CERTIFICATES OF COMPETENCY IN THE MERCHANT NAVY MARINE ENGINEER OFFICER

EXAMINATIONS ADMINISTERED BY THE

SCOTTISH QUALIFICATIONS AUTHORITY

ON BEHALF OF THE

MARITIME AND COASTGUARD AGENCY

STCW 78 as amended MANAGEMENT ENGINEER REG. III/2 (UNLIMITED)

040-32 – APPLIED HEAT MONDAY, 16 OCTOBER 2017 1315 - 1615 hrs Examination paper inserts: Notes for the guidance of candidates: Materials to be supplied by examination centres:

Thermodynamic and Transport Properties of Fluids (5th Edition)

Arranged by Y.R. Mayhew and C.F.C. Rogers

Worksheet Q4 – Specific Enthalpy – Specific Entropy Chart for Steam

1. Non-programmable calculators may be used. 2. All formulae used must be stated and the method of working and ALL intermediate

steps must be made clear in the answer.

[OVER

APPLIED HEAT Attempt SIX questions only All questions carry equal marks Marks for each part question are shown in brackets

1. Ethane, of volume 0.04 m3, expands isentropically from a pressure and temperature of 6.9 bar, 260°C respectively, to 1.05 bar and 107°C. The ethane is then recompressed to the original volume according to the law pV1.4 = constant. (a) Calculate EACH of the following:

(i) the temperature after recompression; (ii) the net work transfer; (iii) the net heat transfer; (iv) the total change in entropy.

(b) Sketch the sequence of processes on a Temperature-specific entropy

diagram.

Note: for ethane R = 277 J/kgK, cv = 1265 J/kgK and = 1.219

(4)

(4)

(3)

(3)

(2)

2. The air standard efficiency of an Otto cycle is 68.53% and the indicated mean effective pressure is 5 bar. The minimum pressure and temperature in the cycle are 1.05 bar and 30ºC respectively. (a) Sketch the cycle on pressure-Volume and Temperature-specific entropy

diagrams. (b) Calculate EACH of the following:

(i) the volume compression ratio; (ii) the specific work output; (iii) the maximum cycle temperature; (iv) the maximum cycle pressure.

Note: for air, = 1.4 and cv= 718 J/kgK

(2)

(2)

(4)

(6)

(2)

3. A pure hydrocarbon fuel is completely burned in air. The volumetric analysis of the dry exhaust gas gives 10.5% CO2, 7.4% O2, and 82.1% N2. Calculate EACH of the following: (a) the percentage mass analysis of the fuel; (b) the air to fuel ratio by mass; (c) the gravimetric analysis of the total exhaust gas. Note: atomic mass relationships H =1, C = 12, O = 16, N = 14. air contains 21% oxygen by volume.

(8)

(4)

(4)

4. A steam turbine plant producing 22 MW expands steam in two stages with reheat between the stages. The first stage expands the steam from a pressure and temperature of 60 bar and 540ºC respectively to a pressure of 5 bar, at which point, the specific entropy of the steam has increased by 2.15%. The steam is then reheated at constant pressure to 470ºC. In the second stage, the steam expands to a condenser pressure of 0.05 bar and the specific entropy increases by 2.5%. The feed water leaves the condenser at a temperature of 28ºC. The feed pump work cannot be ignored. (a) Draw the expansion and reheat processes on Worksheet Q4.

(b) Sketch the cycle on a Temperature-specific entropy diagram. (c) Using Worksheet Q4 determine EACH of the following:

(i) the mass flow rate of steam in tonne per hour; (ii) the specific steam consumption;

(iii) the thermal efficiency of the cycle.

(4)

(2)

(5)

(2)

(3)

[OVER

5. The first stage of an impulse turbine is velocity compounded with two rows of moving blades. The isentropic enthalpy drop in the nozzles is 373.56 kJ/kg and the isentropic efficiency is 90%. The steam leaves the nozzles at an angle of 30º to the plane of blade rotation and the mean blade speed is 200 m/s. The first row of moving blades and the fixed blades are symmetrical. The exit angle on the second row of moving blades is designed such that the absolute velocity of the steam at stage exit is in the axial direction. A blade velocity coefficient of 0.9 may be assumed for all the blade rows. (a) Draw the steam velocity vector diagram to a scale of 1 mm = 5 m/s

(b) Determine EACH of the following:

(i) the blade angles for each row of moving blades; (ii) the blade angle for the fixed blades;

(iii) the diagram power output for 1 kg/s of steam flow;

(iv) the axial thrust for 1 kg/s of steam flow.

(6)

(2)

(2)

(3)

(3)

6. A vapour compression refrigeration plant uses R134a and operates between saturation temperatures of -20ºC and 40ºC. The refrigerant leaves the evaporator at -10ºC and leaves the compressor at 60ºC. The heat removed in the condenser is 199.63 kJ/kg of refrigerant flowing and the cooling load is 60 MJ/hour. (a) Sketch the cycle on Pressure-specific enthalpy and Temperature-specific

entropy diagrams. (b) Calculate EACH of the following:

(i) the degree of undercooling in the condenser;

(ii) the mass flow rate of liquid refrigerant entering the evaporator;

(iii) the coefficient of performance.

(4)

(4)

(6)

(2)

7. A steel pipe has a bore of 150 mm, a wall thickness of 10 mm and carries dry saturated steam at 12 bar. It is covered with a 40 mm thick layer of moulded insulation which in turn is covered with a 60 mm layer of felt with an outer surface temperature of 25°C. A change in regulations requires the felt to be replaced with a polystyrene material which cannot be used above 95°C. The heat transfer rate and outer surface temperature are required to remain unchanged. Calculate EACH of the following: (a) the rate of heat loss per unit length of pipe; (b) the temperature at the moulded insulation/felt interface; (c) the thickness of the polystyrene if the moulded layer is undisturbed. Note: inner heat transfer coefficient = 550 W/m2K thermal conductivity of steel may be ignored thermal conductivity of the moulded insulation = 0.07 W/mK thermal conductivity of the felt = 0.1 W/mK thermal conductivity of the polystyrene = 0.09 W/mK

(7)

(2)

(7)

8. In a two stage single acting reciprocating compressor, air is compressed from suction conditions of 0.9 bar 20ºC to a delivery pressure of 12 bar. The second stage entry conditions are 3 bar and 35ºC. The low pressure cylinder has a bore of 300 mm, a stroke of 150 mm and a clearance volume of 2.5% of the swept volume.

The index of expansion and compression in both stages is 1.25. The compressor speed is 300 rev/min. (a) Sketch the cycle on a pressure-Volume diagram. (b) Calculate EACH of the following:

(i) the free air delivered per hour at conditions of 1 bar and 0ºC; (ii) the indicated power required to drive the compressor.

Note: for air R = 287 J/kgK and cp = 1005 J/kgK

(2)

(6)

(8)

9. A pump delivers fresh water at the rate of 32 tonne/hour. The delivery pipe is 90 mm bore. Suction is from a tank which is 0.9 m below the pump and delivery is to a tank which is 19.5 m above the pump. The discharge pipe has a total length of 25 m and has a friction factor coefficient of 0.01.

The efficiency of the pump is 75%. Friction losses and velocity in the suction pipe can be neglected. Calculate EACH of the following: (a) the total manometric head in the system; (b) the input power of the pump.

(12)

(4)

040-32APPLIED HEAT WORKSHEET Q4 16 OCTOBER 2017

(This worksheet must be returned with your answer book)

Candidate’s Name ………………………………. Examination Centre …………………………………

Enthalpy Entropy Chart for Steam (prepared at Glasgow College of Nautical Studies using data from NEL Steam Tables 1964 and other formulations: for exercises only)

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www.gcns.ac.uk

SCOTTISH QUALIFICATIONS AUTHORITY MARKERS REPORT FORM

PART I SUBJECT: 040-32-Applied Heat DATE: 16h October 2017

General Comments on Examination Paper Candidates should: listen to the instructions prior to the start ie each new question must start at the

top of a fresh page.

Read the whole question carefully paying particular attention to the units given.

Produce a solution based on given data and what has been asked.

Take care when answering questions they are “confident” with. Stating the correct formula and

calculating an incorrect answer was common.

Read what they have written eg 75 + 10 80. General Comments of Specific Examination Questions

Q1. The T-s diagrams were poor, the initial and final points must be on the same volume line. Some

confused the ratio of specific heats and the polytropic index and did not account for the direction of

energy flow in the expansion and compression processes. Units of N/m2 x m3 = Nm = J (work

transfer), J/s = W (rate of work transfer). Entropy change depends only on the end state CV between

3 and 1. Polytropic requires, constant volume between temperature and isothermal between volumes

OR constant pressure between temperatures and isothemal between pressures.

Q2. It would appear that many candidates did not understand the concept of a compression ratio and

aprecaite that in a CI engine it would be around 16 to 18, values of 2.65x10-5 should be flagged as an

error. The OTTO cycle efficiency in terms of compression ratio is the starting point, followed by mep

= Wnet Vswept, temp then obtained from heat supply.

Q3. Start with X kmol of carbon and Y kmol of hydrogen (X+Y=1 kmol of fuel) in combustion

equation. Balance for coefficents in terms of X or Y. DFG used to obtain one coefficient in terms of

another. The % volumes change in the total gas.

Q4. Plot the given points on the h-s chart, isentropic expansion to given pressure and fix exit point

using the specific entropy value on chart. Power output = m ( hhp + hlp -wpump).

Q5. Most produced a good vector diagram and hence solution. Isentropic efficiency reduces the

enthalpy drop in the nozzle and thus the exit velocity. Some used the incorrect formulae and confused

units. Those calculating angles tended to make errors.

Q6.The concept of a dryness fraction (x) being the amount of dry vapour and (1-x) being the amount

of liquid eluded many. The values given are obtained directly from the tables many interpolated what

appeared to be random values!

Q7. Many used diameters instead of radii. Most used the correct formula although did not read the

question ie heat transfer remains unchanged. The polystyrene could be used at the felt interface

temperature. Some errors gave an interface temperatures in excess of 95°C, some close to or

exceeding the fluid temperature, this would have indicated an error which should have either been

flagged as such or by a statement saying the polystyrene cannot be used.

Q8 The diagrams were poor but the calculations in the main were good although they displayed many

“careless” errors. The pressure ratios were not equal neither was there perfect intercooling. Many

confused volumes, V1 is the total cylinder volume = Vswept + Vclearance . Vinduced = V1 – V4 .

Q9.Total head = suction lift + static head + friction head (4flc2 2gd) + kinetic head (c22g)

input power x efficiency = mghtotal . Mass flow = ac. Candidates using the above formulae with the

correct units scored high marks.

CERTIFICATES OF COMPETENCY IN THE MERCHANT NAVY – MARINE ENGINEER OFFICER

EXAMINATIONS ADMINISTERED BY THE

SCOTTISH QUALIFICATIONS AUTHORITY

ON BEHALF OF THE

MARITIME AND COASTGUARD AGENCY

STCW 78 as amended MANAGEMENT ENGINEER REG. III/2 (UNLIMITED)

040-32 – APPLIED HEAT MONDAY, 17 JULY 2017 1315 - 1615 hrs Examination paper inserts:

Notes for the guidance of candidates:

Materials to be supplied by examination centres:

Candidates examination workbook Graph paper

‘Thermodynamic and Transport Properties of Fluids’ by Mayhew & Rogers (5th edition)

1. Non-programmable calculators may be used. 2. All formulae used must be stated and the method of working and ALL intermediate

steps must be made clear in the answer.

[OVER

APPLIED HEAT Attempt SIX questions only. All questions carry equal marks. Marks for each part question are shown in brackets.

1. In a reversible cycle 1.5 kg of air is heated at constant volume, from a pressure and temperature of 1 bar and 25°C respectively to a pressure of 7 bar. It is then isothermally expanded to the original pressure and finally it is cooled at constant pressure to the initial volume. (a) Sketch the cycle on Pressure-Volume and Temperature-specific entropy

diagrams. (b) Calculate EACH of the following:

(i) the net work transfer;

(ii) the thermal efficiency for the cycle;

(iii) the efficiency of a Carnot cycle operating between the same

temperature limits. (c) Sketch the Carnot cycle on a Temperature-specific entropy diagram.

Note: for air cp = 1.005 kJ/kgK and cv = 0.718 kJ/kgK

(4)

(4)

(3)

(3)

(2)

2. Air enters an open cycle gas turbine at an atmospheric temperature and pressure of 15ºC and 1.013 bar respectively. The compressor operates on a pressure ratio of 8.5:1 with an isentropic efficiency of 0.78. The temperature of the gas leaving the combustion chamber is 925ºC and it expands through the turbine to atmosphere with an isentropic efficiency of 0.83. The net power output of the plant is 1800 kW. The mass flow of fuel may be ignored. (a) Sketch the cycle on a Temperature-specific entropy diagram. (b) Calculate EACH of the following:

(i) the temperature at the end of compression;

(ii) the temperature at the end of expansion;

(iii) the mass flow rate of air through the plant;

(iv) thermal efficiency;

(v) the work ratio.

Note: for air cp = 1.005 kJ/kgK and cv = 0.718 kJ/kgK

(2)

(3)

(3)

(3)

(3)

(2)

3. A fuel of mass analysis 84% carbon and 16% hydrogen is completely burned in air. The dry flue gas analysis shows that they contain 14% CO2 by volume. (a) Determine the air supply in molar volumes for 100 kg of fuel. (b) Calculate EACH of the following:

(i) the air fuel ratio by mass;

(ii) the percentage excess air by volume. Note: Relative atomic masses H =1, C =12, N =14, O =16

Air contains 21% oxygen by volume.

(8)

(4)

(4)

[OVER

4. A bend of constant cross sectional area which turns the flow through 75° is shown in Fig Q4. It is fitted in a horizontal section of a 600 mm diameter fresh water cooling system.

The cooling system pressure at this point is 3 bar and the flow rate is 0.85 m3/s. The pressure loss due to the bend is negligible. Calculate EACH of the following: (a) the net force acting on the axis ox; (b) the net force acting on the axis oy; (c) the magnitude of the resultant force acting on the bend; (d) the direction of the resultant force.

(8)

(4)

(2)

(2)

o

y

x 75° c1

c2

Fig Q4

5 Steam at a pressure and temperature of 40 bar and 400ºC respectively is expanded in the nozzles of a two row velocity compounded impulse turbine to a pressure of 15 bar. The steam enters the first row of moving blades with an absolute velocity of 700 m/s.

The outlet angles from the nozzles, first row of moving blades, fixed blades and the second row of moving blades are 18º, 21º, 26º and 35º respectively.

The blade velocity coefficient is 0.9 over each of the three rows of blades.

The turbine shaft speed is 3000 rev/min and the mean blade diameter is 750 mm. (a) Determine the condition of the steam leaving the nozzles. (b) Draw the velocity diagram for each row to a scale of 1 mm = 5 m/s. (c) Determine the diagram efficiency;

(5)

(8)

(3)

6. A vapour compression refrigeration cycle using Ammonia has compressor suction and discharge pressures of 3.413 bar and 11.67 bar respectively. The vapour enters the compressor in a dry saturated state and leaves at a temperature of 105ºC. The liquid refrigerant has 4 K of sub-cooling at entry to the expansion valve. (a) Sketch the cycle on Pressure-specific enthalpy and Temperature-specific

entropy diagrams. (b) Determine EACH of the following:

(i) the percentage of dry vapour entering the evaporator;

(ii) the specific work done;

(iii) the coefficient of performance;

(iv) the isentropic efficiency of the compressor.

(4)

(3)

(3)

(2)

(4)

[OVER

7. An exhaust gas economiser has a total of 60 tubes in a single pass, counterflow arrangement. Each tube has an inner diameter of 20 mm, wall thickness 2.4 mm and a length of 3 m. The feed water enters the tubes at a temperature of 90ºC and leaves at 106ºC. The exhaust gas enters the shell at a rate of 47 tonne/hour and temperature of 350ºC, it leaves at a temperature of 280ºC. The heat lost to the surroundings is negligible.

Calculate EACH of the following: (a) the rate of heat transfer; (b) the mean velocity of the feed water in the tubes; (c) the log mean temperature difference; (d) the overall heat transfer coefficient, based on the tube outer surface area.

Note: for feed water c = 4.2 kJ/kgK and density 1000 kg/m3

for exhaust gas cp = 1.1 kJ/kgK

(2)

(5)

(4)

(5)

8. A single acting, two stage reciprocating air compressor, takes in air at a pressure and temperature of 0.95 bar and 15ºC respectively and delivers it at 30 bar.

The low pressure cylinder has a bore of 300 mm and a stroke of 450 mm with a volumetric efficiency of 82%. The air enters the second stage at a pressure and temperature of 6 bar and 25ºC respectively. The compressor speed is 200 rev/min. The index of compression and expansion in both stages is 1.3. (a) Sketch the process on a Pressure-Volume diagram. (b) Calculate EACH of the following:

(i) the compressor power;

(ii) the heat removed in the inter-cooler;

(iii) the heat removed by the cooling water in the low and high pressure cylinders.

Note: for air R = 0.287 kJ/kgK cp = 1.005 kJ/kgK

(2)

(4)

(4)

(6)

9. In a mixture of methane (CH4) and air there are three volumes of oxygen to one volume of methane. The mixture is isentropically compressed through a volume ratio of five to one from initial conditions of 1 bar and 102ºC. Calculate EACH of the following: (a) the gravimetric analysis of the mixture; (b) the molecular mass of the mixture; (c) the adiabatic index of the mixture; (d) the work done per unit mass of the mixture. Note: The universal gas constant = 8.3145 kJ/kmolK. For each constituent gas the values of cp at 375 K are: Oxygen = 0.934 kJ/kg, Methane = 2.442 kJ/kgK, Nitrogen = 1.042 kJ/kgK . Atomic mass relationships: H =1, C = 12, N = 14, O = 16. Air contains 21% oxygen by volume.

(4)

(2)

(4)

(6)

SCOTTISH QUALIFICATIONS AUTHORITY MARKERS REPORT FORM

PART I SUBJECT: 040-32-Applied Heat DATE: 17th July 2017

General Comments on Examination Paper Candidates should: Read the whole question carefully paying particular attention to the units given.

Produce a solution based on given data and what has been asked.

Take care when answering questions they are “confident” with. Stating the correct formula but

leaving out data on the next step and calculating an incorrect answer from correct data was common.

Read what they have written eg ((1.4-1)1.4)1.4 or 1. General Comments of Specific Examination Questions

Q1. The P-v diagrams were usually good but the T-s diagrams poor, the Carnot cycle forms a

rectangle but the vapour dome does not apply to a gas. Using the diagram numbers in the equations

would eliminate many errors, for example the isothermal process was 2-3 not 1-2. Many confused

ISOTHERMAL with ISENTROPIC

Q2. Many candidates did not read the question. Adding the information given to the diagram would

have eliminated many errors particularly when using the isentropic efficiency formula.

Net work output = Turbine work – Compressor work.

Q3. Mass m = Amount n x Molecular mass M. The % CO2 gives the toatl DRY gas (Wet gas

contains H2O, dry gas does not). Convert fuel to Kmols. Use total DFG to obtain excess O2 and N2 in

terms of O2 supplied and solve in oxygen balance.

Q4. Few attempts. This is an application of the momentum equation in 2D. F = q(C). The back

pressure oposes the inlet pressure.

Q5. Many produced good vector diagrams but also calculated values! Some confused absolute and

relative velocities Nozzle exit velocity was given, this was used to otain the enthalpy at exit and

hence superheat. The velocity cannot increase across an impulse blade.

The symbol for fluid velocity is “C”.

Q6.The concept of a dryness fraction being the fraction of dry vapour escaped many, while others

were unable to convert a fraction to a percentage. An expansion valve is a throttle with an isenthalpic

process not isentropic. Refrigeration effect is a heat tranfer not work transfer. There is no need to

interpolate small differences eg s=5.419 may be taken as 5.417. Isentropic efficiency of the

compressor is based on work (enthalpy change) not heat (entropy change).

Q7. Steam conditions were given allowing heat transfer to be obtained, this could then be used to

obtain the cooling flow mhfg(steam) = mcpT(water). Many confused cross-sectional area (flow)

with surface area ( heat transfer), the tube length only aplies to the latter. Log mean temperature

difference units are Kelvin. Many forgot about the number of tubes.

Q8 The diagrams were poor but the calculations in the main were good although they displayed

many “careless” errors. Parts bii and biii required the aplication of the SFEE not the NFEE.

The pressure ratios were not equal neither was there perfect intercooling. Absolute temperatures are

required for calculations. The compression processes were polytropic not isentropic.

Q9.Few attempts, however for volumes read kmols. 3 volumes of oxygen comes with 11.286

volumes of nitrogen . Also mass = n x M, M = total mass total kmols. Cp mixture=(mcp)

mtotal)

CERTIFICATES OF COMPETENCY IN THE MERCHANT NAVY – MARINE ENGINEER OFFICER

EXAMINATIONS ADMINISTERED BY THE

SCOTTISH QUALIFICATIONS AUTHORITY

ON BEHALF OF THE

MARITIME AND COASTGUARD AGENCY

STCW 78 as amended MANAGEMENT ENGINEER REG. III/2 (UNLIMITED)

040-32 – APPLIED HEAT MONDAY, 27 MARCH 2017 1315 - 1615 hrs

Examination paper inserts: Notes for the guidance of candidates:

Materials to be supplied by examination centres: Candidates examination workbook Graph paper

‘Thermodynamic and Transport Properties of Fluids’ by Mayhew & Rogers (5th edition)

1. Non-programmable calculators may be used. 2. All formulae used must be stated and the method of working and ALL intermediate

steps must be made clear in the answer.

[OVER

APPLIED HEAT Attempt SIX questions only. All questions carry equal marks. Marks for each part question are shown in brackets.

1. A mass of 0.2 kg of helium is compressed reversibly in a cylinder according to the law pVn = constant. The initial pressure and temperature are 1.01 bar and 25ºC respectively. The final pressure and temperature are 9.5 bar and 213ºC respectively. (a) Sketch the process on Pressure-Volume and Temperature-specific entropy

diagrams. (b) Calculate EACH of the following:

(i) the index of compression;

(ii) the work transfer;

(iii) the heat transfer;

(iv) the change in entropy.

Note: for helium cv = 3.116 kJ/kgK, R = 2.077 kJ/kgK

(4)

(2)

(2)

(2)

(6)

2. In an air standard diesel cycle, the volume at the end of heat supply is 1.8 times the volume at the beginning of the heat supply. The temperature at the beginning of compression is 300 K and at the end of expansion it is 678.6 K. The thermal efficiency is 66.9%. (a) Sketch the cycle on Pressure-Volume and Temperature-specific entropy

diagrams. (b) Calculate EACH of the following for 1 kg of air:

(i) the heat supply;

(ii) the network output;

(iii) the maximum cycle temperature;

(iv) the volume compression ratio. Note: for air γ = 1.4 and cp = 1.005 kJ/kgK

(4)

(6)

(2)

(2)

(2)

3. A gaseous fuel has the following volumetric analysis: 44% H2, 28% CH4, 12% CO, 14% N2, 2% O2. The dry volumetric analysis of the combustion products is 9.39% CO2, 86.76% N2, 3.85% O2. (a) Determine the full combustion equation in kmols per kmol of fuel. (b) Calculate EACH of the following:

(i) the percentage excess air supplied;

(ii) the mass analysis of the wet exhaust gas.

Note: Relative atomic masses C = 12, H = 1, O= 16, N = 14

Air contains 21% oxygen by volume.

(10)

(2)

(4)

[OVER

4. An ideal steam reheat cycle operates between pressure of 40 bar and 40 millibar, with a superheat temperature of 400ºC. The first expansion is carried out to the point where the steam is dry saturated. The steam is then reheated at constant pressure to the original superheat temperature. There is 6 K sub-cooling in the condenser and the feed pump work cannot be ignored. (a) Sketch the cycle on a Temperature- specific entropy diagram. (b) Determine EACH of the following:

(i) the quality of the steam entering the condenser;

(ii) the cycle efficiency;

(iii) the specific steam consumption.

(4)

(4)

(5)

(3)

5. The steam condition at a stage in a 50% reaction turbine is 0.16 bar and 0.95 dry. The speed of rotation is 3600 rev/min with a mass flow rate of 36 tonne/hour. At these conditions the stage develops a power of 1000 kW. The moving blade exit angle is 18º and the axial velocity of the steam is 80% of the blade velocity at the mean radius. (a) Sketch the velocity vector diagram for the stage and identify the whirl

velocities at inlet and exit. (b) Calculate EACH of the following:

(i) the mean diameter of the blade ring;

(ii) the blade height;

(iii) the diagram efficiency.

(3)

(6)

(3)

(4)

6. A reverse heat engine operates on the reverse Carnot cycle.

The working fluid is R134a and the cycle operates between temperature limits of -5ºC and +40ºC. (a) Sketch the cycle on a Temperature-specific entropy diagram indicating the

network. (b) Calculate EACH of the following:

(i) the dryness fraction at the beginning of compression;

(ii) the heat removed per kg of fluid from the low temperature reservoir;

(iii) the heat rejected per kg of fluid to the high temperature reservoir;

(iv) the cycle network input;

(v) the cycle co-efficient of performance.

(4)

(3)

(3)

(2)

(2)

(2)

7. The flow rate of lubricating oil to an engine is measured using a vertical venturi meter. The venturi meter has an inlet diameter of 150 mm and the throat, which is 200 mm above the inlet, has a diameter of 100 mm. A differential pressure gauge connected to the inlet and throat gives a reading of 5 kN/m2. The venturi has a coefficient of discharge of 0.95 and the relative density of the oil is 0.82. Calculate EACH of the following: (a) the net increase in kinetic energy for 1 kg of oil; (b) the velocity of the oil at the venturi meter inlet; (c) the mass flow rate of oil in tonne per hour.

(8)

(5)

(3)

8. The overall pressure ratio in a two stage, single acting reciprocating air

compressor designed for minimum work is 12.25:1. At the beginning of the compression stroke the LP cylinder contains 0.0234 kg of air at a pressure and temperature of 1.013 bar and 25ºC respectively.

The polytropic index for all the expansion and compression processes is 1.28. The clearance volume in both stages is 4% of their respective swept volumes.

The stroke of each stage is 300 mm and the speed is 320 rev/min. (a) Sketch the processes on a pressure-Volume diagram indicating ALL the

volumes. (b) Calculate EACH of the following:

(i) the volumetric efficiency of each stage;

(ii) the cylinder bore of each stage;

(iii) the total indicated power. Note: for air R = 0.287 kJ/kgK

(3)

(3)

(6)

(4)

9. Superheated steam at a pressure and temperature of 10 bar 350ºC respectively enters a convergent divergent nozzle with negligible velocity. The steam expands isentropically to a throat pressure of 3 bar and exits the nozzle at a pressure of 0.2 bar. The enthalpy drop from the throat to the exit is 209.367 kJ. The mass flow of steam is 1.713 tonne/hour.

Calculate EACH of the following: (a) the diameter of the nozzle at the throat; (b) the diameter of the nozzle at exit; (c) the isentropic efficiency of the divergent section.

(5)

(6)

(5)

SCOTTISH QUALIFICATIONS AUTHORITY

MARKERS REPORT FORM

PART I SUBJECT: 040-32-Applied Heat DATE: 27

th March 2017

General Comments on Examination Paper Candidates should: Read the whole question carefully paying particular attention to the units given.

Produce a solution based on given data and what has been asked. Apply the given units and use

them to confirm the correct equation and expected outcome. For example mcp = kg x kJ/kgK = kJ/K

not kg, kJ or kJ/kg. Take care when using a calculator. General Comments of Specific Examination Questions Q1. The P-v diagrams were usually good but the T-s diagrams poor. Common errors indicate that

numerous candidates were unable to relate the diagrams to the processes in the calculations.

Heat was confused with entropy and internal energy, for a polytropic process Q W + U

Q2. Many candidates could not identify the beginning of compression and the end of expansion.

Temperature difference was used as heat supply and rejection, many did not realise fluid temperature

increases during heat addition.

Q3. The question stated a “volumetric analysis” and % volume is the same as %kmol. Many did not

account for the oxygen and nitrogen in the fuel while others assumed the CO remained unchanged

despite there being no CO in the exhaust gas. Wet gas contains H2O, dry gas does not.

Q4. The diagrams were variable, few showed the superheat temperature above the critical and the

first expansion on the dry saturated vapour line, undercooling was rarely shown and the expansion

lines should be vertical. When using tables there is no need to interpolate values that are a few Joules

different in this case 6.769 may be taken as 6.761 a difference of 0.12%. Common errors include

missing out feed pump work and not including the reheater in the heat supplied.

Q5.Candidates using symbols such as x,y z to identify velocity components made significantly more

trig errors than those producing a correctly labelled diagram. Many did not use sin, cos and tan

correctly to obtain the whirl velocities in terms of the blade velocity.

The symbol for fluid velocity is “C”.

Q6.The diagrams were poor and inaccurate. Some confused a heat engine with a heat pump. Most

candidates produced calculations based on enthalpy however expansion was isentropic and h3 did

not equal h4. A simpler solution based on Q = TS and W = QS – QR reduced the work content.

Q7. An application of the Bernoulli equation. The few attempting this question produced good

solutions marred by careless mathematical and calculation errors. fluid velocity symbol “C”.

Q8.Many candidates produced a poor diagram not showing the volumes as required. Many confused

the total volume with the induced volume, V1 = Vs + Vc. Many assumed that it was single stage or

the second stage bore would be the same as the first stage. m3/s m

2 will not give m, the stroke was

given not mean piston speed.

Q9. Only the convergent section was isentropic the throat being 3 bar 200C (only 11 J difference

in specific entropy). Many failed to use the throat velocity when applying the SFEE to the divergent

section. The isentropic efficiency only applied to the divergent section.