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CORK INSTITUTE OF TECHNOLOGY
INSTITIÚID TEICNEOLAÍOCHTA CHORCAÍ
Semester 2 Examinations 2011
Module Title: Introductory Thermofluids
Module Code: MECH
School: Mechanical & Process Engineering
Programme Title: Bachelor of Engineering (Honours) in Mechanical Engineering Bachelor of Engineering (Honours) in Biomedical Engineering
Programme Code: EMECH_8_Y EBIOM_8_Y EOMNI_8_Y
External Examiner(s): Mr. John J. Hayes, Prof. Robin Clarke Internal Examiner(s): Mr. W.M. Corr
Instructions: Answer any THREE questions. All Questions carry equal marks.
Duration: 2 Hours
Sitting: Summer 2011
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. If in doubt please contact an Invigilator.
Q1. (a) (i) Show from first principles that the polar moment of area of a circular area is given by
d^4
I p ^ (6 marks)
Hint: consider an infinitesimally thin annulus area. (ii) Using the Theorem of Perpendicular axes (or otherwise) show that the second moments of area for such a circular area about a diametral axis is given by
d^4
I ^ (3 marks)
(b) Calculate the depth h of mud for which the 3-m concrete retaining wall is on the verge of tipping about its forward edge A. The density of mud may be taken to be 1760 kg/m^3 and that of concrete to be 2400 kg/m^3. See Figure 1. (11 marks)
Q2. (a) Establish the necessary and sufficient condition for the stability of a hot-air balloon similar to that shown in Figure 2. (5 marks) (b) (i) The balloon of Figure 2 has an inflated volume of 290 m^3 and is filled with helium at atmospheric pressure and temperature. The uninflated balloon, together with its gondola, equipment, and two persons has a total mass of 220 kg. Calculate the tension T in the vertical cable to which the balloon is tethered before release. The densities of air and helium at atmospheric conditions are 1.2062 kg/m^3 and 0. kg/m^3 , respectively. (9 marks) (ii) Calculate the atmospheric air density at the design altitude of the balloon. Neglect the volumes of gondola, equipment, etc. (4 marks) Hint: The balloon is stationary at this altitude (iii) Could you hold this balloon in place at ground? (2 marks)
Q5. (a) Derive an expression for the work done during an isothermal process on an ideal gas of the
form 2
1
P
W mRTlnP (6 marks)
(b) For the cycle in Figure 5 find the net work and the net heat transfer if the 0.1 kg of air is contained in a piston-cylinder arrangement. (10 marks)
Hint: start by establishing the temperatures around the cycle. Take Cp, Cv for air 1.005 and 0.718 kJ/kgK respectively.
(c) Does this cycle absorb or produce net work? net heat? Explain. (4 marks)
