# GATE Mechanical Engineering

GATE 2013 Mechanical Engineering objective type questions and answers
GATE Paper I

1. The critical value of Reynolds number for transition from laminar to turbulent boundary layer in external flows is taken as

(b) 4000
(c) 5 x 105
(d)
3 X 106
(
Expl : Critical value of Reynolds number for transition from laminar to turbulant layer in external flows is taken as 2300.)

2. The by-pass factor of single coil in an air-conditioner is 0.7. The by-pass factor, if three such cooling coils with the same appartus dew point are kept one behind the other will be
(a) 0.210
(b) 0.292
(d) 0.412

3. Which one of the following statements is true for air conditioning duct design ?
(a) Static regain method is used, when the duct work is extensive, total pressure drop is low and flow is balanced
(b) Static regain method is used, when the duct work is extensive, total pressure drop is high and flow is unbalanced
(c) Equal friction method is used, when the duct work is extensive, total pressure drop is low and flow is balanced    -    Answer
(d) Equal friction method is used, when duct work is extensive, total pressure drop is low and flow is unbalanced.

4. For an-conditioned space, RTH = 100 kW; RSHF = 0.75, volume flow rate is equal to 100 m3/minute and indoor design specific humidity is 0.01 kg/(kg of dry air). The specific humidity of supply air is
(a) 0.010
(b) 0.0075
(d) 0.0025

5. For an air-conditioning system, the outdoor and indoor design dry bulb temperature are 45o C and 25oC respectively. The space to be air-conditioned is 20 m X 30m X 5 mand infiltration is estimated to be one air change. If the density and specific heat of air are 1.2 (kg of dry air)/m3 and 1.02 kJ/(Kg of dry air)oC, then the sensible heat load due to infiltration is nearly
(a) 122.4 kW
(b) 61.2 kW
(c) 12.24 kW

6. Match List -I and List ii and select the correct answer using the codes given below the lists:
(hm -    mass transfer coefficient,              D   -  molecular diffusion coefficient
L     -    characteristic length dimension   k   - thermal conductivity , p -  density
Cp   -    specific heat at constant pressure u    -   dynamic viscosity ) Codes :
A    B    C    D

(a)            4    3    2    1
(b)            3    4    2    1            -    Ans
(c)            4    3    1    2
(d)            3    4    1    2

7. In the operation of four-stroke diesel engines, the term 'squish' refers to the
(a) injection of fuel ! in the precombustion chamber    -    Ans
(b) discharge of gases from the precombustion chamber
(c) entry of air into the combustion chamber
(d) stripping of fuel from the core

8. Consider the following statements regarding the advantages of fuel injection over carburetion in S.I. engines :
1. Higher power output and increased volumetric efficiency
2. Simple and inexpensive injection equipment
3. Longer life of injection equipment
4. Less knocking and reduced tendency for back-fire
Select the correct answer using the codes given below :
Codes :
(a) 1, 2 and 3
(b) 1, 2 and 4
(c) 2 and 3
(d) 1 and 4    -    Ans

9. Match List -I(Performance Parameter Y) with List-II (Curves labelled 1,2,3,4 and 5 BHP vs. Y) regarding a C.I. engine run at constant speed and select the correct answer using the codes given below the lists: Codes :
A    B    C    D
(a)            5    3    4    2              -    Ans

(b)            1    3    4    2
(c)            5    4    2    3
(d)            1    4    2    3

10. Match List -I with List -II(Use) and select the correct answer using the codes given below the list:
List - I                                        List - II
A. Supercharging                        1. Multicylinder engine
B. Morse test                               2. C.I. engine
C. Heterogeneous combustion    3. Calorific value
D. Ignition quality of petrol        4. Aircraft engine
5. Octane number
6. Single cylinder S.I. engine

Codes :
A        B      C       D
(a)           4        1        2        5        -    Ans

(b)           6        3        2        5
(c)           6        1        5        2
(d)            4       3        5        2

11. With reference to Turbojet and Rocker engines, consider the following statements :
1. Efficiency of Rocket engines is higher than that of Jet engines
2. Exit velocities of exhaust gases in Rocker engines are much higher than those in Jet engines
3. Stagnation conditions exist at the combustion chamber in Rocket engines
4. Rocket engines are air-breathing engines
Which of these statements are correct ?
(a) 1 and 2    -    Ans
(b) 1, 3 and 4
(c) 2,3 and 4
(d) 1, 2 and 3

12. With respect to I.C. engine emission, consider the following statements :
1.   Evaporative emissions have no carbon monoxide and oxides of nitrogen
2. Blow by emission are essentially carbon monoxide and suspended particulate matter
3. Exhaust emissions contain 100% of carbon monoxide , 100 % of oxides of nitrogen and around 50-55% of hydrocarbons emitted by the engine.
4. There are no suspended particulates in the exhaust.
Of these statements
(a) 1 and 4 are correct
(b) 1 and 3 are correct
(c) 2 and 3 are correct    - Ans
(d) 1,2,3 and 4 are correct

13. A hydrocarbon fuel was burnt with air and the Orsat analysis of the dry products of combustion yielded the following data :
____________________________________________________
Initial volume of dry gas sample                              ---        100 cc
Volume after absorption in pipette 1 containing       ---        89 cc
potassium hydroxide solution
Volume after absorption in pipette 2 containing        ---        84 cc
solution of pyrogallic acid and potassium hydroxide
Volume after absorption in pipette 3 containing        ---        82 cc
cuprous chloride solution
____________________________________________________
The percentage (by volume) of CO2 in the dry product was
(a) 2%
(b) 5%
(c) 11%    -    Ans
(d) 18%

14. Match List -I with List -II(Use) and select the correct answer using the codes given below the list:
List -I (Material)                            List-II (Use)
A. Graphic                                        1. Coolant
B. Thorium-233                                2. Moderator
C. Molten Sodium                             3. Fissionable material
D. Plutonium-239                              4. Fissile material
Codes :
A    B    C    D

(a)            1    4    2    3
(b)            2    4    1    3        -    Ans
(c)            2    3    1    4
(d)            1    3    2    4

15. The data given in the table refers to an engine based on Carnot cycle, where
Q1 = Heat received (kJ/min),     Q2=Hear rejected (kJ/s),    W=Work output (kW)
_______________________________________________
S. No.                Q1                    Q2                    W
_______________________________________________
1.                    1500                    16.80                8.20
2.                    1600                    17.92                8.75
3.                    1700                    19.03                9.30
4.                    1800                    20.15                9.85
If heat received by the engine is 2000 kJ/minute the work output will be, nearly,
(a) 9.98
(b) 10.39
(c) 11.54
(d) 10.95    -    Ans

16.  A system while undergoing a cycle
A__B__C__D__A has the values of heat and work transfers as given in the table :
_____________________________________________________
Q                                       W

Process                   kJ/min                                 kJ/min
A__B                    +687                                       +474
B__C                     -269                                            0
C__D                    - 199                                        -180
D__A                    +75                                              0
The power developed in kW is, nearly,
(a) 4.9     -    Ans
(b) 24.5
(c) 49
(d) 98

17. In a new temperature scale say op, the boiling and freezing points of water at one atmosphere are 100op and 300op respectively. Correlate this scale with the Centigrade scale. The reading of 0o p on the Centigrade scale is
(a) 0oC
(b) 50oC
(c) 100oC
(d) 150oC    -    Ans

18. Match List-I (Name of entity) with List-II (Definition) and select the correct answer using the codes given below the lists:
List-I (Name of entity)                 List-II (Definition) Codes :

A            B          C          D
(a)                2            1            4         3
(b)                2            3            4        1
(c)                4            3            2        1        -    Ans
(d)                4            1            2        3

19. If Pu and pv denote respectively the partial pressure of dry air and that of water in moist air, the specific humidity of air is given by
(a)     Pv
Pu + Pv

(b) Pv
Pu

(c)  0.622 Pv            -    Ans
Pu

(d)  0.622 Pv
Pu +Pv
20. Consider the phase diagram of a certain substance as shown in the given figure. Match List I(Process) with List-II (Curves/lines) and select the correct answer using the codes given below the lists:
List I(Process)                         List-II (Curves/lines)

A. Vaporization                          1.  EF
B. Fusion                                    2.  EG
C. Sublimation                            3.  ED Codes :
A        B        C
(a)                 1        3        2        -    Ans
(b)                 1        2        3
(c)                 3        2        1
(d)                 3        1        2

21. Number of components (C),phase (P) and degrees of freedom (F) are related by Gibbs-phase rule as
(a) C__P__F = 2
(b) F__C__P = 2
(c) C+F - P   = 2
(d) P + F-C = 2    - Ans

22. Consider the following statements :
1. Availability is the maximum theoretical work obtainable.
2. Clapeyron's equaation for dry saturated steam is given by 3. A gas can have any temperature at a given pressure unlike a vapour which has a fixed temperature at a given pressure.
4. Joule Thomson coefficient is expressed as  Of these statements
(a) 1, 2 and 3 are correct     -    Ans
(b) 1, 3 and 4 are correct
(c) 2 and 3 are correct
(d) 1, 2 and 4 are correct

23. Match List-I with List-II and select the correct answer using the codes given below the lists :  Codes :
A        B        C        D
(a)                3        4        1        2        -     Ans
(b)                1        4        3        2
(c)                3        2        1        4
(d)                1        2        3        4

24. The temperature -entropy diagram for a steam turbine power plant, operating on the Rankine cycle with reheat and regenerative feed heating is shown in the given figure. If m denotes the fraction of steam bled for feed heating, the work developed in the turbine per kg steam entering the turbine at state 5 is (a) (h5 -h4) + (1-m)(h3-h1)                -    Ans
(b) (h5-h4)+(h3-h2)+(1-m)(h2-h1)
(c) 2h5-h4-h2+(1-m)(h2-h1)
(d) (h5-h4) +(1-m)(h3-h2

25. The working temperature in the evaporator and condenser coils of a refrigerator are -30oC and 32oC respectively. If the actual refrigerator has a C.O.P of 0.75 of the maximum. the required power input for a refrigerating effect of 5 kW is, nearly,
(a) 1.7 kW        -    Ans
(b) 2.94 kW
(c) 3.92 kW
(d) 4.0 kW

26. Match List -I with List-II and select the correct answer using the codes given below the lists:
List -I                                            List-II
A. Air standard efficiency of Otto cycle              1. Mechanical efficiency
B. Morse test                                                  2. Diesel cycle
C. Constant volume cycle                                3. Brake thermal efficiency
D. Constant pressure heat addition                   4. Otto cycle
5. 1-      1
r(r-1)
Codes :
A        B        C          D
(a)                5        1        4            2            -    Ans

(b)                3        5        2            4
(c)                3        5        4            2
(d)                5        1        2            4

27. Match List -I (fuels)  with List-II (Characteristics/Usages) and select the correct answer using the codes given below the lists:
List -I (fuels)                                List-II (Characteristics/Usages)
A. Semi-bituminous coal                      1. Methane and carbon dioxide
B. High -speed diesel oil                       2. Propane and butane
C. Biogas                                               3. Calorific value of 10,6000 kCal/kg
D. LPG                                                  4. Power plants

Codes :
A        B        C          D
(a)                3        4        1            2
(b)                4        3        2            1    -    Ans
(c)                3        4        2            1
(d)                4        3        1            2

28. Consider the following statements :
1. Motor gasoline is mixture of various hydrocarbons with a major proportion being aromatic hydrocarbons.
2. Compressed natural gas is mainly composed of methane
3. Producer gas has a predominant component of hydrogen with lesser proportion of carbon monoxide.
4. Cetane number of fuel used in diesel engines in India is in the range of 80 to 90.
Which of these statements are correct ?
(a) 1 and 2
(b) 1 and 3        -    Ans
(c) 2, 3 and 4
(d) 1,2, 3 and 4

29. Consider the following statements :
1. For the combustion of pulverised coal, 5 to 10% excess air is required.
2. Air contains 21% oxygen by weight
3. The flue gases from a coal -fired furnace contain around 70% nitrogen by volume.
4. In the combustion of liquid fuels, the number of moles of the products are invariably greater than the number of moles of the reactants.
Of these statements
(a) 1, 2 and 4 are correct
(b) 1, 3 and 4 are correct
(c) 2,3 and 4 are correct
(d) 1 and 3 are correct

30. Match items in List-I (Process) with those in List-II(Characteristic) and Select the correct answer using the codes given below the lists :
List -I (Process)                List - II (Characteristic)
A. Throttling process                1. No work done
B. Isentropic process                2. No change in entropy
C. Free-expansion                    3. Constant internal energy
D. Isothermal process               4. Constant enthalpy
Codes :
A        B        C          D
(a)                4        2        1            3        -    Ans

(b)                1        2        4            3
(c)                4        3        1            2
(d)                1        3        4            2

31. A rectangular tank of square cross-section is having its height equal to twice the length of any side at the base. If the tank is filled up with a liquid, the ratio of the total hydrostatic force on any vertical wall to that at the bottom is
(a) 2.0
(b) 1.5
(c) 1.0    -    Ans
(d) 0.5

32. Differential pressure head measured by mercury oil differential manometer (specific gravity of oil is 0.9) equivalent to a 600 mm difference of mercury levels will nearly be
(a) 7.62m of oil
(b) 76.2 m of oil
(c) 7.34m of oil
(d) 8.47 m of oil    -    Ans

33. A block of aluminium having mass of 12 kg is suspended by a wire and lowered until sub-merged into a tank containing oil of relative density 0.8. Taking the relative density of aluminium as 2.4, the tension in the wire will be (take g=10 m/s2
(a) 12000 N
(b) 800 N
(c) 120 N
(d) 80 N    -    Ans

34. A barge 30 m long and 10 m wide has a draft of 3 m when floating with its sides in vertical position. if it s centre of gravity is 2.5 m above the bottom, the nearest value of metacentric height is
(a) 3.28 m
(b) 2.78 m    -    Ans
(c) 1.78 m
(d) zero

35. A cylindrical vessel having its height equal to its diameter is filled with liquid and moved horizontally at an acceleration equal to acceleration due to gravity. The ratio of the liquid left in the vessel to the liquid at static equilibrium condition is
(a) 0.2
(b) 0.4
(c) 0.5    -    Ans
(d) 0.75

36. The shear stress developed in a libricating oil, of viscosity 9.81 poise, filled between two parallel plates 1 cm apart and  moving with relative velocity of 2 m/s is
(a) 20 N/m 2
(b) 19.62 N/m 2     -    Ans
(c) 29.62 N/m 2
(d) 40 N/m 2

37. The convective acceleration of fluid in the x-direction is given by 38. Match List-I (Types of flow) with List-II (Basic ideal flows) and select the correct answer : using the codes given below the lists :
List-I (Types of flow)                                 List-II (Basic ideal flows)

A. Flow over a stationery cylinder 1. Source + sink + uniform flow
B. Flow over a half Ranking body 2. Doublet + uniform flow
C. Flow over a rotating body        3. Source + uniform flow
D. Flow over a Rankine oval        4. doublet + free vortex + uniform flow
Codes :
A       B           C            D
(a)                1        4            3           2
(b)                2        4            3           1
(c)                1        3            4           2
(d)                2        3            4           1        -    Ans

39. A glass tube with a 90oC bed is open at both the ends. it is inserted into a flowing stream of oil, S=0.90, so that one opening is directed upstream and the other is directed upward oil inside the tube is 50 mm higher than the surface of flowing oil. The velocity measured by the tube is, nearly,
(a) 0.89m/s
(b) 0.99 m/s
(c) 1.40 m/s. -    Ans
(d) 1.90 m/s

40. At location -I of a horizontal line, the fluid pressure head is 32 cm and velocity head is 4 cm. The reduction in area at location II si such that the pressure head drops down to zero.  The ratio of velocities at location-II to that at location -I is (a) 3        -    Ans

(b) 2.5
(c)2
(d) 1.5

41. For maximum transmission of power through a pipe line with total head H, the head lost due to friction hf is given by
(a) 0.1H
(b)  H                  -    Ans
3

(c)   H
2

(d)  2H
3

42. Two pipelines of equal length and with diameters of 15 cm and 10 com are in parallel and connect two reservoirs. The difference in water levels inthe reservoirs is 3 m. if the friction is assumed to be equal, the ratio of the discharge due to the larger dia pipe to that of the smaller dia pipe is, nearly,
(a) 3.375
(b) 2.756
(c) 2.25
(d) 1.5        -    Ans

43. The critical depth of a rectangular channel of width 4.0 m for a discharge of 12 m3/s is nearly,
(a) 300 mm
(b) 30 mm
(c) 0.972 m    -    Ans
(d) 0.674 m

44. An open channel flow encounters a hydraulic jump as shown in the figure. The following fluid flow conditions are observed between A and B : 1. Critical depth
The correct sequence of the flow conditions in the direction of flow is
(a) 1,2,3,4
(b) 1,4,2,3
(c) 2,1,4,3    -    Ans
(d) 4,2,3,1

45. Laminar developed flow at an average velocity of 5 m/s occurs in a pipe of 10 cm radius. The velocity at 5 com radius is
(a) 7.5 m/s.
(b) 10 m/s
(c) 2.5 m/s
(d) 5 m/s       -    Ans

46. In a fully-developed turbulent pipe flow, assuming 1/7th power law, the ratio of the mean velocity at the centre of the pipe to the average velocity of the flow is
(a) 2.0
(b) 1.5
(c) 1.22
(d) 0.817    -    Ans

47. The pressure drop in a 100 mm diameter horizontal pipe is 50 kPa over a length of 10 m. The shear stress at the pipe wall is
(a) 0.25 kPa
(b) 0.125 kPa
(c) 0.50 kPa    -    Ans
(d) 25.0 kPa

48. Which portion of the centrifugal compressor characteristics shown in the figure is difficult to obtain experimentally? (a) RS    -    Ans
(b) ST
(c) TU
(d) UV

49. Consider the following statement regarding the axial flow in an air compressor:
1. Surging is a local phenomenon while stalling affects the entire compressor
2. Stalling is a local phenomenon while surging affects the entire compressor
3. The pressure ratio of an axial compressor stage is smaller than that of a centrifugal compressor stage.
Of these statements
(a) 1, 2 and 3 are correct
(b) 1 and 2 are correct
(c) 2 and 3 are correct
(d) 1 and 3 are correct     -    Ans

50. Consider the specific speed ranges of the following types of turbines :
1. Francis    2. Kaplan    3.Pelton
(a) 1,2,3
(b) 3,1,2    -    Ans
(c) 3,2,1
(d) 2,3,1

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