the water is:
(a) at the top of the tank
(b) 10 m up the sounding pipe above the tank top.

2. A rectangular bulkhead is 10 m wide and 8 m deep. It is loaded on one side only

with oil of relative density 0.8.
Calculate the load on the bulkhead if the oil is:
(a) just at the top of the bulkhead.
(b) 3 m up the sounding pipe.

3. A bulkhead 9 m deep is supported by vertical stiffeners 750 mm apart. The

bulkhead is flooded to the top edge with sea water on one side only. Calculate:
(a) shearing force at top
(b) shearing force at bottom
(c) position of zero shear.

4. A double bottom tank is 1.2 m deep and has a sounding pipe extending 11 m
above the tank top. The tank is filled with oil (rd 0.89) to the top of the sounding
pipe the double bottom floors are spaced 750 mm apart and are connected to the
tank top by riveted angles, the rivets having a pitch of 7 diameters. If the
maximum allowable stress in the rivets is 30 MN/m 2 , calculate the pressure in
kN/m2 on the outer bottom and the diameter of the rivets.

5. A vertical bulkhead 9 m wide and 8 m deep has sea water on one side only t a
depth of 6 m. Calculate the pressure in kN/m 2 at the bottom of the bulkhead and
the load on the bulkhead.

6. A bulkhead is in the form of a trapezoid 9 m wide at the deck, 5 m wide at the

bottom and 8 m deep. Find the load on the bulkhead if it has oil (rd 0.85) on one
side only:
(a) to a depth of 6 m
(b) with 4 m head to the top edge.

7. The end bulkhead of an oil fuel bunker is in the form of a rectangle 10 m wide and
12 m high. Find the total load and the position of the centre of pressure relative to
the top of the bulkhead if the tank is filled with oil (rd 0.9):
(a) to the top edge
(b) with 3 m head to the top edge
8. A triangular bulkhead is 7 m wide at the top and has a vertical depth of 8 m.
Calculate the load on the bulkhead and the position of the centre of pressure if the
bulkhead is flooded with sea water on only one side:
(a) to the top edge
(b) with 4 m head to the top edge.

9. A watertight bulkhead is 8 m high and is supported by vertical stiffeners 700 mm

apart, connected at the tank top by brackets having 10 rivets 20 mm diameter. The
bulkhead is flooded to its top edge with sea water. Determine:
(a) shearing force at top of stiffeners,
(b) shear stress in the rivets,
(c) position of zero shear.

10. A ship 135 m long. 18 m beam and 7.6 m draught has a displacement of 14000
tonne. The area of the load water plane is 1925 m 2 and the area of the immersed
midship section 130 m2 Calculate (a) Cw; (b) Cm; (c) Cb; (d) Cp.

11. A ship of 5000 tonne displacement, 95 m long, floats at a draught of 5.5 m.

Calculate the wetted surface area of the ship:
(a) Using Denny’s formula
(b) Using Taylor’s formula with c = 2.6

12. A cylinder 15 m long and 4 outside diameter floats in sea water with its axis in the
waterline. Calculate the mass of the cylinder.

13. A vessel 40 m long has a constant cross-section in the form of a trapezoid 10 m

wide at the top, 6 m wide at the bottom and 5 m deep. It floats in sea water at a
draught of 4 m. Calculate its displacement.

14. The waterplane areas of a ship at 1.25 m intervals of draught, commencing at the
7.5 m waterline, are 1845, 1690, 1535, 1355 and 1120 m2. Draw the curve of
tonne per cm immersion and determine the mass which must be added to increase
the mean draught from 6.10 m to 6.30 m.

15. The length of a ship is 18 times the draught, while the breadth is 2.1 times the
draught. At the load waterplane, the waterplane area coefficient 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.

16. A ship of 14000 tonne displacement, 130 m long, floats at a draught of 8 m.

Calculate the wetted surface area of the ship using:
(a) Denny’s formula
(b) Taylor’s formula with c = 2.58.
17. The wetted surface area of a ship is twice that of a similar ship. The displacement
of the latter is 2000 tonne less than the former. Determine the displacement of the
latter.

18. The TPC values for a ship at 1.2 m intervals of draught commencing at he keel,
are 8.2, 16.5, 18.7, 19.4, 20.0, 20.5 and 21.1 respectively. Calculate the
displacement at 7.2 m draught.

19. A fore peak bulkhead is 4.8 m deep and 5.5 m wide at the deck. At regular
intervals of 1.2 m below the deck, the horizontal widths are 5.0, 4.0, 2.5 and 0.5
m respectively. The bulkhead is flooded to the top edge with sea water on one side
only. Calculate:
(a) area of bulkhead
(b) load on bulkhead
(c) position of centre of pressure

20. A ship 180 m long has ½ widths of waterplane of 1, 7.5, 12, 13.5,14, 14, 14, 13.5,
12, 7 and 0 m respectively. Calculate:
(a) waterplane area
(b) TPC
(c) Waterplane area coefficient.

21. A ship 140 m long and 18 m beam floats at a draught of 9 m. The immersed cross-
sectional areas at equal intervals are 5, 60, 116, 145, 152, 153, 153, 151, 142, 85
and 0 m2 respectively.
Calculate:
(a) displacement
(b) block coefficient
(c) midship section area coefficient
(d) prismatic coefficient.

22. The ½ ordinates of a waterplane 120 m long are as follows:

Section AP ½ 1 1 ½ 2 3 4 5 6 7 8 8 ½ 9 9 ½ FP
½ ord 1.2 3.5 5.3 6.8 8.0 8.3 8.5 8.5 8.5 8.4 8.2 7.9 6.2 3.5,0m
Calculate:
(a) waterplane area
(b) distance of centroid from midships.

23. The TPC values of a ship at 1.5 m intervals of draught, commencing at the keel,
are 4.0, 6.1, 7.8, 9.1, 10.3, 11.4 and 12.0 m respectively. Calculate at a draught of
9 m:
(a) displacement
(b) KB
24. The widths of a deep tank bulkhead at equal intervals of 1.2 m commencing at the
top, are 8.0, 7.5, 6.5, 5.7, 4.7, 3.8 and 3.0 m. Calculate the load on the bulkhead
and the positon of the centre of pressure, if the bulkhead is flooded to the top edge
with sea water on one side only,

25. A ship of 6000 tonne displacement is composed of masses of 300, 1200 and 2000
tonne at distances 60, 35 and 11 m aft of midships, and masses of 1000, 1000 and
500 tonne at distances 15, 30 and 50 m forward of midships. Calculate the
distance of the centre of gravity of the ship from midships.

26. A ship of 4000 tonne displacement has its centre of gravity 1.5 m aft of midships
and 4 m above the keel. 200 tonne of cargo are now added 45 m forward of
midships and 12 m above the keel. Calculate the new position of the centre of
gravity.

27. A ship of 10000 tonne displacement has a mass of 60 tone lying on the deck. A
derrick, whose head is 7.5 m above the centre of gravity of the mass, is used to
place the mass on the tnnk top 10.5 m below the deck. Calculate the shift in the
vessel’s centre of gravity when the mass is:
(a) just clear of the deck
(b) at the derrick head
(c) in its final position

28. A ship has 300 tonne of cargo in the hold, 24 m forward of midships. The
displacement of the vessel is 6000 tonne and its centre of gravity is 1.2 m forward
of midships.
Find the new position of the centre of gravity if this cargo is moved to an after
hold, 40 m from midships.

29. An oil tanker of 17000 tonne displacement has its centre of gravity 1 m aft of
midships and has 250 tonne of oil fuel in its forward deep tank 75 m from
midships.
This fuel is transferred to the after oil fuel bunker whose centre is 50 m from
midships.
200 tonne of fuel from the after bunker is now burned.
Calculate the new position of the centre of gravity:
(a) after the oil has been transferred
(b) after the oil has been used.

30. A ship of 3000 tonne displacement has 500 tonne of cargo on board. This cargo is
lowered 3 m and an additional 500 tonne of cargo is taken on board 3 m vertically
above the original position of the centre of gravity. Determine the alteration in
position of the centre of gravity.
31. A ship of 10000 tonne displacement has its centre of gravity 3 m above the keel.
Masses of 2000, 300 and 50 tonne are removed from positions 1.5, 4.5, and 6 m
above the keel. Find the new displacement and position of the centre of gravity.

32. A vessel of constant triangular cross-section has a depth of 12 m and a breadth at

the deck of 15 m.
Calculate the draught at which the vessel will become unstable if the
centre of gravity is 6.675 m above the keel.

33. A ship of 12000 tonne displacement has a second moment of area about the
centerline of 72 x 103 m4. If the metacentric height is – 0.05 m, calculate the angle
of loll.

34. A vessel of 10000 tonne displacement has a second moment of area of waterplane
about the centerline of 60 x 10 3 m4. The centre of buoyancy is 2.75 m above the
keel. The following are the disposition of the masses on board the ship.
4000 tonne 6.30 m above the keel
2000 tonne 7.50 m above the keel
4000 tonne 9.15 m above the keel

Calculate the metacentric height.

35. A vessel of constant triangular cross-section is 9 m wide at the deck and has a
depth to deck of 7.5 m. Draw the metacentric diagram using 0.5 m intervals of
draught up to the 3.0 m waterline.

36. An inclining experiment was carried out on a ship of 8000 tonne displacement. A
mass of 10 tonne was moved 14 m across the deck causing a pendulum 8.5 m long
to deflect 110 mm. The transverse metacentre was 7.15 m above the keel.
Calculate the metacentric height and the height of the centre of gravity above the
keel.

37. A ship of 5000 tonne displacement has a rectangular double bottom tank 9 m wide
and 12 m long, half full of sea water. Calculate the virtual reduction in metacentric
height due to free surface.

38. A ship of 8000 tonne displacement has its centre of gravity 4.5 m above the keel
and transverse metacentre 5.0 m above the keel when a rectangular tank 7.5 m
long and 15 m wide contains sea water. A mass of 10 tonne is moved 12 m across
the deck. Calculate the angle of heel:
(a) if there is no free surface of water.
(b) If the water does not completely fill the tank.

39. A ship 150 m long has draughts of 7.70 m forward and 8.25 m aft, MCTI cm 250
tonne m, TPC 26 and LCF 1.8 m forward of midships. Calculate the new draughts
after the following masses have been added:
 50 tonne, 70 m aft of midships
170 tonne, 36 m aft of midships
100 tonne, 5 m aft of midships
130 tonne, 4 m forward of midships
40 tonne, 63 m forward of midships

40. A ship 125 m long has a light displacement of 4000 tonne with LCG 1.60 m aft of
midships. The following items are now added:

Cargo 8500 tonne Lcg 3.9 m forward of midships

Fuel 1200 tonne Lcg 3.1 m aft of midships
Water 200 tonne Lcg 7.6 m aft of midships
Stores 100 tonne Lcg 30.5 m forward of midships.

At 14000 tonne displacement the mean draught is 7.80 m, MCTI cm 160

tonne m, LCB 2.00 m forward of midships and LCF 1.5 m aft of midships.

41. A box barge 30 m long and 8 m beam floats at a level keel draught of 3 m and has
a mid-length compartment 6 m long. Calculate the new draught if this
compartment is bilged:
(a) with µ = 100%
(b) with µ = 75%

42. A ship consumes 360 tonne of fuel, stores and water when moving from sea water
of 1.025 t/m3 into fresh water of 1.000 t/m3 and on arrival it is found that the
draught has remained constant.
Calculate the displacement in the sea water.

43. A box barge 60 m long and 10 m wide floats at an even keel draught of 4 m. It has
a compartment amidships 12 m long. Calculate the new draught if this
compartment is laid open to the sea when:
(a) µ is 100%
(b) µ is 85%
(c) µ is 60%

44. A 6 m model of a ship has a wetted surface area of 8 m 2 . When owed at a speed
of 3 knots in fresh water the total resistance is found to be 38 N.
If the ship is 130 m long, calculate the effective power at the corresponding
speed.

45. A ship is 125 m long, 16 m beam and floats at a draught of 7.8 m. Its block
coefficient is 0.72. Calculate the power required to overcome frictional resistance
at 17.5 knots if n = 1.825 and f = 0.423. Use Taylor’s formula for wetted surface,
with c = 2.55.
46. The residuary resistance of a one-twentieth scale model of a ship in sea water is 36
N when towed at 3 knots. Calculate the residuary resistance of the ship at its
corresponding seed and the power required to overcome residuary resistance at
this speed.

47. A 6 m model of a ship has wetted surface area of 7 m 2 , and when towed in fresh
water at 3 knots, has a total resistance of 35 N. Calculate the effective power of
the ship, 120 m long, at its corresponding speed.
n = 1.825: f from formula : SCF = 1.15

48. A ship of 15000 tonne displacement has a fuel coefficient of 62500. Calculate the
fuel consumption per day at 14 ½ knots.

49. The daily fuel consumption of a ship at 15 knots is 40 tonne. 1100 nautical miles
from port it is found that the bunkers are reduced to 115 tonne. If the ship reaches
port with 20 tonne of fuel on board, calculate the reduced speed and the time taken
in hours to complete the voyage.

50. A ship uses 23 tonne of fuel per day at 14 knots. Calculate the speed if the
consumption per day is:
(a) increased by 15%
(b) reduced by 12%
(c) reduced to 18 tonne.

51. The total resistance of a ship at 13 knots is 180 kN, the QPC is 0.70, shaft losses
5% and the mechanical efficiency of the machinery 87%.
Calculate the indicated power.

52. A ship travels at 14 knots when th propeller, 5 m pitch, turns at 105 rev/min. If the
wake fraction is 0.35, calculate the apparent and real slip.

53. A propeller of 5.5 m diameter has a pitch ratio of 0.8. When turning at 120
rev/min, the wake fraction is found to be 0.32 and the real slip 35%.
Calculate the ship speed, speed of advance and apparent slip.

54. A ship of 15000 tone displacement has an Admiralty Coefficient, based on shaft
power, of 420. The mechanical efficiency of the machinery is 83%, shaft losses
6%, propeller efficiency 65% and QPC 0.71. At a particular speed the thrust
power is 2550 kW.

55. The pitch of a propeller is measured by means of a batten and cord. The horizontal
ordinate is found to be 40 cm while the vertical ordinate is 1.15 m at a distance of
2.6 m from the centre of the boss. Calculate the pitch of the propeller and the
blade width at that point.
56. A ship 150 m long and 8.5 m draught has a rudder whose area is one sixtieth of the
middle-line plane and diameter of stock 320 mm. Calculate the maximum speed at
which the vessel may travel if the maximum allowable stress is 70 MN/m 2 , the
centre of stock 0.9 m from the centre of effort and the maximum rudder angle is
35˚.

57. A block of wood of uniform density has a constant cross section in the form of a
triangle, apex down. The width is 0.5 m and the depth 0.5m. It floats at a draught
of 0.45 m. Calculate the metacentric height.

58. The ½ ordinates of a waterplane 96 m long are 1.2, 3.9, 5.4, 6.0, 6.3, 6.3, 5.7, 4.5,
2.7 and 0 m respectively. A rectangular double bottom tank with parallel sides is
7.2 m wide, 6 m long and 1.2 m deep. When the tank is completely filled with oil
of 1.15 m3 / tone the ship’s draught is 4.5 m. Calculate the draught when the
sounding in the tank is 0.6m.

The End