1 UNIVERSITY OF PRETORIA Department of Mechanical and Aeronautical Engineering Exam 2012 THERMOFLUIDS (MTV 310) Lecturer: Mr. Johnathan Vadasz External Examiner: Prof. G. Ziskind (Ben-Gurion University of the Negev) Time: 180 min. Total: 100 marks Check that there are 18 question pages including this one. Answer all questions and show all working and assumptions. Question paper must be handed in with answer booklet including moody diagram!!! Name:________________________________ Surname: _____________________________ Student Number:________________________ Question 1: please turn the page please turn the page
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UNIVERSITY OF PRETORIADepartment of Mechanical and Aeronautical Engineering
Exam 2012
THERMOFLUIDS (MTV 310)
Lecturer: Mr. Johnathan VadaszExternal Examiner: Prof. G. Ziskind (Ben-Gurion Universityof the Negev)Time: 180 min.Total: 100 marks
Check that there are 18 question pages including this one. Answer all questions andshow all working and assumptions.Question paper must be handed in with answer bookletincluding moody diagram!!!
Question 1: please turn the pageplease turn the page
2
Question 1 (15)
In the figure below gate AB is 3 m wide into the paper and is connected by a rod andpulley to a concrete sphere (SG = 2.4). What sphere diameter is just right to close thegate? Note B is the pivot point.SG is relative to water, or air for a gas.
Evaluation Matrix:Has the student used a correct and logical method to solve the problem. √ XHas the student shown all working in his/her derivation to achieve the solution. √ XHas the student made all the necessary assumptions to solve the problem. √ XHas the student explained his/her reasoning behind using the relevant equations/method to solve theproblem.
√ X
Has the student considered if the solution is viable in practice under physics laws in the physical world. √ XHas the student made correct numerical approximations. √ X
Total √ X
3
Question 2 (10)
A spar buoy is a buoyant rod weighted to float and protrude vertically, as in figure below.It can be used for measurements or markers. Suppose that the buoy is maple wood (SG =0.6), 2 cm by 2 cm by 120 cm, floating in seawater (SG = 1.025). How many kilogramsof steel (SG = 7.85) should be added to the bottom end so that h = 18 cm?SG is relative to water, or air for a gas.
Evaluation Matrix:Has the student used a correct and logical method to solve the problem. √ XHas the student shown all working in his/her derivation to achieve the solution. √ XHas the student made all the necessary assumptions to solve the problem. √ XHas the student explained his/her reasoning behind using the relevant equations/method to solve theproblem.
√ X
Has the student considered if the solution is viable in practice under physics laws in the physical world. √ XHas the student made correct numerical approximations. √ X
Total √ X
4
Question 3 (15)
An 8 m internal diameter spherical tank made of 1.5 cm thick stainless steel (k = 15W/m⋅°C) is used to store iced water at 0°C. The tank is located in a room whosetemperature is 25°C. The walls of the room are also at 25°C. The outer surface of the tankis black (emissivity ε = 1), and heat transfer between the outer surface of the tank and thesurroundings is by natural convection and radiation. The convection heat transfercoefficients at the inner and outer surfaces of the tank are 80 W/m2⋅°C and 10 W/m2⋅°C,respectively. Determine (a) the rate of heat transfer to the iced water in the tank and (b)the amount of ice at 0°C that melts during a 24 hour period. The heat of fusion of water atatmospheric pressure is hif = 333.7 kJ/kg.hrad = εσ T2
2 + Tsurr2( ) T2 + Tsurr( )
Evaluation Matrix:Has the student used a correct and logical method to solve the problem. √ XHas the student shown all working in his/her derivation to achieve the solution. √ XHas the student made all the necessary assumptions to solve the problem. √ XHas the student explained his/her reasoning behind using the relevant equations/method to solve theproblem.
√ X
Has the student considered if the solution is viable in practice under physics laws in the physical world. √ XHas the student made correct numerical approximations. √ X
Total √ X
5
Question 4 (15)
Given is a three-pipe series system as in the figure below. The total pressure drop ispA-pB = 150 kPa, and the elevation drop is zA-zB = 7 m. The pipe data are:
Pipe L, m d, cm ε, mm ε/d1 100 2 0.2 0.012 150 5 0.3 0.0063 80 7 0.07 0.001
The fluid is water, ρ = 998 kg/m3 and υ = 0.000001 m2/s. Calculate the flow rate Q inm3/h through the system.You MUST use the Moody diagram attached to solve this problem!!!
Evaluation Matrix:Has the student used a correct and logical method to solve the problem. √ XHas the student shown all working in his/her derivation to achieve the solution. √ XHas the student made all the necessary assumptions to solve the problem. √ XHas the student explained his/her reasoning behind using the relevant equations/method to solve theproblem.
√ X
Has the student considered if the solution is viable in practice under physics laws in the physical world. √ XHas the student made correct numerical approximations. √ X
Total √ X
6
Question 5 (15)
The Asphalted cast-iron pipes are laid in parallel with these dimensions:
Pipe 1 L1 = 600 m d1 = 12 cmPipe 2 L2 = 800 m d2 = 6 cmPipe 3 L3 = 900 m d3 = 20 cm
The total flow rate is 200 m3/h of water at 20°C. Determine (a) the flow in each pipe; and(b) the pressure drop across the system.You MUST use the Colebrook’s formula to solve this problem!!!
Evaluation Matrix:Has the student used a correct and logical method to solve the problem. √ XHas the student shown all working in his/her derivation to achieve the solution. √ XHas the student made all the necessary assumptions to solve the problem. √ XHas the student explained his/her reasoning behind using the relevant equations/method to solve theproblem.
√ X
Has the student considered if the solution is viable in practice under physics laws in the physical world. √ XHas the student made correct numerical approximations. √ X
Total √ X
7
Question 6 (15)
Consider a 5 m high, 8 m long, and 0.22 m thick wall whose representative cross sectionis given in the figure below. The thermal conductivities of various materials used, inW/m⋅°C, are kA = kF = 2, kB = 8, k`C = 20, kD = 15, and kE = 35. The left and right surfacesof the wall are maintained at uniform temperatures of 300°C and 100°C, respectively.Assuming heat transfer through the wall to be one-dimensional, determine (a) the rate ofheat transfer through the wall; (b) the temperature at the point where the sections B, D,and E meet; and (c) the temperature drop across the section F. Disregard any contactresistances at the interfaces.
Evaluation Matrix:Has the student used a correct and logical method to solve the problem. √ XHas the student shown all working in his/her derivation to achieve the solution. √ XHas the student made all the necessary assumptions to solve the problem. √ XHas the student explained his/her reasoning behind using the relevant equations/method to solve theproblem.
√ X
Has the student considered if the solution is viable in practice under physics laws in the physical world. √ XHas the student made correct numerical approximations. √ X
Total √ X
8
Question 7 (15)
Consider a 2 m high electric hot-water heater that has a diameter of 40 cm and maintainsthe hot water at 55°C. The tank is located in a small room whose average temperature is27°C, and the heat transfer coefficients on the inner and outer surfaces of the heater are50 and 12 W/m2⋅°C, respectively. The tank is placed in another 46 cm diameter sheetmetal tank of negligible thickness, and the space between the two tanks is filled withfoam insulation (k = 0.03 W/m⋅°C). The thermal resistances of the water tank and theouter thin sheet metal shell are very small and can be neglected. The price of electricity is$0.08/kWh, and the home owner pays $280 a year for water heating. Determine thefractions of the hot-water energy cost of this household that is due to the heat loss fromthe tank.Hot-water tank insulation kits consisting of 3 cm thick fibre-glass insulation (k = 0.035W/m⋅°C) large enough to wrap the entire tank are available in the market for about $30. Ifsuch an insulation is installed on this water tank by the home owner himself, how longwill it take for this additional insulation to pay for itself?
Evaluation Matrix:Has the student used a correct and logical method to solve the problem. √ XHas the student shown all working in his/her derivation to achieve the solution. √ XHas the student made all the necessary assumptions to solve the problem. √ XHas the student explained his/her reasoning behind using the relevant equations/method to solve theproblem.
√ X
Has the student considered if the solution is viable in practice under physics laws in the physical world. √ XHas the student made correct numerical approximations. √ X