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CORK INSTITUTE OF TECHNOLOGY
INSTITIÚID TEICNEOLAÍOCHTA CHORCAÍ
Semester 1 Examinations 2012/
Module Title: Ocean Energy Conversion
Module Code: MECH 8015
School: Mechanical, Electrical and Process Engineering
Programme Title: Bachelor of Science (Honours) in Sustainable Energy Technology
Certificate in Energy & Environmental Engineering
MEng in Civil Engineering (Environment & Energy)
Programme Code: ESENT_8_Y
EENEN_8_Y
CENEN_9_Y
External Examiner(s): Mr Paul Kenny, Mr Conor Buckley
Mr P.J. Rudden, Prof. Padraic O’Donoghue
Internal Examiner(s): Mr Dermot O’Reilly
Instructions: Answer THREE questions out of FOUR.
Duration: 2 Hours
Sitting: Winter 2012
Requirements for this examination:
Note to Candidates: Please check the Programme Title and the Module Title to ensure that you have received the
correct examination paper.
If in doubt please contact an Invigilator.
Q1. (a) The 2-D velocity potential of a wave is given by:
A cosh k h z cos ky cos t
Where the y axis is in the still water plane and the z axis is vertically upward
Show that this velocity potential satisfies the Laplace equation (8)
(b) A tank 120 m long has a wave maker at one end that generates long-crested regular
waves. A generated regular deep water wave is generated with amplitude z= 0.18 m and
wave period T = 1.6 s. The velocity potential of the wave is given by:
sin
a kz w
g
e kx t
Determine:
(i) The circular frequency w, the wave number k , and the wavelength l.
(ii) The maximum fluid velocities umax and wmax in the x and z directions in the
fluid in the tank. (5)
(iii) The path of a fluid particle 0.4 m below the still water level. (2)
(iv) The phase and group velocities c and cg of the waves. (2)
Q2. (a) A box barge has a length of 60 m, a breadth of 15 m and a depth of 4 m.
Draw a metacentric diagram for the barge for a draft range of 0.0 m to 4.2 m at 0.6 m
intervals. (6)
(b) The barge in (a) floats at a draught of 3.25 m in water of density 1025 kg/m
3
. A mass
of 20 t on board is moved transversely across the deck through a distance of 12 m. The
movement of the mass results in an angle of heel of 7.
0 .
Determine the height of the centre of gravity of the barge above the keel. (6)
(c) A centreline double bottom tank in the barge in (a) is 40 m long and 12 m wide. This
tank is partially filled to a depth of 1.0 m with water of density 1025 kg/m
3 .
Determine the new GM. (8)
Formulae
1 cos(^ ) cos
1
o a c
o
w h
F
o cos(^ o )
c
F
G
w
cosh cos( )
o o
X G
^
cosh o a c
F
X G h G w
^
sinh sinh o a c
X X
l G G G
