Download Wave Number - Ocean Energy Conversion - Old Exam Paper and more Exams Materials science in PDF only on Docsity!
CORK INSTITUTE OF TECHNOLOGY
INSTITIÚID TEICNEOLAÍOCHTA CHORCAÍ
Semester 1 Examinations 2010/
Module Title: Ocean Energy Conversion
Module Code: MECH 8015
School: Mechanical and Process Engineering
Programme Title: Bachelor of Science (Honours) in Sustainable Energy Technology Certificate in Energy & Environmental Engineering
Programme Code: ESENT_8_Y EENEN_8_Y
External Examiner(s): Prof. Eugene Coyle, Mr. Richard Linger Internal Examiner(s): Mr. Dermot O’Reilly
Instructions: Answer THREE questions out of FOUR
Duration: 2 Hours
Sitting: Winter 2010
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 marks)
(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:
w a kz sin^
g e kx t
Determine: (i) The circular frequency w, the wave number k , and the wavelength l. (3 marks) (ii) The maximum fluid velocities umax and wmax in the x and z directions in the fluid in the tank. (5 marks) (iii) The path of a fluid particle 0.4 m below the still water level. (2 marks) (iv) The phase and group velocities c and cg of the waves. (2 marks)
Q2. A spar buoy of uniform immersed diameter 7.2 m and 5220 t displacement floats in sea water of density 1025 kg/m^3. A mass of 100 t moved transversely through 20 m causes a heel of 1^0. (a) Determine the height of the centre of gravity of the spar buoy above the keel. (10 marks)
(b) A circular compartment of 7.0 m diameter whose base is 120 m above the keel is now partially filled to a depth of 20 m with sea water. Determine the new metacentric height. (10 marks)
