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 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.
(a, 0,0. 15.09, 3.622. b, 100.6, 24.144, 115.6, 27.744)
2 A box barge 40 m long and 9 m wide floats in sea water at a draught of 3.5 m.
Calculate the Displacement of the barge. ( 1292 t)
3. A ship displaces 12240 m3 of sea water at a particular draught.
a) Calculate the displacement of the ship
b) How many tonnes of cargo would have to be discharged for the vessel to float at
the same draught in fresh water.
(12546 t, 306 T)
4. The water plane area of a ship is 1730m2, Calculate the TPC and the increase in
draught if a mass of 270 tonne is added to the ship. (17.73, 15.23 cm)
5. A ship 135 m long, 18m beam and 7.6 m draught has a displacement of 14000T.
The area of the load water plane is 1925 m2 and the area of the immersed midship
section is 130m2. Calculate (a) Cw, (b) Cm, (c) Cb, (d) Cp. ( 0.792, 0.950, 0.740, 0.778)
6. A box barge 65 m long and 12 m wide floats at a draught of 5.5 m in sea water.
Calculate (a) The displacement of the barge, (b) its draught in fresh water. (4397 t,
5.637 m)
7. 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. (96.62 t)
8. 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. (1246 T)
9. A ship displaces 9450 tonne and has a block coefficient of 0.7. The area of
immersed midship section is 106 m2. If beam = 0.13 * Length = 2.1* Draught, Calculate
the length of the ship and the Prismatic coefficient. (117.9, 0.738)
10. The equally spaced half ordinates of a watertight flat 27m long are 1.1, 2.7, 4.0,
5.1, 6.9 and 7.7 m respectively. Calculate the area of the flat. ( 263.4 m2)
11. The immersed cross sectional areas through a ship 180 m long at equal intervals
are 5, 118, 233, 291, 303, 304, 304 ,302, 283, 171 and 0 m2 respectively. Calculate the
displacement of the ship in sea water of 1.025 tonne / m3. ( 43019 t)
12. The TPC values for a ship at 1.2 m intervals of draught commencing at the 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. (13292 T)
13. The half ordinates of a cross section through a ship are as follows:
Calculate the area of the cross section to the 7.0 m waterline. (104.42 m2)
14. A Ship 180 m long has 1/2 widths of water-plane of 1, 7.5, 12, 13.5, 14, 14, 14,
13.5, 12, 7 and 0 m respectively. Calculate:
a) Water-plane area
b) TPC
c) Water -plane area coefficient. (3924m2, 40.22, 0.778)
15. The water-plane areas of a ship at 1.5 m intervals of draught commencing at the
keel are 865, 1735, 1965, 2040, 2100, 2145 and 2215 m2 respectively. Calculate the
displacement at 9.0 m draught. (17881 T)
16. A ship 140 m long and 18 m beam floats at a draught of 9m. 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. (16775T, 0.722, 0.944, 0.764).
17. A ship of 8500T displacement is composed of masses of 2000, 3000, 1000, 2000,
and 500 T at positions 2, 5 8, 10 and 14 m above the keel. Determine the height of the
centre of gravity of the ship above the keel. ( 6.353 m)
18. A ship of 6000T displacement is composed of masses of 300, 1200 and 2000 T at
distances 60, 35 and 11 m aft of midships, and masses of 1000, 1000 and 500 T at
distances of 15, 30 and 50 m forward of midships. Calculate the distance of the centre of
gravity of the ship from midships. (2.0 m)
19. A ship of 4000T displacement has its centre of gravity 15m aft of midships and 4 m
above the keel. 200 T of cargo are now added 45 m forward of midships and 12m above
the keel. Calculate the new position of centre of gravity. ( 0.714 m forward of midships,
4.381 m above keel)
20. A ship of 5000T displacement has a mass of 200 t on the fore deck 55m forward of
midships. Calculate the shift in cg of the ship if teh mass is moved to a position 8m
forward of midships. ( 1.88m aft)
21. A ship of 10,000T displacement has a mass of 60 T lying on the deck. A derrick
whose head is 7.5 m above the CG of the mass, is used to place the mass on the tank
top 10.5 m below the deck. Calculate the shift tin the vessel’s CG when the mass is
a) just clear of the deck
b) at the derrick head
c) in its final position. ( 0.045m up, 0.045 m up, 0.063m down)
