Pome

Principles of Mechanical Engg. Science

DEPARTMENT OF MECHANICAL ENGINEERINGBIRLA INSTITUTE OF TECHNOLOGY

MESRA, RANCHI

Sheet No. 1

(ME 3007) PRINCIPLES OF MECHANICAL ENGINEERING SCIENCE

B.E. 3RD SEMESTER

1. Define the following terms with suitable examples for each system, surrounding, boundary, property, state, process and cycle. What is a quasi-static process? What do you mean by Thermodynamic Equilibrium?

2. Distinguish between (with suitable examples). (a) Closed and open system(b) Extensive and intensive property (c) Microscopic and Macroscopic point of view (d) Isobaric and Isochoric process (e) Isothermal and Adiabatic process(f) Point function and path function

3. Why is it difficult to define Temperature? What do you understand by equality of temperature?

4. State and explain the zeroth law of thermodynamics. Why is it called the Zeroth Law? What is its importance?

5. What is a pure substance? What do you mean by Two-property Rule? Is air a pure substance?

6. (a) What do you understand by the critical point and the triple point for water? Explain with suitable diagrams.

7. Determine the specific volume and the specific enthalpy of water (H2O) at 10 bar when it is (a) saturated liquid (b) Saturated vapour (c) Wet steam having a quality of 60 percent (d) Superheated steam at a temp. of 300 deg. C.

8. Using steam Tables, find the following:

(a) The specific Vol. and specific enthalpy and specific entropy at 70 bar and 400 deg. C.

(b) The temperature at 100 bar for which the specific enthalpy is the same as in (a)

(c) The quality at 45 bar for which the specific volume is the same as in (a) (d) The temp. of quality as the case may be at 50 bar for which the sp.

Entropy is same as in (a).

9. The radiator of heating system has a volume of 0.05 m3 and contains saturated steam at 1.8 bar. The valves are then closed on the radiator and as a result of heat transfer to the room the pressure drops to 1.3 bar calculates. (a) the total mass of steam in the radiator (b) the volume and mass of liquid in the final state (c) the volume and mass of vapour in the final state

10. A rigid cylinder contains wet steam at 12 bar and quality 0.4 if the volume of the vessel is 0.12 m3, find the quality, the mass of liquid and vapour, when the pressure in the cylinder has increased to 20 bar due to heat transfer.


11. A rigid vessel contains wet steam at 2.5 bar. Find the proportions by volume of liquid and vapour necessary to make the water pass through the critical state when heated.

12. A vessel having a capacity of 0.85 contains steam at 11 bar and 0.92 dry. Steam is blown off until the pressure drops to 5.5 bar. Assuming that the enthalpy/kg of steam remains constant during the blowing off period calculate:

(a) the quality of steam at the final state (b) the quantity of steam blown off

13. Steam initially at a press of 15 bar and 0.95 quality expands isentropically to 7.5 bar and is then throttled until it is dry saturated. Determine per kg. Of steam.

(a) Total heat supplied to feed water per hour to produce wet steam. (b) Take Cp water = 4.18 KJ/kg-k and Cp superheated steam = 2.2 KJ/kg-k.

14. 1000 kg of steam at a pressure of 16 bar and 0.9 dry is generated by a boiler per hour. The steam passes through a super heater via boiler stop valve where its temperature is raised to 380 deg. If the temp. of feed water is 30 deg. Determine:

(a) Total heat supplied to feed water per hour to produce wet steam. (b) Take Cp water = 4.18 KJ/kg-k and Cp superheated steam = 2.2 KJ/kg-k.

15. A vessel of 0.9 m2 contains at 8 bar and quality of 0.9 steam is blown off until the pressure drops to 4 bar. The valve is then closed and the steam is allowed to cool until the pressure falls to 3 bar. Assuming that the blowing-off process is a constant enthalpy process and the cooling is a constant volume process determine:

(a) mass of steam blown off(b) dryness fraction of steam in the vessel after blowing off (c) quality of steam after cooling (d) heat lost by steam during cooling.


HEAT AND WORK Sheet No. 2

16. (a) Define Heat and work (c) What are the similarities between them? (d) With the help of a suitable example show the difference between them.

17. (a) What are the limitations of the equation W =

(b) What is meant by “Free expansion”?

18. Draw neat sketches of the following systems and indicate the system boundaries. Label open or closed system and show the directions of heat and work transfer.

(i) Mercury in glass thermometer surrounded by a medium at a higher temperature.

(ii) Inflation of a flat tyre by forcing air into the tyre with the tyre walls as the system boundary, the trye walls being non-conducting.

(iii) A combustible mixture of carbon and oxygen in a perfectly insulated rigid container ignited by a spark from a spark plug placed inside the container and connected to an external source of power.

(iv) A non-insulated nozzle receiving steam with a higher pressure with negligible velocity and expanding it down to a lower pressure in absence of friction and turbulence.

(v) A perfectly insulated constant pressure chamber containing a mixture of ice and water and constantly stirred by a motor driven stirrer.

19. Examine the validity of the statements:

(i) Heat is that which invariably causes a change in temperature. (ii) Work is that which invariably causes a change in volume.

20. State giving reasons whether neat and work transfers are positive, negative or zero in each of the following processes. The systems to be considered are underlined. (a) A rigid vessel containing ammonia gas is connected through a valve to an evacuated rigid vessel the vessel, the valve and the connecting pipes are well insulated. The valve is opened and after a while the conditions in the two vessels become uniform.

(b) A ______ of ice and water is contained in a vertical cylinder closed at the top by a non-conducting piston, the upper surface of the piston being exposed to the atmosphere. The piston is held stationary while a flame applied to the base of the cylinder causes some of the ice to melt.

(c) As under (b) but the piston is allowed to move so as to keep the mixture pressure constant.

(d) Air in a rigid metallic container is kept on a stove and the pressure and temperature of air rise.

(e) Air flows adiabatically into a previously evacuated bottle through a valve.

21. A cylinder fitted with a piston contains 1 kg of air at a pressure of 20 bar and having a volume of 0.05 m3. Air is allowed to expand according to the law pv = const. Until the volume is doubled. Air is then cooled at constant pressure until the piston regains its initial position. Air is then heated with the piston firmly locked in this position until pressure rises to the initial value of 20 bar. Calculate the net work done during the cycle. Sketch the cycle on a p-v diagram.


22. An electrical resistance, wired to the surroundings, is placed within the cylinder of a piston-cylinder machine. A current of 5 amperes is established through the circuit with a drop of 100 volts across the resistance. At what speed must the piston move with a constant force of 90 kN in order to maintain the rate of displacement work equal to electrical work?

23. A cylinder fitted with a piston contains 1.5 kg of saturated water vapour at a pressure of 10 bar. The steam is heated until the temperature is 300oC. During the process the pressure remains constant. Calculate the work done by the steam during this processes.

24. A cylinder in which the piston is restrained by a spring contains 0.04 m2 of air at a pressure of 1.1 bar, which just balances the atmospheric pressure of 1.1 bar. Assume the weight of the piston is negligible. In this initial state the spring exerts no force on the piston. The air is then heated until the volume is doubled. The final pressure of the air is 3 bar.

(a) Show the process on a p-v diagram (b) Considering the air as the system, calculate the total work done by the

system. (c) Of the total work how much is done against the atmosphere and how

much against the spring?

25. A balloon which is initially flat is inflated by filling it with air from a tank of compressed air. The final volume of the balloon is 1.5m2. The barometer reads 755 mm of Hg. Consider the tank, the balloon, and the connecting pipe as the system. Determine the work done for this process.

26. A spherical balloon has a diameter of 30 cm and contains air at a pressure of 2 bar. The diameter of the balloon increases to 40 cm due to heating, and during this process the pressure is directly proportional to the diameter. Calculate the work done by the air.

27. In a piston-cylinder arrangement, 1 kg of air at a pressure of 1 bar and volume of 0.2m2 expands under constant pressure to a volume of 0.8m3; it then undergoes a constant volume process in such a manner that under isothermal compression, which follows after constant volume process, the air returns to its initial state. Represent the cycle on a p-v diagram and determine the net work done by the system.

28. A gas expands in a cylinder from a volume of 0.18 m3 and a pressure of 5 bar to a volume of 0.36 m3 according to the law pv1/2 = constant. Calculate the final pressure and work done.

29. A fluid undergoes a cycle consisting of the following processes:

(a) It is heated at a constant pressure of 1.05 bar until it has a specific volume of 0.1 m3/kg.

(b) It is then compressed according to the law pv = constant to a pressure of 4.2 bar.

(c) It is then allowed to expand according to the law pv1.3 = constant. (d) Finally it is heated at constant volume back to its initial state.

The work done in the constant pressure process is 515 N-m and the mass of the fluid is 0.2 kg. Calculate the net work done in the cycle. Sketch the cycle on a p-v diagram.


SHEET NO. 3.

THE FIRST LAW OF THERMODYNAMICS

30. A fluid contained in a piston-cylinder arrangement executes a cycle consisting of 4 processes. The net heat transferred during the cycle is – 340 kJ. The system executes 200 cycles per minute:

Complete the following tale showing the method of calculation and compute the cycle output in KW

Processes Q W U

1-2 0 43402-3 42000 0 3-4 -4200 …. -73200 4-1 ……… ……. ………

31. A sealed bomb containing certain chemicals is placed in a tank of water which is open to atmosphere. When the chemicals react heat is transferred from the bomb to the water causing the temperature of water to rise. A stirring device is used to circulate the water and the power input to the rod driving the stirrer is 0.055 KW. In a 15 minute period the heat transfer from the bomb is 1000 kJ and the heat transfer from the tank to the surrounding air is 50 kJ. Assuming no evaporation of water, determine the chain in internal energy of the water.

32. A radiator of a steam heating system has a volume of 0.08m3. When the radiator is filled with dry saturated steam at a pressure of 1.6 bar all valves to the radiator are closed. How much heat will have been transferred to the room when the pressure of steam falls to 1.0 bar?

33. A rigid vessel having a volume of 0.8m3 is filled with steam at 10 bar and 300oC. Heat is transferred from the steam until it exists as saturated vapour. Calculate the heat transferred during the process.

34. A sealed tube has a volume of 30 cm3 and initially contains certain fraction of liquid and vapour H2O in equilibrium at 1 bar. The fraction of liquid and vapour is such that when heated the steam passes through the critical point. Calculate the heat transfer when the steam is heated from the initial state to the final state.

35. A steam boiler has a total volume of 3m3. The boiler initially contains 2m3 of liquid water and 1m3 of vapour in equilibrium at 1 bar. The boiler is fired up and heat is transferred to the water and steam in the boiler. Somehow the values on the inlet and delivery of the boiler are both left closed. The relief valve lifts when the pressure reaches 50 bar. How much heat was transferred to the water and steam in the boiler before the relief valve lifted.

36. A cylinder fitted with a piston contains 2.5 kg of H2O at a pressure of 10 bar and a quality of 0.8 the piston is restrained by a spring which is so arranged that for zero volume in the cylinder the spring is full extended. The spring force is proportional to the spring displacement and the weight of the piston is neglected. Heat is transferred to the H2O until its volume is 150% of the initial volume. (a) What is the final pressure?(b) What is the quality (if wet) or temperature (if superheated) in the final

state? (c) Draw a p-v diagram and determine the work.

37. Steam which is contained in a cylinder expands against a piston. Following are the conditions before and after expansion.


Before expansion After expansion

Pressure: 10 bar Pressure: 0.5 bar Temperature: 300oC Volume 0.02 m3

The heat transfer during expansion is equal to –2.5 kJ. Calculate the work done during the process.

38. 0.5 kg of steam is confined inside a spherical balloon which supports an internal pressure proportional to its diameter. The initial condition of the steam is 1 bar and 150oC. Heat is transferred to the steam until the pressure reaches 1.2 bar. Determine

(a) The final temperature (b) The heat transfer

39. 5 kg of water at 15oC is contained, in a vertical cylinder by a frictionless piston of a mass such that the pressure of the water is 7 bar. Heat is transferred slowly to the water causing the piston to rise until it reaches the stops at which point t volume inside the cylinder is 0.5m2. More heat is transferred to the water until it exists as saturated vapour.

(a) Find the final pressure in the cylinder and the heat transfer and work done during the process.

(b) Show this process on a t-v diagram and a p-v diagram.

40. Consider a piston-cylinder arrangement in which a frictionless piston with a cross sectional area of 0.06m2. The mass of the piston is such that 3 bar pressure is required to raise the piston against atmospheric pressure. When the piston has moved to a position where the contained volume is 0.075m2, it encounters a linear spring that require 360 kN to deflect it 1 m. Initially the cylinder contains 4 kg of saturated water (two phase) as 35oC. The final pressure is 70 bar. Determine the final state of the H2O and the work done during the process. Also find out the net change of internal energy and heat transfer.

41. Define “Enthalpy” is it an energy quantity?

42. State the conditions under which an open flow process becomes a steady flow process.

43. Write down the steady flow energy equation and explain the different terms.

44. What is a throttling process? Examine the validity of the statement. “A throttling process”.

45. 12 kg of air per minute is delivered by a centrifugal air compressor. The inlet and outlet conditions of air are :

V1 = 12 m/sec, P1 = 1 bar, V1 = 0.5m3/kg and V2 = 90 m/sec, P2 = 8 bar, V2 = 0.14 m3/kg.

The increase in internal energy of air passing through the compressor is 25 kJ/kg. Cooling water in the compressor jacket flows at the rate of 15 kg/min and its temperature increases by 10oC find:

(a) Motor power required to drive the compressor (b) Ratio of inlet to outlet pipe diameter

46. Steam enters the nozzle of a steam turbine with low velocity at a pressure of 30 bar and 300oC and leaves the nozzle at 1 bar with a velocity of 300 m/sec. The rate of steam flow is 1500 kg/hr. Calculate the quality or temperature of steam (as the case may be) at the exit of the nozzle and the exit area.


The Second Law of Thermodynamics SHEET NO. 4

54. Discuss the limitations of the first law of thermodynamics. How does the second law overcome these limitations?

55. Give the Kelvin-Planck and the Clausius statements of the second law of thermodynamics and establish their equivalence.

56. Define heat engine, refrigerator and hest pump. What do you mean by thermal efficiency of a heat engine and co-efficient of performance (C.O.P.) of a refrigerator and heat pump?

57. What do you mean by a thermodynamic temperature scale?

58. State and prove Carnot theorem.

59. Define a reversible process. Name some of the factors which render a process irreversible.

60. A reversible heat engine operates between a heat source at 227 and a heat

sink at 27 . It receives 250 KJ of heat from the source. Find out;(a) The work output and(b) The heat rejected to the sink.

61. Find the C.O.P. of a reversed Carnot cycle working between temperature limits of 40 and -10 when (a) it works as a refrigerator, (b) it works as a heat pump.

62. A reversible engine operates between two reservoirs at temperatures of 600 . The engine drives a reversible refrigerator which operates between reservoirs at temperatures of 40 and -20 . The heat transfer to the heat engine is 2000KJ and the work output of the combination is 360 KJ. Calculate the net heat transfer to the reservoir at 40 .

63. Source “A” can supply heat at a rate of 11000KJ/min. at 320 and source “B”

can supply heat at a rate of 22000KJ/min. at 68 . Which of the two sources you will choose for supplying heat to a reversible engine in order to get more power? Take the temperature of the surroundings as 30 .

64. A fish freezing plant requires 50 ton of refrigeration. The freezer temperature is -40 while the ambient temperature is 35 . If the C.O.P. of the plant is 25% of the maximum possible C.O.P., calculate the power required to run the plant.

65. The efficiency of the reversible engine can be increased either by increasing the temperature of the high temperature reservoir, Keeping the temperature of the low temperature reservoir constant or by decreasing the temperature of the low temperature reservoir, keeping the temperature of the high temperature reservoir constant. Out of these two methods which one is more efficient way for increasing the efficiency of reversible engine? Discuss the limitations of the above methods.

66. A heat engine derives a refrigerator whose C.O.P. is 4.5. If the efficiency of the heat engine is 35% and 1500 KJ of heat is removed per hour by the refrigerator from the cold body, find the rate of heat supplied to the heat engine.

67. A refrigerator that operates on a reversed Carnot cycle removes 600 KJ of heat per minute from a low-temperature reservoir at -12 . Determine the C.O.P. of the refrigerator and the power required by it.


68. It is proposed to heat a house using a heat pump. The heat transfer from the house is 95000 KJ/hr. The house is to be maintained at 30 while the outside

air is at a temperature of 6 . While the minimum power required to run the heat pump is 30 kW, find the C.O.P. of the pump.

69. The thermal efficiency of the heat engine is 28%. Find (a) the ratio of work done to the heat rejected and (b) the amount of heat transferred from the high temperature reservoir to the engine per KWh of work delivered by the engine.

70. Two reversible heat engines are placed in series. The first one receives 6400 KJ of heat per minute from a high temperature reservoir at 1300 and rejects heat to a low temperature reservoir at T K. The second one in turn receives the heat rejected by the first reversible engine and rejects heat to another low-temperature reservoir at 400K. Determine the heat rejected per minute by the first and second engines when equal work is delivered by each of them.

71. A reversible heat engine works between three thermal reservoirs A, B and C. The engine absorbs equal amount of heat from the thermal reservoirs A and B kept at temperatures of and respectively and rejects heat to the thermal reservoir

C kept at a temperature of . The efficiency of the engine is “a” times the

efficiency of the reversible engine which works between the two reservoirs A and C. Prove that

72. Two Carnot engines A and B are connected in series between two thermal reservoirs maintained at 1000 K and 100 K respectively. Engine A receives 1680 KJ of heat from the high temperature reservoir and rejects heat to the Carnot engine B. Engine B takes in heat rejected by engine A and rejects heat to the low temperature reservoir. If engines a and B have equal thermal efficiencies, determine (a) the heat rejected by engine B (b) the temperature at which heat is rejected by engine A (c) the work done by engines A and B respectively.

73. If in the problem (72) engines A and B deliver equal work, determine (a) the amount of heat taken in by engine B and (b) efficiencies of the engine A and B.

74. A working fluid goes through a Carnot cycle. The upper and lower absolute temperatures being and respectively. Heat received is and rejected is

. On account of heat losses, the heat source temperature is higher than

and heat sink temperature is lower than . If and

, where K is a dimensional constant and and being absolute temperatures,

show the efficiency is given by

Entropy

75. State and prove “Inequality of Clausius”.76. Define entropy and prove that it is a property.77. Prove that the effect of irreversiblities increases the entropy. What is lost work?

78. What is the “Principle of increase of entropy”?

79. 2 kg of water at 200 is mixed with 3 kg of water at 50 in an isolated system. Calculate the change of entropy of the universe due to mixing process.

80. 2 kg of water at 100 is mixed with 1 kg of ice at 0 in an isolated system. Calculate the change of entropy of the universe due to mixing process.


82. 2 kg of water at 100 is mixed with 5 kg of ice at 0 in an isolated system. Calculate the change of entropy of the universe due to mixing.

83. 500 Kcal of heat is transferred by conduction from a reservoir at 437 . Determine the change in entropies of the two reservoirs. Is there any change of entropy in universe?

84. During a reversible process the entropy and temperature are related by where A and B are dimensional constants. Find the heat transfer

when temperature changes during the process from to .

85. (a) 1 kg of water at 500 K is brought into contact with a heat reservoir at 600 K. When the water has reached 600 K, calculate the entropy change (i) of the water (ii) of the heat reservoir (iii) of the universe.

b) If the water had been heated from 500 K to 600 K by first bringing it into contact with a reservoir at 550 K and then with a reservoir at 600 K, what would have been the entropy change of the universe?

c) Explain how the water might be heated from 500 K to 600 K with almost no change of entropy of the universe.

86. In a reversible cycle 200 Kcal of heat is received at 500 K, then an adiabatic process reduces the temperature of 400 K at which 100 Kcal of heat is received, then a further adiabatic expansion reduces the temperature to 300 K, at which 200 Kcal of heat is rejected.

a) Find the change of entropy as the system is restored to its initial state in the remainder of the cycle.

b) If during the remainder of the cycle heat is transferred only at 400 K, how much heat is transferred and in what direction?

87. Compare the thermal efficiencies of reversible cycles 1231 and 12’31, which are shown in the figure below.

88. What do you mean by available and unavailable energy?

89. A reversible engine operates between three reservoirs as shown in figure below. If its thermal efficiency is 40% and W = 2100 KJ, calculate the temperature

and the heat quantities and and also indicate the direction of with 7.0 reservoir.

90. A reversible engine as shown in figure below draw 1250 KJ from 525 K reservoir and does 210 KJ of work. Find the amount of heat interactions and directions with the other two reservoirs. What is the thermal efficiency of the engine?

91. Solve the above problem if the temperatures of the reservoir s A, B and C are respectively 225 K, 165 K and 112.5 K.

Thermodynamic cycles

92. What do you understand by Air-standard cycles as referred to I.C. engines? State the assumption made there in.

93. Derive the expression for the thermal efficiency of an Otto cycle in terms of compression ratio. What do you mean by mean effective pressure?


94. Derive the expression for the thermal efficiency of a Diesel cycle in terms of compression ratio and cut-off ratio.

95. At the beginning of the compression in an air-standard Otto cycle = 50 ,

= 1 bar and = 0.2 . The compression ratio is 6. The maximum temperature

is 1400 . Compute the heat added, heat rejected, network, the air standard thermal efficiency and the mean effective pressure.

96. An engine of 250 mm bore and 375 mm stroke works on Otto cycle. The clearance volume is 0.00263 . The initial pressure and temperature are 1 bar and 50 . If the maximum pressure is limited to 25-bar, find the following (a) the air-standard efficiency of the cycle, (b) the mean effective pressure of the cycle.

97. An engine working on Otto cycle has a volume of 0.45 , pressure of 1 bar and temperature of 30 at the beginning of the compression stroke. At the end of the compression the pressure is 11-bar. 210 KJ of heat is added at constant volume. Determine: (a) pressures, temperatures and volumes at Salient points (b) percentage clearance (c) efficiency (d) network per cycle (e) mean effective pressure (f) power developed by the engine if the number of working cycles per minute is 210.

98. Show the efficiency of the Diesel cycle is less than that of the Otto cycle for the same compression ratio and heat supplied, whereas the Diesel cycle is more efficient than the Otto cycle for the same maximum pressure and heat supplied.

99. In an air-standard Diesel cycle the temperature and pressure at the beginning of compression are 40 and 1 bar. The temperatures before and after the supply are 400 and 1500 respectively. Calculate (a) heat supplied, heat rejected and work done per kg of air (b) thermal efficiency and (c) mean effective pressure.

100. The stroke length and cylinder diameter of a C.I. engine (working on ideal Diesel cycle) are 250mm and 150 mm respectively. If the clearance volume is 0.0004and fuel injection takes place for 5% of the stroke. Determine: (a) the ideal thermal efficiency of the engine (b) If the fuel cut-off is delayed from 5% to 8%, calculate the percentage loss in the ideal efficiency.

101. An engine with 200 mm cylinder diameter and 300 mm stroke works on Diesel cycle. The initial pressure and temperature of air are 1 bar and 27 . The cut-off is 8% of the stroke and compression ratio is 15. Determine (a) pressure and temperature at salient points (b) air-standard efficiency (c) mean effective pressure (d) power developed by the engine if number of cycles per minute is 380.


Sheet No. 5BOILERS AND MOUNTINGS

102 a) What is a boiler? b) What is a fire tube boiler? c) What is a water tube boiler? d) Give examples of water and fire tube boilers.

103. What are important mountings of a boiler? Why boiler mountings are used?104. What are the accessories of a boiler? Why boiler accessories are used?105. What are the points to be taken care of before starting a boiler?106. What are high and low pressure boilers? 107. What do you mean by internally fired and externally boilers?108. What is the function of a super heater?109. Why economizers are used in a boiler plant?110. How are boilers classified? Give the basis on which the classification is based.

Also give the name of at least one boiler of each type.111. Sketch and explain a) Lancashire boiler b) Babcock and Wilcox boiler c) Cochran boiler112. A boiler plant supplies 2700 kg of steam per hour at a pressure of 7.5-bar and

0.98 dry from feed water at 41.5 when using 375 kg of coal having a calorific value of 31000 KJ/kg. Determine the efficiency of the boiler and the equivalent evaporation from and at 100 . Find the saving in fuel per hour if by fitting an economizer it is estimated that the feed water could be raised to 100assuming other conditions remain unaltered and the efficiency of the boiler increases by 6 percent.

113. Steam leaving the boiler at a pressure of 12-bar enters the super heater where it receives heat at constant pressure. The condition of steam entering the super heater is 0.95 dry and leaves it at temperature of 250 . Calculate the heat received by the steam in the super heater and increase in volume of all steam as it passes through the super heater.

114. The following observations were made in a boiler plant consisting of six boilers and an economizer Equivalent evaporation from and at 100 per kg of dry coal = 9.1 kgTemperature of feed water to economizer = 15Temperature of feed water to boiler = 100Calorific value of coal per kg = 30000 KJ/kgTemperature of air = 15Temperature of flue gases entering the economizer = 367Mass of flue gas per kg of dry coal = 18 kgSpecific heat of flue gases = 1.005 KJ/kgCalculate a) efficiency of the boiler alone b) efficiency of the economizer alone c) efficiency of the whole plant.

115. A coal fired boiler plant consumes 400 kg of coal per hour. The boiler evaporates 3200 kg of water at 44.5 into superheated steam at a pressure of 12-bar and 275 . If the calorific value of fuel is 32660 KJ/kg of coal. Determine a) equivalent evaporation from and at 1010 and b) thermal efficiency of the boiler.

116. A boiler evaporates 8 kg of water per kg of coal into dry saturated steam at 10-bar pressure. The feed water temperature is 46 . Find the equivalent evaporation from and at 100 . Also calculate the factor of evaporation.

117. The following observations were made in a boiler:Coal used = 200kgCalorific value of coal = 29800 KJ/kgSteam pressure = 11.5-barWater evaporated = 2000kg


Feed water temperature = 34Calculate the equivalent evaporation from and at 100 per kg of coal and efficiency of the boiler if the steam is 0.95 dry.

118. (a) What is meant by “Draught”? (b) What do you mean by “Natural Draught” and “Artificial Draught”?(c) Derive expression for height of the chimney.(d) Find the condition for maximum discharge through a chimney.


Sheet No. 6HEAT TRANSFER

119. Enumerate the three bodies by which heat can transferred from one place to another. Which is the slowest of all?

120. How do you define the thermal conductivity of a material?

121. What do you understand by the terms “convective heat transfer co-efficient” and “overall heat transfer co-efficient”?

122. Derive an expression for heat loss in through a composite wall of layers (i) without considering convective heat transfer co-efficient and (ii) considering the convective heat transfer co-efficient.

123. Derive an expression for critical thickness of insulation.

124. Derive an expression for heat flow through composite walls (one dimensional steady state conduction).

125. Derive an expression for one dimensional steady state heat flow through cylinder.

126. The inner surface of a plane brick wall is at 40 and the outer surface is at 20. Calculate the rate of heat transfer per of surface area of wall, which is

250 mm thick. The thermal conductivity of the brick is 0.52 .

127. Determine the rate of heat flow through the boiler wall made of 2 cm thick and covered with an insulating material of 0.5 cm thick. The temperatures at the inner and outer surfaces of the wall are 300 and 50 respectively.

k(steel) = 58 k(insulation) = (0.116)

128. A mild steel tank of wall thickness 10 mm contains water at 90 . Calculate the rate of heat loss per of tank surface area when the atmospheric temperature is 15 . The thermal conductivity of mild steel is 50 , and the heat transfer co-efficient for inside and outside the tank are 2800 and 11 , respectively. Calculate also the temperature of the outside surface of the tank.

129. A cold storage room has walls of 0.23 m of brick on the outside, 0.08 m of plastic foam, and finally 15 mm of wood on the inside. The outside and inside air temperatures are 22 and -2 respectively. If the inside and outside heat transfer co-efficient is respectively 29 and 12 and the thermal conductivities of brick, foam and wood are 0.98, 0.02 and 0.17 respectively. Determine (i) the rate of heat removal by refrigeration if the total wall area is 90 , and (ii) the temperature of the inside surface of the brick.

130. Calculate the heat flowing through a furnace wall 0.23 m thick, the inside and outside surface temperatures are 1000 and 200 respectively. Assume the mean thermal conductivity of the wall is 1.1 . Assuming that 7 mm of insulation (k = 0.075 ) is added to the outside surface of the wall and reduces the heat loss 20%; calculate the outside surface temperature of the wall. If the cost of insulation is Rs. 70 per square meter what time will be required to pay for the insulation? Base the calculations on the 24 hours operation per day and 199 days per year. Heat energy may be valued at Rs. 10 per 1000 .


131. Hot air at a temperature of 60 is flowing through a steel pipe of 100 mm diameter. The pipe is covered with two layers of different insulating materials of thickness 50 mm and 30 mm, and their corresponding thermal conductivities are 0.23 and 0.37 . The inside and outside heat transfer co-efficient is 58 and 12 . The atmosphere is at 25 . Find the rate of heat loss from a 50 m length of pipe. Neglect the resistance of steel pipe.

132. A steam pipe of 160 mm inside diameter and 170 mm outside diameter (k = 58) is covered with first layer of insulating material of 30 mm thickness (k =

0.17 ) and second layer of insulating material of 50 mm thickness (k = 0.093 ). The temperature of steam passing through the pipe is 30 . Taking inner and outer heat transfer co-efficient 30 and 5.8 respectively, find the heat loss per meter length of pipe.

133. A steel pipe of 100 mm bore and 7 mm wall thickness, carrying steam at 260 , is insulated with 40 mm of an insulated high temperature diatomaceous earth covering. This covering is in turn insulated with 60 mm of asbestos felt. If the atmospheric temperature is 15 , calculate the rate at which the steam per m length of the pipe loses heat. The heat transfer co-efficient for the inside and outside surfaces are 550 and 15 , respectively and the thermal conductivities of steel, diatomaceous earth and asbestos felt are 50, 10.09 and 0.07 respectively. Calculate:(i) The total heat loss per hour(ii) The total heat loss per meter square of outer surface.(iii) The heat loss per meter square of pipe surface.(iv) The temperature between the two layers of insulation.


Sheet No. 7Shear Force and Bending Moment Diagrams

134. Draw the bending moment and shear force diagrams for the cantilever beam as shown in the figure.

20 KN 20 KN 10 KN

1 m 1m 1.5 m.

135. The simply supported beam as shown in the figure carries two concentrated loads and a uniformly distributed load. Draw shear force diagram and bending moment diagram.

10 KN 20 KN 10 KN/m2 m 2 m 4 m

136. A simply supported beam of AB of 6 m span is loaded as shown in the figure. Draw the shear force diagram and bending moment diagram.

80 KN40 KN/m

A B3 m 1.5 m 1.5 m

137. Draw the shear force and bending moment diagram for the beam as shown in the figure.

20 KN/m 40 KN 120 KN-m

A C B3 m 1.5 m 1.5 m

138. Draw the shear force and bending moment diagram for the overhanging beam as shown in the figure and indicate the point of contra flexure.

20 KN/m 40 KN 20 KN

A B C D2 m 2 m 1 m


139. Draw the shear force and bending moment diagram for the overhanging beam as shown in the figure. Indicate all the significant values indicating point of contra flexure.

60 KN/m 20 KN

A B C D E1 m 2 m 1 m 1 m

140. For the beam AC shown below, determine the magnitude of the load P acting at C, such that the reaction at supports A and B are equal. Draw the shear force and bending moment diagram for the beam. Mark the salient points and their values on the diagram. Locate the point of contra flexure if any.

P=?45 KN/m

A D 30 KN-m B C

4 m 2 m 1 m

141. A girder 6 m long rests on two supports with equal overhangs on either side and carries a uniformly distributed load of 30 KN per meter run over the entire length. Calculate the overhangs if the maximum bending moment, positive or negative is to be as small as possible. Draw the shear force and bending moment diagram for the double overhang beam.

30 KN/m

A a B C a D

6 m

142. Draw the shear force and bending moment diagram for the beam as shown in the figure. Indicate the salient values on the diagram.

3 KN/m 3 KN/m 24 KN-m 6 KN

A B C E FD

4 m 2 m 4 m 4 m 4 m

143. Draw the shear force and bending moment diagram for the cantilever beam as shown in the figure.

4 KN/m 20 KN 10 KN

D C B A2 m 1 m 2 m


Sheet No. 8Balancing Of Rotating And Reciprocating Masses

144. Why balancing of the rotating and reciprocating parts of the engine is necessary?

145. Discuss how a single revolving mass is balanced by two masses revolving in different planes.

146. Explain the method of balancing of different masses revolving in a same plane.

147. How the different masses rotating in different planes are balanced?

148. What do you understand by primary and secondary unbalanced force?

149. Explain the terms “Primary balancing” and “Secondary balancing”.

150. Four masses A, B, C, and D is attached to a shaft and revolves in the same plane. The masses are 12 kg, 10 kg, 18 kg and 15 kg respectively and their radii of rotations are 4 cm, 5 cm, 6 cm and 3 cm. The angular positions of the masses B, C and D are , and from the mass A. Find the magnitude and position of the balancing mass at a radius of 10 cm.

151. A circular disc, rotating around a vertical spindle, has the following masses placed on it.

Mass Position of Mass

( With respect to Y-Y in degree)Position of Mass

(Distance from center in mm)

Magnitude of mass

(kg)A 0 260 2.5

B 60 300 3.5

C 150 225 5.0

Determine the magnitude and angular position of a mass that should be placed at 262.5 mm to give balance when rotating. Also, determine the unbalanced force on the spindle, when the disc is rotating at 250 r.p.m.

152. A rotating shaft carries four masses A, B, C and D that are radially attached to it. The mass centers are 3 cm, 3.8 cm, 4 cm and 3.5 cm respectively from the axis of rotation. The masses A, C and D are 7.5 kg, 5 kg and 4 kg respectively. The axial distance between the planes of rotation of A and B is 40 cm and between B and C is 50 cm. The masses A and C are right angles to each other. Find for a complete balance,(i) The angles between the masses B and d from mass A.(ii) The axial distance between the planes of rotation of C and D.(iii) The magnitude of mass B.

153. A, B, C and D are four masses carried by a rotating shaft at radii of 10 cm, 12.5 cm, 20 cm and 15 cm respectively. The planes in which the masses revolve are spaced 60 cm apart and the weights of B, C and D are 10 kg, 5 kg and 4 kg respectively. Find the required mass A and relative angular settings of the four masses so that the shaft is in complete balance.

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