me321:spring 2007 endterm test _______________________name:___________________________
* Closed notes, open book test. You may also use a single handwritten
8.5 x 11" help sheet.
* Answer any four of the six questions. Each question is worth
50 points. Please indicate which questions you do not
wish to have graded by drawing a line through the respective
question statement.
[The various numerical answers to the
problems below are shown in red]
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Questions 1, 2, 3 and 4 relate to the steam power plant shown in the following figure, however all four questions are completely independent and can be solved in any order.
1. Consider the steam power plant shown above operating under the conditions shown in the diagram. Using values obtained from the tables, determine
a) The power output of the adiabatic turbine (kW) [999 kW]
b) The thermal efficiency of the power plant (hth) [19.5%]
c) Draw the complete cycle on the p-h diagram provided below, clearly showing the four
processes (1) - (2) - (3) - (4) - (1).
Justify all values used and derive all equations
used starting from the basic steady flow energy equation and the
basic definition of thermal efficiency of a heat engine.
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2. Consider the adiabatic turbine only in the power plant shown
above. Using the conditions shown on the diagram together with
values obtained from the steam tables, carefully draw the turbine
process (1) - (2) on the h-s diagram provided below. Evaluate
the turbine adiabatic efficiency (hT)
[hT=108%
- not possible!]. Discuss your results and determine if
the turbine alone (not the entire system) is feasible.
Justify all values used and derive all equations
used starting from the basic steady flow energy equation and total
entropy change (turbine and surroundings) for a flow system, and
the basic definition of turbine adiabatic efficiency.
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3. Consider the feedwater pump only in the power plant shown
above. Notice that there is a 1°C temperature drop across
the pump due to internal friction. Determine the actual power
required to drive of the pump [8.64 kW]
as well as the minimum power required [1.53
kW], and determine the pump efficiency [hP=18%], defined
as the minimum (isentropic) power divided by the actual power
required. Discuss your results and determine if the very small
temperature drop of 1°C is of any significance [1°C
is significant - the only reason for the extremely low efficiency].
Justify all values used and derive all equations
used starting from the basic steady flow energy equation, the
equation of enthalpy and the isentropic relation of an incompressible
liquid.
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4. Consider the condenser only in the above power plant. Determine
the cooling power required to condense the steam at station (2)
and subcool it to 60°C at station (3) [4123
kW]. If the cooling water is not allowed to experiance
a temperature rise of more than 10°C, determine the minimum
required mass flow rate of the cooling water [98.6
kg/s].
Justify all values used and derive all equations
used starting from the basic steady flow energy equation and the
equation of enthalpy of an incompressible liquid.
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5. During an experiment conducted in senior lab at 25°C,
a student measured that a Stirling cycle refrigerator that draws
250W of power has removed 1000kJ of heat from the refrigerated
space maintained at -30°C. The running time of the refrigerator
during the experiment was 20min. Determine if these measurements
are reasonable, and state the reasons for your conclusions.
Derive all equations used starting from the basic definition
of the Coefficient of Performance of a refrigerator (COPR). [(actual COPR)/(Carnot
COPR)
= (3.33/4.42) = 75%. - not feasible (must be < 60%)]
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6. An ideal air-standard Otto cycle engine has a compression ratio of 8:1 (i.e. maximum/minimum volume ratio) and undergoes adiabatic compression according to the relation P vk = constant. If the initial conditions at the start of compression are 100kPa, 25°C, determine
a) the pressure and temperature at the end of the process [1838 kPa, 685 K]
b) the boundary work done and heat transferred during this compression process [w = -278 kJ/kg, q = 0]
c) Sketch the P-v diagram of the process with respect to the relevant constant temperature lines, and indicate the work done on this diagram.
Justify all values used and derive all equations
used starting with the basic energy equation for a system and
the basic definition of boundary work done. Assume constant specific
heats over this process.
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