GATE 2024 Question Paper for Naval Architecture and Marine Engineering (NM)

GATE
2024
Question Paper | Answer Key
Graduate Aptitude Test in Engineering
(GATE) is a prestigious national-level exam
that assesses candidates for
comprehensive understanding in various
undergraduate-level subjects in
Engineering, Technology, Science,
Architecture, and Humanities.

General Aptitude (GA)
Q.1 – Q.5 Carry ONE mark Each

Q.1 If ‘→’ denotes increasing order of intensity, then the meaning of the words

[dry → arid → parched] is analogous to [diet → fast → ________ ].

Which one of the given options is appropriate to fill the blank?

(A) starve

(B) reject

(C) feast

(D) deny

Q.2 If two distinct non-zero real variables 𝑥 and 𝑦 are such that (𝑥 + 𝑦) is proportional
𝑥
to (𝑥 − 𝑦) then the value of
𝑦

(A) depends on 𝑥𝑦

(B) depends only on 𝑥 and not on 𝑦

(C) depends only on 𝑦 and not on 𝑥

(D) is a constant

Page 1 of 42

Q.3 Consider the following sample of numbers:

9, 18, 11, 14, 15, 17, 10, 69, 11, 13

The median of the sample is

(A) 13.5

(B) 14

(C) 11

(D) 18.7

Q.4 The number of coins of ₹1, ₹5, and ₹10 denominations that a person has are in the
ratio 5:3:13. Of the total amount, the percentage of money in ₹5 coins is

(A) 21%

(B) 2
14 7%

(C) 10%

(D) 30%

Page 2 of 42

Q.5 For positive non-zero real variables 𝑝 and 𝑞, if

log (𝑝2 + 𝑞 2 ) = log 𝑝 + log 𝑞 + 2 log 3 ,

𝑝4 +𝑞4
then, the value of is
𝑝2 𝑞 2

(A) 79

(B) 81

(C) 9

(D) 83

Page 3 of 42

Q.6 – Q.10 Carry TWO marks Each

Q.6 In the given text, the blanks are numbered (i)−(iv). Select the best match for all the
blanks.

(i) (ii)
Steve was advised to keep his head before heading to bat;
(iii)
for, while he had a head batting, he could only do so with a cool head
(iv)
s his shoulders.

(A) (i) down (ii) down (iii) on (iv) for

(B) (i) on (ii) down (iii) for (iv) on

(C) (i) down (ii) out (iii) for (iv) on

(D) (i) on (ii) out (iii) on (iv) for

Page 4 of 42

Q.7 A rectangular paper sheet of dimensions 54 cm × 4 cm is taken. The two longer
edges of the sheet are joined together to create a cylindrical tube. A cube whose
surface area is equal to the area of the sheet is also taken.

Then, the ratio of the volume of the cylindrical tube to the volume of the cube is

(A) 1/π

(B) 2/π

(C) 3/π

(D) 4/π

Page 5 of 42

Q.8 The pie chart presents the percentage contribution of different macronutrients to a
typical 2,000 kcal diet of a person.

Macronutrient energy contribution

Trans
fat
5%
Saturated fat
20% Carbohydrates
35%

Unsaturated fat
20%
Proteins
20%

The typical energy density (kcal/g) of these macronutrients is given in the table.

Macronutrient Energy density (kcal/g)
Carbohydrates 4
Proteins 4
Unsaturated fat 9
Saturated fat 9
Trans fat 9

The total fat (all three types), in grams, this person consumes is

(A) 44.4

(B) 77.8

(C) 100

(D) 3,600

Page 6 of 42

Q.9 A rectangular paper of 20 cm × 8 cm is folded 3 times. Each fold is made along the
line of symmetry, which is perpendicular to its long edge. The perimeter of the final
folded sheet (in cm) is

(A) 18

(B) 24

(C) 20

(D) 21

Q.10 The least number of squares to be added in the figure to make AB a line of
symmetry is

(A) 6

(B) 4

(C) 5

(D) 7

Page 7 of 42

Q.11 – Q.35 Carry ONE mark Each

Q.11 𝑑𝑧
The value of the contour integral ∮ 2𝑧−𝑧 2 along the circle |𝑧| = 1, oriented in the
counterclockwise sense is

(A) 𝜋𝑖

(B) 0

(C) 2𝜋𝑖

(D) 4𝜋𝑖

Q.12 The tangent plane to the surface 𝑥 2 + 𝑦 2 + 𝑧 = 9 at the point (1, 2, 4) is

(A) 2𝑥 + 4𝑦 + 𝑧 = 14

(B) 4𝑥 + 2𝑦 + 𝑧 = 12

(C) 𝑥 + 4𝑦 + 2𝑧 = 17

(D) 4𝑥 + 𝑦 + 2𝑧 = 14

Page 8 of 42

Q.13 The value of the line integral ∮ 𝑥 2 𝑑𝑥 + 2𝑥 𝑑𝑦 along the ellipse 4𝑥 2 + 𝑦 2 = 4
oriented in the counterclockwise sense is

(A) 𝜋

(B) 2𝜋

(C) 4𝜋

(D) 8𝜋

Q.14 The system of linear equations

𝑥 + 2𝑦 + 3𝑧 = 4

2𝑥 − 𝑦 − 2𝑧 = 𝑎2

−𝑥 − 7𝑦 − 11𝑧 = 𝑎

has a solution if the values of 𝑎 are

(A) −1 and 5

(B) −2 and 3

(C) −5 and 1

(D) −3 and 4

Page 9 of 42

Q.15 A ship with a standard right-handed coordinate system has positive 𝑥, 𝑦 and 𝑧 axes
respectively pointing towards bow, starboard and down as shown in the figure. If
the ship takes a starboard turn, then the drift angle, sway velocity and the heel angle
of the ship for a steady yaw rate respectively are

(A) positive, negative and positive

(B) negative, positive and positive

(C) negative, positive and negative

(D) positive, negative and negative

Page 10 of 42

Q.16 A ship with controls fixed, is modeled as a two degrees of freedom system. For the
linear maneuvering equations of motion for coupled sway and yaw, if the derived
eigenvalues are real and negative, then the ship must possess

(A) positional motion stability

(B) directional stability

(C) straight line stability

(D) both directional and positional motion stabilities

Q.17 Which one of the following cooling systems is used in large marine diesel engines?

(A) Thermosyphon

(B) Forced coolant circulation

(C) Evaporative

(D) Air circulation

Page 11 of 42

Q.18 Which one of the following reduces the ratio of vibratory response amplitude to the
forcing amplitude, in large stationary engine shaft design?

(A) Reduction in axial vibrations of the rotating shaft

(B) Increase in the fundamental frequency of the rotating shaft

(C) Decrease in the rotational speed of shaft

(D) Operating the shaft at a speed exceeding the critical speed

Page 12 of 42

Q.19 The GZ curve for a stable ship is shown in the figure, where P is a point of inflection
on the curve. Match the labels in Column 1 with the corresponding descriptions in
Column 2.

Column 1 Column 2

P I: Angle of vanishing stability

ST II: Maximum GZ

R III: Initial GM

Q IV: Deck edge immersion

(A) R - I; Q - II; ST - III; P - IV

(B) P - I; Q - II; ST - III; R - IV

(C) ST - I; Q - II; R - III; P - IV

(D) R - I; Q - II; P - III; ST - IV

Page 13 of 42

Q.20 Consider an initially perfectly straight elastic column with pinned supports at both
ends. If 𝐸 is the Young’s modulus of the material, 𝐿 is the length of the column
between the supports, and 𝐼 is the least moment of inertia of the constant cross-
sectional area of the column, then the Euler load is given by

(A) 𝜋 2 𝐸𝐼
𝐿2

(B) 𝜋 2 𝐸𝐼
4𝐿2

(C) 𝜋 2 𝐸𝐼
√2𝐿2

(D) 2𝜋 2 𝐸𝐼
𝐿2

Q.21 For a plane strain problem in the x-y plane, it is necessary that

(A) normal stress 𝜎𝑧 is zero

(B) normal strain 𝜀𝑧 is zero

(C) both the normal stresses 𝜎𝑥 and 𝜎𝑦 are zero

(D) (𝑥 −𝑦 )
shear strain 𝛾𝑥𝑦 is equal to 2

Page 14 of 42

Q.22 How many independent material constants in solids are required to define isotropic
materials?

(A) 2

(B) 3

(C) 9

(D) 21

Page 15 of 42

Q.23 Which one of the following is the mass conservation equation?

(A)
𝐷
∭ 𝜌 𝑣.
⃗⃗⃗ 𝑛̂ 𝑑𝑉 = 0
𝐷𝑡
𝑉

(B)
𝜕
∭ 𝜌𝑑𝑉 = 0
𝜕𝑡
𝑉

(C)
𝜕
− ∭ 𝜌𝑑𝑉 = ∬ 𝜌𝑣.
⃗⃗⃗ 𝑛̂ 𝑑𝑠
𝜕𝑡
𝑉 𝑆

(D)
𝐷
− ∭ 𝜌𝑑𝑉 = ∬ 𝜌𝑣.
⃗⃗⃗ 𝑛̂ 𝑑𝑠
𝐷𝑡
𝑉 𝑆

Page 16 of 42

Q.24 Identify the type of flow from the time series plots of instantaneous fluid
velocity (u) at a point.

(A) I - unsteady turbulent flow; II - steady turbulent flow; III - steady laminar flow; IV
- unsteady laminar flow

(B) I - steady turbulent flow; II - unsteady turbulent flow; III - unsteady laminar flow;
IV - steady laminar flow

(C) I - steady turbulent flow; II - unsteady turbulent flow; III - steady laminar flow; IV
- unsteady laminar flow

(D) I - steady turbulent flow; II - unsteady laminar flow; III - unsteady turbulent flow;
IV - steady laminar flow

Page 17 of 42

Q.25 Which of the following hull distortion(s) is/are resisted by a ship’s transverse
bulkhead?

(A) Racking

(B) Torsion

(C) Longitudinal bending

(D) Horizontal bending

Q.26 Which of the following boiler(s) is/are NOT used in a nuclear propulsion system
for ships?

(A) Water tube boiler

(B) Cochran boiler

(C) Double evaporation boiler

(D) Boiled water reactor boiler

Page 18 of 42

Q.27 Which of the following statement(s) is/are correct about strip theory?

(A) It can be used to calculate the surge added mass

(B) It is a two-dimensional theory

(C) It can be used to calculate the pitch added mass

(D) It can be used to calculate the coupled sway, roll and yaw added mass

Q.28 Consider an ideal Rankine cycle as shown in the figure, where T and S represent the
temperature and entropy respectively. The overall efficiency of the cycle can be
improved by

(A) increasing the pressure at which heat is added

(B) decreasing the pressure at which heat is rejected

(C) employing an intercooler

(D) superheating the steam

Page 19 of 42

Q.29 Which of the following statement(s) is/are correct for a thermodynamic closed
system?

(A) The entropy change is positive for a reversible adiabatic process

(B) The entropy change is positive for a reversible cycle

(C) The entropy change is positive for a reversible isothermal heat addition process

(D) The entropy change is negative for a reversible isothermal heat rejection process

Q.30 The arc length of the one arch of the cycloid given by 𝑥 = 𝑡 − sin 𝑡 and
𝑦 = 1 − cos 𝑡 is ________.

Q.31 A 10 m long pipe with inlet and outlet diameters of 40 cm and 20 cm respectively,
is carrying an incompressible fluid with a flow rate of 0.04 m3/s. The ratio of the
velocity at the outlet to that at the inlet is _____ (rounded off to one decimal place)

Page 20 of 42

Q.32 An 80 m long barge with rectangular cross-section of 12 m beam and 4 m draft
floats at even keel. The transverse metacenter (KM) above the keel is _______ m.

Q.33 A 100 m long ship has a cruising speed of 25 knots. A geometrically similar model
of 4 m length is used for resistance prediction in a towing tank. The corresponding
speed of the model is ___________ knots.

Q.34 A cube-shaped pontoon with 200 tonnes of mass placed on it, floats with a freeboard
of 1 m in fresh water. When the mass is removed, the pontoon floats with a
freeboard of 3 m. The length of the pontoon is ______ m (rounded off to two
decimal places).

Page 21 of 42

Q.35 Consider a fluid between two horizontal parallel flat plates 5 mm apart as shown in
the figure. The top plate of dimensions 0.5 m × 2 m is towed with an applied
horizontal force F of 0.01 N, while the infinitely long bottom plate is kept fixed.
The horizontal velocity profile between the plates is assumed to be linear. If the
dynamic viscosity (𝜇) of the fluid is 0.89 × 10-3 N-s/m2, then the towing velocity of
the top plate is _______ m/s (rounded off to three decimal places).

Page 22 of 42

Q.36 – Q.65 Carry TWO marks Each

Q.36 1 0 0
2 1
Consider the matrices 𝑀 = ( ) and 𝑁 = (1 2 0). Which one of the
0 2
1 1 0
following is true?

(A) 𝑀 is not diagonalizable but 𝑁 is diagonalizable

(B) Both 𝑀 and 𝑁 are not diagonalizable

(C) Both 𝑀 and 𝑁 are diagonalizable

(D) 𝑀 is diagonalizable but 𝑁 is not diagonalizable

Page 23 of 42

Q.37 A simply supported beam is subjected to a concentrated moment M at the mid span
as shown in the figure. The magnitude of the bending moment at a distance of L/4
from the left support A is equal to

(A) M

(B) ML
4

(C) M
4

(D) M
2

Page 24 of 42

Q.38 Consider a two-dimensional ship section as shown in the figure. About the point O,
let the sway added mass components be 𝑎22 and 𝑎24 and roll added moment of
inertia be 𝑎44 . The clockwise roll angle is considered positive. The roll added mass
due to roll, about P which is at a distance 𝑧𝑃 above O is given by

(A) 𝑎44 − 𝑎24 𝑧𝑃

(B) 𝑎44 − 𝑎22 𝑧𝑃 − 𝑎24 𝑧𝑃

(C) 𝑎44 − 𝑎22 𝑧𝑃 + 𝑎24 𝑧𝑃

(D) 𝑎22 + 𝑎24 + 𝑎44

Page 25 of 42

Q.39 A ship with a displacement of 10000 tonnes has the center of gravity at 4 m above
the keel and 1.5 m forward of midship. If 2000 tonnes of cargo is placed at 10 m
above the keel and 1.5 m aft of midship, then the new position of the center of
gravity is

(A) 5 m above the keel and 1 m aft of midship

(B) 6 m above the keel and 1 m forward of midship

(C) 6 m above the keel and 1 m aft of midship

(D) 5 m above the keel and 1 m forward of midship

Q.40 The waterplane area of a ship floating in sea water is 2000 m2. The density of
seawater is 1025 kg/m3. If a mass of 246 tonnes is added to the ship, then the TPC
(Tonnes Per Centimeter immersion) and increase in draft (in cm) respectively are

(A) 20.50 and 12

(B) 20 and 12.3

(C) 20.50 and 24

(D) 10.25 and 24.6

Page 26 of 42

Q.41 The open water characteristics of a propeller is shown in the figure. Match the
labels in Column 1 with the corresponding descriptions in Column 2.

Column 1 Column 2

R I: Bollard pull condition

Q II: Feathering condition

P III: Wind milling condition

O IV: Efficiency curve

(A) O - I; P - II; Q - III; R - IV

(B) O - I; Q - II; P - III; R - IV

(C) O - I; R - II; Q - III; P - IV

(D) P - I; Q - II; O - III; R - IV

Page 27 of 42

Q.42 Which one of the following p-h plots represents the ideal vapour compression cycle
with intercooling?

Here, p and h denote pressure and specific enthalpy respectively.

(A)

(B)

(C)

(D)

Page 28 of 42

Q.43 A steel deck plate of a tanker is supported by two longitudinal stiffeners as shown
in the figure. The width of the plate is 𝑎 and its length is 5 times the width. Assume
that the long edge is simply supported, and the short edge is free. The plate is loaded
𝜋𝑦
by a distributed pressure, 𝑝 = 𝑝0 sin ( 𝑎 ), where 𝑝0 is the pressure at 𝑦 = 𝑎/2. The
flexural rigidity of the plate is 𝐷. The plate equation is given by

𝜕4𝑤 𝑝0 𝜋𝑦
(A) 4
= sin ( )
𝜕𝑦 𝐷 𝑎
𝜕2𝑤 𝑝0 𝜋𝑦
(B) = sin ( )
𝜕𝑥 2 𝐷 𝑎
𝜕2𝑤 𝑝0 𝜋𝑦
(C) 2
= sin ( )
𝜕𝑦 𝐷 𝑎
𝜕4𝑤 𝑝0 𝜋𝑦
(D) 4
= sin ( )
𝜕𝑥 𝐷 𝑎

Page 29 of 42

Q.44 Which one of the following psychrometric processes is represented by the line 1-2
in the figure?

(A) Cooling and humidification

(B) Cooling and dehumidification

(C) Heating and humidification

(D) Heating and dehumidification

Page 30 of 42

Q.45 Consider model testing where 𝜆 is the prototype to model length scale ratio. Let ν𝑝
and ν𝑚 denote the corresponding fluid kinematic viscosities. If Froude and
Reynolds similarities are maintained between the prototype and model, then which
one of the following is correct?

(A) ν𝑚 = −3/2 ν𝑝

(B) ν𝑚 = 3/2 ν𝑝

(C) ν𝑚 = 2/3 ν𝑝

(D) ν𝑚 = −2/3 ν𝑝

Page 31 of 42

Q.46 A uniform flow, a point source of strength + at (𝑎, 0) and a point sink of strength
− at (−𝑎, 0) are shown in the figure. The velocity potential 𝜙 resulting from the
superposition of these flow fields is given by

(A) 𝜎 𝜎
𝜙 = −𝑈∞ 𝑥 + 𝑙𝑛√(𝑥 + 𝑎)2 + 𝑦 2 − 𝑙𝑛√(𝑥 − 𝑎)2 + 𝑦 2
2π 2π

(B) 𝜎 𝜎
𝜙 = −𝑈∞ 𝑥 + 𝑙𝑛√(𝑥 − 𝑎)2 + 𝑦 2 − 𝑙𝑛√(𝑥 + 𝑎)2 + 𝑦 2
2π 2π

(C) 𝜎 𝜎
𝜙 = 𝑈∞ 𝑥 + 𝑙𝑛√(𝑥 − 𝑎)2 + 𝑦 2 − 𝑙𝑛√(𝑥 + 𝑎)2 + 𝑦 2
2π 2π

(D) 𝜎 𝜎
𝜙 = 𝑈∞ 𝑥 + 𝑙𝑛√(𝑥 + 𝑎)2 + 𝑦 2 − 𝑙𝑛√(𝑥 − 𝑎)2 + 𝑦 2
2π 2π

Page 32 of 42

Q.47 In the solution of statically indeterminate problems, Castigliano’s second theorem
employs the

(A) principle of virtual work

(B) virtual displacement method

(C) virtual force method

(D) principle of least work

Q.48 Consider the function 𝑓(𝑥, 𝑦) = 𝑥 4 + 𝑦 4 − 4𝑥𝑦 + 1. Which of the following
is/are correct?

(A) The minimum value of 𝑓occurs at (0, 0)

(B) The point (0, 0) is a point of inflection

(C) 𝑓 has three critical points

(D) The minimum value of 𝑓 is −1

Page 33 of 42

Q.49 Consider the 2𝜋 – periodic function defined by

−1 𝑖𝑓 − 𝜋 < 𝑥 ≤ 0
𝑓(𝑥) = {
1 𝑖𝑓 0 < 𝑥 < 𝜋

Which of the following is/are correct about its Fourier series expansion,
𝑎0
+ ∑∞
𝑛=1 𝑎𝑛 cos 𝑛𝑥 + 𝑏𝑛 sin 𝑛𝑥 ?
2

(A) 1
𝑎𝑛 = ∀ 𝑛 = 1, 2, ….
𝑛

(B) 𝑎0 = 0

(C) 4
𝑏𝑛 = 𝑛𝜋 if 𝑛 is odd

(D) 4
𝑏𝑛 = − 𝑛𝜋 if 𝑛 is even

Page 34 of 42

Q.50 Consider the following momentum equation. Let A, B and C denote the first, second
and third term on the left-hand side respectively and, D and E denote the first and
second term on the right-hand side respectively. Which of the following statement(s)
is/are correct?

𝜕𝑽 𝑽𝟐
𝜌[ + 𝑔𝑟𝑎𝑑 | | + (𝑐𝑢𝑟𝑙 𝑽) × 𝑽] = −𝑔𝑟𝑎𝑑(𝑃 + 𝜌𝑔𝑧) + 𝜇∇2 𝑽
𝜕𝑡 2

(A) If terms A, C and E vanish, then the flow is irrotational.

(B) If term A vanishes, then the flow is steady.

(C) If term D vanishes, then it leads to the Euler’s equation.

(D) If terms A, B, C and E vanish, then it leads to the hydrostatic equation.

Page 35 of 42

Q.51 Consider the flow past a curved wall as shown in the figure. Which of the
following statement(s) is/are correct?

(A) P is the separation point.

(B) Between T and U, the pressure gradient in the streamwise direction at the wall is
positive.

(C) U is the stagnation point.

(D) Between T and U, the streamwise-velocity gradient in the normal direction at the
wall is negative.

Q.52 If 𝑋 is a Poisson random variable with mean 𝜇 = 1, then the conditional probability
of the event {𝑋 ≥ 2} given that the event {𝑋 ≥ 4} has occurred, is ________
(rounded off to two decimal places).

Page 36 of 42

Q.53 The value of the triple integral ∭(𝑥𝑦 2 + 𝑦𝑧 3 ) 𝑑𝑥 𝑑𝑦 𝑑𝑧 over the region given by
−1 ≤ 𝑥 ≤ 1, 3 ≤ 𝑦 ≤ 4, 0 ≤ 𝑧 ≤ 2, is _______.

Q.54 A 4-cylinder, 4-stroke diesel engine operating at 3000 rpm has a compression
ratio r of 12 and cut-off ratio rc of 2.5. The temperature rise during the heat addition
process is 2400 K. The efficiency of an air-standard diesel cycle is given by
𝛾
1 1 𝑟 −1
𝜂 = 1 − 𝑟 𝛾−1 (𝛾 𝑟𝑐 −1 ) . Assume the working fluid as air with a mass flow rate of
𝑐
0.05 kg/s, 𝛾 = 1.4, and 𝐶𝑝 = 1.004 kJ/kg-K.

The power output of the engine is ________ kW (rounded off to the nearest integer).

Q.55 A ship travelling in head seas experiences a bending moment of 200 MN-m. The
ship’s cross section is assumed to be a box girder of 30 m beam and 10 m depth
with a 10 mm plate thickness. The maximum bending stress is _______ MPa
(rounded off to the nearest integer).

Page 37 of 42

Q.56 A single degree of freedom system has a mass, stiffness and damping of 200 kg,
20 N/m and 62 N-s/m respectively. For a forced oscillation system, if the excitation
frequency is equal to the undamped natural frequency, then the dynamic
magnification factor is ________ (rounded off to three decimal places).

Q.57 The wave spectrum and the ship heave Response Amplitude Operator (RAO) are
shown in the figure. The variance of the heave motion is ______ m2 (rounded off
to three decimal places).

Page 38 of 42

Q.58 Consider a thin-walled closed cylindrical steel vessel with an internal pressure of
2 N/mm2. The inner diameter is 1 m, and the thickness of the wall is 10 mm. The
hoop stress is _______ N/mm2 (rounded off to one decimal place).

Q.59 A propeller disc of diameter 2 m produces a thrust of 88 kN while advancing at a
speed of 5 m/s in fresh water of density 1000 kg/m3. Based on the axial momentum
theory, the propeller efficiency is _____________ % (rounded off to one decimal
place).

Page 39 of 42

Q.60 Consider a rectangular plate with in-plane loads. The state of the stress at an
arbitrary angle 𝜃 is defined by 𝑥 , 𝑦 and 𝜏𝑥𝑦 as shown in the figure. If the principal
plane is at 𝜃 = 45o, and the principal stresses are 𝑥 = 8 N/mm2 and 𝑦 = 3 N/mm2,
then the corresponding 𝜏𝑥𝑦 = _______ N/mm2.

Q.61 A ship of 5000 tonnes displacement has a rectangular tank 6 m long and 10 m wide,
half-filled with oil of relative density 0.8. The virtual reduction in the transverse
metacentric height of the ship due to free surface effect of the oil in the tank is
______ cm.

Page 40 of 42

Q.62 An ocean wave of period 8 s and height 2 m is propagating in the Indian Ocean from
south to north. According to linear wave theory, for the wave to be considered as a
deep-water wave, the minimum water depth should be ______ m (rounded off to
the nearest integer).

Q.63 Consider a gas turbine combustor with air as the working fluid. The flow enters the
device at 500 K and leaves at 1400 K with a mass flow rate of 0.1 kg/s. The changes
in kinetic energy and potential energy of the flow are neglected. Assuming
𝐶𝑣 = 0.717 kJ/kg-K and R = 0.287 kJ/kg-K, the rate of heat addition is ______ kW
(rounded off to the nearest integer).

Q.64 Consider a circular cylinder of diameter 0.5 m and length 2 m, rotating in clockwise
direction at a speed of 100 rpm in a flow of velocity 2 m/s. Assume the density of
the fluid as 1.225 kg/m3 and  = 3.14. By Kutta-Joukowski theorem, the lift force
on the cylinder is _______ N (rounded off to the nearest integer).

Page 41 of 42

Q.65 A new absolute temperature scale is proposed based on a Carnot engine operating
between hot and cold reservoirs of temperatures 𝑇𝐿 and 𝑇𝐻 respectively. Let 𝑄𝐿 and
𝑇 𝑄
𝑄𝐻 be the respective heat transfers, with the relation given by 𝑇 𝐿 = 𝑄 𝐿 . On the new
𝐻 𝐻
scale, the difference between the steam and ice points of water is 500 units and the
efficiency of the engine is 0.268. The steam point of water on this scale is ________
units (rounded off to the nearest integer).

Page 42 of 42

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