GATE Previous Years Solved Papers The Gate Coach

CHAPTER
3
• Fluid Mechanics

(Gate 2001) (B) Decreases and the then increase

1. The operation of a rotameter is based (C) Remains constant

on (D) Increases and then decrease
(A) Variable flow area
(B) Rotation of a turbine 5. For flow past a flat plate, if x is the
distance along the plate in the direction of
(C) Pressure drop across a nozzle
flow. The boundary layer thickness is
(D) Pressure a a stagnation point proportional to

2. Applying a pressure drop across a 1

(A) x (B)
capillary result in a volumetric flow rate Q x
under laminar flow conditions. The flow 1
(C) x (D)
rate, for the same pressure drop, in a x
capillary of the same length but half the 6. For turbulent flow of an incompressible
radius is fluid through a pipe, the flow rate Q is
Q Q proportional to Pn where P is the
(A) (B)
2 4 pressure drop. The value of exponent n is
Q Q (A) 1 (B) 0
(C) (D)
8 16 (C) < 1 (D) > 1

3. A Bingham fluid of viscosity  = 10 Pa (Gate 2003)

s, and yield stress  0 10 is sheared

between flat parallel plates separated by a 7. A lubricant 100 times more viscous
distance 10-3 m. the top plate is moving than water would have a viscosity
with a velocity of 1 m/s. parallel plates (in pa–s)
separated by a distance 10-3 m. the top
(A) 0.01 (B) 0.1
plate is moving with a velocity of 1 m/s the
shear stress on the plate is (C) 1 (D) 10
(A) 10 kPa (B) 20 kPa
(C) 30 kPa (D) 40 kPa 8. The velocity profile for a Bingham
plastic fluid flowing (under laminar
(Gate 2002) conditions) in a pipe is
(A) Parabolic
4. With increasing flow rate, the hydraulic (B) Flat
efficiency of a centrifugal pump (C) Flat near the wall and parabolic in the
(A) Monotonically decreases middle

THE GATE COACH, All Rights Reserved 75 |

GATE Previous Years Solved Papers The Gate Coach

(D) Parabolic near the wall and flat in the 11. A centrifugal pump is used to pump
middle water through a horizontal distance of 150
m and then raised to an overhead tank 10
m above. The pipe is smooth with an I.D of
9. The variable required to be known in 50 mm. What head (m of water) must the
correlations used for estimating the horse pump generate at its exit (E) to deliver
power of a centrifugal gas compressor and water at a flow rate of 0.001 m3/s? (The
hence its cost is fanning friction factor, f is 0.0062.)
P. inlet pressure Q. compressor RPM

R. delivery pressure S. volumetric flow

rate at inlet

(A) P, Q and R (B) P and R

(C) R and S (D) Q, R and S

10. A pipe has a porous section of length L

as shown in the figure velocity at the start (A) 10 m (B) 11 m
of this section is V0, if fluid leaks into the (C) 12 m (D) 20 m
pipe through the porous section at a
volumetric rate per unit area q (x/L)2,
12. Match the following dimensionless
what will be the axial velocity in the pipe
number with appropriate ratio of force
at any x? Assume incompressible one
dimensionless number
dimensional flow i.e., no gradients in the
radial direction
P. fraud number
Q. Reynolds number
R. Friction factor
S. Nusselt number
1. Shear force/inertial force
2. Convective heat transfer/conductive
heat transfer
3. Gravitational force/viscous force
x3
(A) Vs  V0  q 2 4. Inertial force/viscous force
LD
5. Inertial force/gravitational force
3
1 x
(B) Vs  V0  q
3 L2 (A)P – 1, Q – 2, R – 5, S – 3
x 3
(B)P – 5, Q – 4, R – 3, S – 2,
(C) Vx  V0  2q
LD (C)P – S, Q – 4, R – 1, S – 2,
4 x3 (D)P – 3, Q – 4, R – 5, S – 1
(D) Vx  V0  q
3 L2 D
13. The pressure differential across a
vertical venturimeter (shown in figure) is

THE GATE COACH, All Rights Reserved 83 |

GATE Previous Years Solved Papers The Gate Coach

measured with the help of a mercury 16. Viscosity of water at 40℃ lies in the
manometer to estimate flow rate of water range of
flowing through it. The expression for the
velocity of water at the throat is (A)1 x 10-3 – 2 x 10-3 kg/(m-s)
(B)1 – 2 kg/ (m-s)
(C)0.5 x 10-3 – 1 x 10-3 kg/(m-s)
(D)0.5 – 1 kg/ (m-s)

17. For the manometer setup shown in the

figure, the pressure difference PA – PB is
given by

V22  V12
(A)  h m /  w
2g

𝑉22 −𝑉12
(B) 2𝑔
= ℎ(𝜌𝑚 − 𝜌𝑤 )/ 𝜌𝑤

V22
(C)  H  h  m  w  / w
2g (A)(ρH – ρL ) gH + (ρL – ρair ) g (L – H)
(B)(ρH – ρair ) gH
V 2  V12
(D) 2  h  m  w  / w (C)(ρH – ρL ) gL + (ρL – ρair ) gH
2g
(D)(ρH – ρL ) gH

(Gate 2004)
18. A conical tank with a bottom opening
14. The equivalent diameter for flow of cross-sectional area A is filled with
through a rectangular duct of width B and water and is mounted on supports, as
height H is shown in the figure. What is the force F
with which plate X must be pushed up to
prevent water from leaking? Assume that
HB HB
(A) (B) the density of air is negligible as compared
2(H  B) (H  B)
to the density of water ρL.
2HB 4HB
(C) (D)
(H  B) (H  B)

15. What is the force required (in Newton)

to hold a spherical balloon stationary in
water at a depth of H from the air-water
interface? The balloon is of radius 0.1 m
and is filled with air.
4gH 4 g
(A) (B) (A) ρLVg (B) ρLAhg
3 3
0.1 gH 0.04 gH (C) ρLVg / 2 (D) ρLVg / 3
(C) (D)
8 3

THE GATE COACH, All Rights Reserved 84 |

GATE Previous Years Solved Papers The Gate Coach

19. Three piping networks, as shown in (C) F = 50 x 106 N

the figure, are placed horizontally. They (D) F = 5 x 106 N
are made using identical pipe segments
22. The relation between the stress τ and
and are subjected to the same pressure
the strain rate (dux / dy) for the rapid flow
drop across them. Assuming no pressure
losses at junctions, the flow rates across of a granular material is given by
2
the three networks are related as Q1 : Q2 :  du 
  B  x  where B is a constant. If M, L
Q3 :  dy 
and T are the mass, length and time
dimension respectively, what is the
dimension of the constant B?

(A) ML-1 T-1 (B) ML-1 T-2

(C) MT-1 (D) ML-1

(A)1 : 3 :2 (B) 1 : 2 : 3
Common Data Question 23–24:
(C) 1 : 2 : 2 (D) 1 : 2: 2 Two tanks, A and B, of cross sectional area
1 m2 each, contain a fluid of density 1000
kg/m3 and viscosity 1 kg / (m – s). The
(Gate 2005)
tanks are connected by a pipe of diameter
0.02 m and length 1 m, and a check valve,
20. Match the following types of fluid
at the bottom. Assume that the flow is
(in group I) with their respective
laminar, and there is no friction in the
constitutive relations (in group II), where
check valve. In the initial state, the height
τ is the stress and γ is the strain rate,
of the fluid in the tank A and 6m and the
Group I Group II height of the fluid in tank B is 2 m (as
P. Pseudoplastic I.     shown in the figure below). The check
II.   0  K  
Q. Bingham valve is opened, and the fluid flows from
plastic tank A to tank B till the levels in the two
tanks are equal in the final state. Assume
n
 K  n 1
III.
 K 
n
n 1
g = 10 m/s2 in the calculations.
IV.

(A) P-I, Q-IV (B)P-IV, Q-I

(C) P-II, Q-III (D)P-III, Q-II

21. A dam of width 50 m is used to

hold water in a reservoir. If the water
height is 10 m from the bottom of the
dam, what is the total force F acting on the
dam due to the water? Assume g = 10 23. What is the average fluid velocity in
m/s2, and the fluid density is 1000 hg/m3. the pipe as soon as the valve is opened?

(A) F = 12.5 x 106 N (A) 0.25 m / s (B) 0.5 m / s

(B) F = 25 x 106 N (C) 1 m / s (D)2 m / s

THE GATE COACH, All Rights Reserved 85 |

GATE Previous Years Solved Papers The Gate Coach

(C) (3/4) ΔP (D) ΔP

24. What is the total energy loss between
the initial and final stats due to the fluid
28. In a laminar flow through a pipe of
flow?
radius R, the fraction of the total fluid
(A) 2 x 104 J (B) 16 x 104 J
(C) 8 x 104 J (D) 4 x 104 J flowing through a circular cross-section of
radius R/2 centered at the pipe axis is

(A) 3/8 (B) 7/16

(C) 1/2 (D) ¾

(Gate 2006) 29. The liquid surface in a cylindrical

bucket of radius R, rotating about its axis a
25. Match the following for a centrifugal acquired a parabolic profile given by the
pump with impeller speed n. equation y = a+br2, where y is height of
the liquid surface from the bottom of the
(P) Capacity (1) proportional to n bucket at a radial distance r from the
(Q) Head (2) proportional to n2 bucket axis. If the liquid has density ‘ρ’ the
(3) proportional to n3 mass of the liquid in the bucket is

(A) P – 2, Q – 1
 a  bR2 
(B) P – 1,Q – 3 (A) R2  
(C) P – 2, Q – 3  2 
(D) P – 1, Q – 2  bR2 
(B) R2  a  
 2 
26. The magnitude of the force (in N) (C) R a2

required to hold a body of volume 0.05 m3

(D) R2 (a  bR2 )
and mass 40 kg in water (density 1000
kg/m3) at a depth of 0.1 m is (g = 9.81
m/s2). (Gate 2007)

(A) Zero (B) 98.1 30. A pipeline system carries crude oil of
density 800 kg/m3. The volumetric flow
(C) 490.5 (D) 882.9 rate at point 1 is 0.28 m3/s. The cross
sectional areas of the branches 1, 2 and 3
27. A liquid is pumped at the flow rate Q are 0.012, 0.008 and 0.004 m2
through a pipe of length L. The pressure respectively. All the three branches are in
drop of the fluid across the pipe is ΔP, now a horizontal plane and the friction is
a lead develops at the mid-point of the negligible. If the pressures at the points 1
length of the pipe and the fluid leaks at the and 3 are 270 kPa and 240 kPa
rate of Q/2. respectively, then the pressure at point 2 is
Assuming that the friction factor in the
pipe remains unchanged, the new pressure
drop across the pipe for the same inlet
flow rate (Q) will be

(A) (1/2) ΔP (B) (5/8) ΔP

THE GATE COACH, All Rights Reserved 86 |

GATE Previous Years Solved Papers The Gate Coach

5
(A) 2a  bQ12 (B) 2a  bQ12
4
(C) 2a  2bQ12 (D) a  bQ12

(A) 202 kPa (B) 240 kPa 33. The pressure differential across a
Venturimeter, inclined at 45° to the
(C) 284 kPa (D) 3 55 kPa
vertical (as shown in the figure) is
measured with the help of a manometer to
31. The figure shows the idealized view of estimate the flowrate of a fluid flowing
a return elbow or U bend, which is through it. If the density of the flowing
connected to two pipes by flexible hoses fluid is ρ and the density of the
that transmit no force. Water with density manometer fluid is ρm , the velocity of the
1000 kg / m3 flows at velocity of 10 m / s fluid at the throat can be obtained from
through the pipe, which has a uniform ID the expression.
of 0.1m. The gauge pressure at points 1
and 2 are 304 kPa and 253 kPa
respectively. The horizontal force F
required to keep the elbow in position is

V22  V12 h  m   
  Hsin 450
2g 
(A)
(A)1574 N (B)1970N
V22  V12 hm
(C)5942 N (D)7533 N   Hsin 450
(B) 2g 

V22  V12 hm

32. The figure shows a series – parallel 
(C) 2g 
configuration of three identical centrifugal
pumps. The head increases H across a V22  V12 h  m   

single such pump varies with flowrate Q 2g 
(D)
according to H  a  bQ 2 . The expression
for the total head increase H  H 2  H1 in (Gate 2008)
terms of a and b and the total flowrate Q 1
34. Three containers are filled with water
for this configuration is given by
up to the same height as shown. The
pressures at the bottom of the containers

THE GATE COACH, All Rights Reserved 87 |

GATE Previous Years Solved Papers The Gate Coach

are denoted as P1, P2 and P3. Which ONE List II

of the following relationships is true? 1. Viscous force/ inertial force
2. Pressure force/ inertial force
3. Inertial force/ gravitational force
4. Inertial force/ surface tension force

(A)P – 1, Q – 2, R -3
(A) P3> P1> P2 (B) P2>P1> P3
(C) P1> P2 = P3 (D) P1=P2=P3 (B)P -2, Q -3, R - 4
(C)P - 3, Q - 2, R – 1
35. Losses for flow through valves and (D)P – 4, Q -3, R – 2
fittings are expressed in terms of

39. A steady flow field of an

(A) Drag coefficient
incompressible fluid is given by
(B) Shape factor
(C) Equivalent length of a straight pipe V   Ax  By  ˆi  Ay ˆj,
(D) roughness factor.
where A  1 s 1 , B  1 s 1 & x,y are in

36. Given a pipe of diameter D, the meters. The magnitude of acceleration (in
entrance length necessary; to achieve fully m/s2 ) of a fluid particle at (1,2) is
developed laminar flow is proportional to
(NRe is Reynolds number). (A)1 (B) 2
D (C) 5 (D) 10
N Re
(A) DNRe (B)
D Linked Answer Questions 40 & 41:
2 2
NRe A siphon tube having a diameter of 2 cm
(C) DNRe (D)
draws water from a large open reservoir
and discharges into the open atmosphere
37. A pump draws oil (specific gravity 0.8)
as shown in the figure. Assume
from a storage tank and discharges it to an
incompressible fluid and neglect frictional
overhead tank. The mechanical energy
losses. (g = 9.8 m/s2)
delivered by the pump to the fluid is 50
J/kg. The velocities at the suction and the
discharge points of the pump are 1 m/s and
7 m/s, respectively. Neglecting friction
losses and assuming kinetic energy
correction factor to be unity, the pressure
developed by the pump (in kN / m2) is

(A) 19.2 (B) 20.8

(C) 40 (D) 80
40. The velocity (in m/s) at the discharge
38. Match the following point is
List I
P. Euler number (A) 9.9 (B) 11.7
Q. Froude number (C) 98 (D) 136.9
R. Weber number

THE GATE COACH, All Rights Reserved 88 |

GATE Previous Years Solved Papers The Gate Coach

41. The volumetric flow rate (in L/s) of nozzle. Use g = 9.81 m/s2 and density of
water at the discharge is water = 1000 kg/m3.

(A) 3.11 (B) 3.67 43. The velocity of water at the tip of the
(C) 30.77 (D) 42.99 nozzle (in m/s) is

(A) 13.4 (B) 18.0

(Gate 2009)
(C) 23.2 (D) 27.1
42. Two identical reservoirs, open at the
top, are drained through pipes attached to 44. The gauge pressure (in kPa) at point B
the bottom of the tanks as shown is
below. The two drain pipes are of the (A) 80.0 (B) 100.0
same length, but of different diameters (C) 239.3 (D) 367.6
(D1> D2).

(Gate 2010)

45. The stream function in a [x–y] plane

is given below:
1 2 3
 x y . The velocity vector for this
2
stream function is:
Assuming the flow to be steady and
laminar in both drain pipes, if the 
3  3  
(A) xy 3 i  x 2 y 2 j (B) x 2 y 2 i  xy 3 j
volumetric flow rate in the larger pipe is 16 2 2
times of that in the smaller pipe, the ratio 3 2 2   3 
(C) x y i  xy 3 j (D) xy 3 i  x 2 y 2 j
D1/D2 is 2 2

(A) 2 (B) 4 46. A storage vessel exposed to

atmosphere (absolute pressure = 10.3 m of
(C) 8 (D) 16
water) has a diameter of 3 m and is
initially filled with water to a height of 2
Linked Answer Question 43 & 44: m. The pump draws water from the vessel
A free jet of water is emerging from a and is located at an elevation of 5 m above
nozzle (diameter 75 mm) attached to a the bottom of the vessel. The frictional
pipe (diameter 225 mm) as shown below. head loss in the suction pipe is 2 m of
water. If the vapor pressure of the liquid
at the temperature of operation is 3 m of
water, then the available NPSH is

(A) 2.3 m (B) 5.3 m

(C) 6.3 m (D) 8.3 m

47. In Hagen-Poiseuille’s flow through a

The velocity of water at point A is 18 cylindrical tube, the radial profile of shear
m/s. Neglect friction in the pipe and stress is

THE GATE COACH, All Rights Reserved 89 |

GATE Previous Years Solved Papers The Gate Coach

50. In an orifice meter, if the pressure

(A) Constant (B) Cubic drops across orifice is over estimates by 5
(C) Parabolic (D) Linear % then the percentage error in the
measured flow rate is the percentage error
in the measured flow rate is
48. A hydrometer, with stem cross-
sectional area of 2.82 × 10-5 m2, is (A) +2.47 (B) +5
immersed in a very large vessel containing
water as shown in the figure. The (C) -2.47 (D) -5
immersed volume is 15 x 10 m and the
-6 3
51. Two liquids (P and Q) having same
length of the stem above water surface is
viscosity are flowing through a double
Lw. If the entire volume of water is
pipe heat exchanger as shown in the
replaced by a liquid with specific gravity
schematic below.
1.5 and if the length of the stem above the
liquid surface is Ll , then the difference, Ll
– Lw , is

Densities of P and Q are 1000 and 800

kg/m3 respectively. The average velocities
of the liquids P and Q are 1 and 2.5 m/s
respectively. The inner diameters of the
(A)–177 mm (B) 177 mm pipes are 0.31 and 0.1 m. Both pipes are 5
(C)–266 mm (D) 266 mm mm thick. The ratio of the Reynolds
numbers Rep to Req is

(A) 2.5 (B) 1.5

(C) 1 (D) 4
(Gate 2011)
52. A liquid is flowing through the
49. Match the pumps in Group I with the following piping network. The length of
corresponding fluids in Group II. pipe sections P, Q, r and S shown in the
GROUP I GROUP II schematic are equal. The diameters of the
P. Gear pump. I. Highly viscous sections P and R are equal and the
liquid diameter of the section Q is twice that of S.
Q. Peristaltic pump II. Aqueous sterile The flow is steady and laminar.
liquid Neglecting curvature and entrance effects,
III. Slurry the radio of the volumetric flow rate in the
pipe section Q to that in S is
(A) P – III; Q – I,
(B) P – II, Q–I,
(C) P – III, III, Q – II
(D) P – I, Q–II

THE GATE COACH, All Rights Reserved 90 |

GATE Previous Years Solved Papers The Gate Coach

A Newtonian fluid of viscosity  flow b/w

two parallel plates due to the motion of
the bottom plate as shown below which is
moved with velocity V. The top plate is
stationary

(A) 16 (B) 8
(C) 2 (D) 1

(Gate 2012)

56. The steady laminar velocity profile in

53. Water is flowing under laminar X direction is
condition in a pipe of length L. if the
diameter of the pipe is doubled, for a y  y  2 
(a)n V    (B) V    1
constant volume flow rate, the pressure b  
b 
drop across the pipe
 y 
2
  y 
(A) Decreases 2 times (C) V 1    (D) V 1    
  b    b 
(B) Decreases 16 times
(C) Increases 2 times
(D) Increases 16 times 57. The force per unit area [ in x direction
] that must be exerted on the bottom plate
maintain flow is
54. The local velocity of a fluid along a
streamline can be measured by v v
(A) (B)
b b
(A) Piton tube
2v 2v
(B) Ventura meter (C) (D)
b b
(C) Rota meter (Gate 2013)
(D) Orifice meter
58. An open tank contains two immiscible
55. For uniform laminar flow (in the x liquids of densities (800 kg/m3 and 1000
direction) past a flat plate at high kg/m3) as shown in the figure. If g = 10
Reynolds number the local boundary layer m/s2, under static conditions, the gauge
pressure at the bottom of the tank in Pa
thickness   varies with the distance
is___
along the plate (x) as
(A)   x1/ 4 (B)   x 3
1

(C)   x 2 (D)   x
1

Common Data Question 56 & 57:

THE GATE COACH, All Rights Reserved 91 |

GATE Previous Years Solved Papers The Gate Coach

59. The apparent viscosity of a fluid is  r  R2 

(A) R2 (B r
dV
0.3
 dV  R2  R1 
given by 0.07 where   the velocity
dy  dy  r  R1  r  R1 
(C) R1  (D) R 
gradient. The fluid R2  R1  R2  R1  2

(A) Bingham plastic 62. For a Newtonian fluid flowing in a

(B) Dilatants circular pipe under steady state conditions
(C) Pseudo plastic in fully developed laminar flow, the
Fanning friction factor is
(D) Thixotropic
(A) 0.046Re-0.2
60. The mass balance for a fluid with (B) 0.0014+0.125Re0.32
density ( ρ ) and velocity vector ( Ṽ ) is (C) 16Re-1
(D) 24Re-1
(A)   .  V   0
t 63. Match the question
List I
(B)   V .    0 (p) Viscosity
t
(Q) Pressure
(C)     .V   0 (R) Velocity
t
(S) Temp.
(D)   V .     0
t List II
61. An incompressible Newtonian fluid, (1) Pyrometer
filled in an annular gap between two (2) Hot wire anemometer
concentric cylinders of radii R1 and R2 as (3) Rheometer
shown in the figure, is flowing under (4) Piezoelectric element
steady state conditions. The outer cylinder
is rotating with an angular velocityof Ω (A) P–4, Q–3, R-1, S-2
while the inner cylinder is stationary. (B) P -3, Q-4, R-2, S-1
Given that (R2 – R1 )& R1 the profile of the
(C) P-3, Q-4, R-1, S-2
θ − component of the velocity Vθ can be
approximated by, (D) P-4, Q-3, R-2, S-1

64. Water (density 1000 kg/m3) is flowing

through a nozzle, as shown below and
exiting to the atmosphere. The
relationship between the diameters of the

THE GATE COACH, All Rights Reserved 92 |

GATE Previous Years Solved Papers The Gate Coach

nozzle at locations 1 and 2 is D1 = 4 D2. (A) Syringe pump

The average velocity of the stream at (B) diaphragm pump
location 2 is 16 m/s and the frictional loss
(C) Vacuum pump
between location 1 and location 2 is 10000
Pa. Assuming steady state and turbulent (D) Gear pump
flow, the gauge pressure in Pa, at location
1 is ___
68. A incompressible fluid is flowing
through a contraction section of length L
and has a 1-D (x direction) steady state
velocity distribution,
 2x 
u  u0  1  
 L 
If u0 = 2m/s and L = 3m, the convective
(Gate 2014) acceleration (in m/s2) of the fluid at L is
___.
65. In case of a pressure driven laminar
flow of a Newtonian fluid of viscosity (µ) 69. In a steady incompressible flow, the
through a horizontal circular pipe, the velocity distribution is given by
velocity of the fluid is proportional to
Ṽ = 3xȋ − Pyĵ + 5zǩ, where, V is in m/s and
x, y, and z are in m. In order to satisfy the
(A) µ (B)µ0.5
mass conservation, the value of the
(C) µ – 1 (D)µ−0.5 constant P
66. Which of the following statements are (ins– 1) is ______.
CORRECT?
70. Match the following
(P) For a rheopectic fluid, the apparent Group I Group II
viscosity increases with time under a (P) Turbulence (I) Reciprocating
constant applied shear stress pump
(Q) For a pseudoplastic fluid, the apparent (Q) NPSH (II) Packed bed
viscosity decreases with time under a (R) Ergun (III)Fluctuating
constant applied shear stress equation velocity
(R) For a Bingham plastic, the apparent (S) Rotameter (IV) Impeller
viscosity increases exponentially with the (T) Power number (V) Vena contracta
deformation rate
(S) For a dilatant fluid, the apparent (A)P-III, R-II, T-IV
viscosity increases with increasing
(B)Q-V, R-II, S-III
deformation rate
(A) P and Q only (C)P-III, R-IV, T-II

(B) Q and R only (D)Q-III, S-V, T-IV

(C) R and S only

(D) P and S only 71. In a steady and incompressible flow of
a fluid (density = 1.25 kg m-3), the
difference between stagnation and static
67. Slurries are most conveniently
pressures at the same location in the flow
pumped by______
is 30 mm of mercury (density = 13600 kg

THE GATE COACH, All Rights Reserved 93 |

GATE Previous Years Solved Papers The Gate Coach

m-3). Considering gravitational Data: Fanning friction factor for pipe flow
acceleration as 10 m s-2, the fluid speed (in is f = 0.004. Neglect other head losses
m s-1) is ______ Take gravitational acceleration, g = 9.8
m/s2 and density of water is 1000 kg/m3.
The height H, in meters, to which the
water can be delivered (up to one decimal
(Gate 2015) place) is _______.

72. Two different liquids are flowing 75. For fanning friction factor f (for flow
through different pipes of the same in pipes) and drag coefficient CD(for flow
diameter. In the first pipe, the flow is over immersed bodies), which of the
laminar with centerline velocity, Vmax.1, following statements are true?
whereas in the second pipe, the flow is P: f accounts only for the skin friction
turbulent. For turbulent flow, the average Q: CD accounts only for the form friction
velocity is 0.82 times the centerline R: CD accounts for both skin friction and
velocity, Vmax.2. For equal volumetric flow form friction
rates in both the pipes, the ratio Vmax.1 : S: Both f and CD depend on the Reynolds
Vmax.2 (up to two decimal places) is number
______. T: For laminar flow through a pipe, f
doubles on doubling the volumetric flow
73. The Characteristics curve (head – rate.
capacity relationship of a centrifugal
pump is represented by the equation (A) R,S,T (B) P,Q, S
Hpump  43.8  0.19Q.where Hpump is the (C) P,R,S (D) P,Q,S,T
head developed by the pump (in m) and Q
is the flowrate (in m3/h) through the (Gate 2016)
pump. This pump is to be used for
pumping water through a horizontal 76. For a flow through a smooth pipe, the
pipeline. The frictional head loss Fanning friction factor ( f ) is given by
Hpump (inm) is related to the water f  m Re0.2 in the turbulent flow regime,
flowrate (in m3/h) by the equation where Re is the Reynolds number and is a
Hpiping  0.0135QL2  0.045QL . constant. Water flowing through a section
The flowrate (in m3/h, rounded off to the of this pipe with a velocity 1 m/s results in
first decimal place) of water pumped a frictional pressure drop of 10 kPa.
through the above pipeline, is _____ What will be the pressure drop across this
section (in kPa), when the velocity of
water is 2 m/s?
74. A centrifugal pump delivers water at
the rate of 0.22 m3/s from a reservoir at (A) 11.5 (B) 20
ground level to another reservoir at a (C) 34.8 (D) 40
height H, through a vertical pipe of 0.2m
diameter. Both the reservoirs are open to
atmosphere. The power input to the pump 77. A vertical cylindrical vessel has a layer
is 90 kW and it operates with an efficiency of kerosene (of density 800 kg/m3) over a
of 75%. layer of water (of density 1000 kg/m3). L-
shaped glass tubes are connected to the

THE GATE COACH, All Rights Reserved 94 |

GATE Previous Years Solved Papers The Gate Coach

column 30 cm apart. The interface the pipe. Water (density = 1000 kg m‒3,
between the two layers lies between the viscosity = 1 × 10‒3 kg m‒1 s‒1) flows at an
two points at which the L-tubes are
average velocity of 1 m s‒1 through the
connected. The levels (in cm) to which the
pipe. For this flow condition, the friction
liquids rise in the respective tubes are
shown in the figure below. factor f is 0.005. At a distance of 0.05
mm from the wall of the pipe (in the
viscous sub-layer), the velocity (in m s‒1,
rounded off to the third decimal place), is
_______

Gate 2017)

80. In a venturi meter P1 and P2 are the

pressure drops corresponding to
The distance (x in cm, rounded off to the
volumetric flowrates
first decimal place) of the interface from
Q2 P
the point at which the lower L-tube is Q1 and Q 2 If  2, then 2 equal
Q1 P1
connected is _______

(A) 2 (B) 4
78. Water (density=1000 kg m‒3) is
pumped at a rate of 36 m3/h, from a tank (C) 0.5 (D) 0.25
2 m below the pump, to an overhead
pressurized vessel 10 m above the pump. 81. The thickness of laminar boundary
The pressure values at the point of suction layer over a flat plate varies along the
from the bottom tank and at the discharge distance from the leading edge of the
point to the overhead vessel are 120 kPa plate. As the distance increases, the
and 240 kPa, respectively. All pipes in the boundary layer thickness
system have the same diameter. Take
(A) Increases
acceleration due to gravity, g = 10 m s‒2.
Neglecting frictional losses, what is the (B) Decreases
power (in kW) required to deliver the (C) Initially increases and then decreases
fluid? (D) Initially decreases and then increases

(A) 1.2 (B)2.4 82. The following table provides four sets
of fanning friction factor data, for different
(C) 3.6 (D) 4.8 values of Reynolds number (Re) and
k
79. Water flows through a smooth circular roughness factor  
D 
pipe under turbulent conditions. In the
Re 102 103 105 105
viscous sub-layer, the velocity varies
k 0 0.001 0 0.001
linearly with the distance from the wall.  
The Fanning friction factor is defined as, D 

f  where   is the shear stress Set F 0.16 .016 16  16 
u 2 / 2
I 105 10-5
at the wall of the pipe,  is the density of
Set F 0.016 0.16 0.0055 0.0045
the fluid and u is the average velocity in

THE GATE COACH, All Rights Reserved 95 |

GATE Previous Years Solved Papers The Gate Coach

II (C) Angular deformation

Set F 0.16 0.016 0.0045 0.0055
(D) Vorticity
III
Set F 0.0045 0.0055 0.016 0.16
IV 87. At a shear rate of 10s-1, the apparent
Which of the above sets of friction factor viscosity of a non-Newtonian liquid was
data is correct? found to be 1 Pa s. At a shear rate of 100s-1,
the apparent viscosity of the same liquid
(A) Set I (B) St II was found to be 0.5 Pa s. If the liquid
follows power law behavior, the apparent
(C) Set III (D) Set IV viscosity (in Pa s) at a shear stress of
10Nm2 is ___ (rounded off to two
83. Oil is being delivered at a steady state
decimal place).
flow rate through a circular pipe of a
88. The volume of liquid filled in a
radius 1.25 x 10-2 m and length 10m the spherical storage tank of radius R is
pressure drop access the pipe is 500Pa the computed from height of liquid, h, in the
shear stress at the pipe wall, rounded to 2 outside tube (neglecting the volume of
decimal place ____Pa liquid in the outside tube) as
3R  h
84. A propeller (diameter D = 15 M) V   h2 ( )
3
rotates at N = 1 revolution per second
(rps). To understand the flow around the
propeller, a lab scale model is made.
Important parameters to study the flow

are velocity of the propeller tip V  ND , 
diameter D and acceleration due to gravity
(g) . The lab scale model is 1/100th of the
size of the actual propeller. The rotation
speed of the lab scale model, to the nearest
integer, should be ______rps The estimate of liquid height (in m) to
store V = 30 m3 of water in R = 3m tank,
after performing ONE iteration of Secant
(Gate 2018)
method, using 1m and 3m as two initial
guesses of liquid height is _____
85. A venturi meter is installed to
(rounded off to second decimal place.)
measure the flow rate of water in a 178
mm diameter (D)pipe. The throat 89. Under isothermal condition, a vertical
diameter is 102mm. The differential tube of length L = 100 m contains a gas of
pressure measured using a manometer is molecular weight equal to 60. The
154.3kN/m2. The data given are: discharge pressure and temperature at the top of the
coefficient = 0.98; Water density = 1000 tube are 100 kPa and 250C respectively.
kg/m3. The volumetric flow rate of water
(in kg/m3) is_____. Consider the universal gas constant and
acceleration due to gravity as 8.314 J mol–1
K-1 and 9.81 m s-2 respectively. If the gas is
86. Pitot tube is used to measure
ideal, the pressure (in kPa) at the bottom
(A) Liquid level in a tank
of the tube will be ______.
(B) Flow velocity at a point

THE GATE COACH, All Rights Reserved 96 |

GATE Previous Years Solved Papers The Gate Coach

(Gate 2019) another pipe of diameter D2 = Di /2 at the

same flow rate Q. The transition length
required for achieving fully- developed
90. For a fully- developed turbulent
flow is I i for the tube of diameter Di while
hydrodynamic boundary layer for flow
past a flat plate, the thickness of the it is l2 for the tube of diameter D2
Assuming steady laminar flow in both case
boundary layer increases with distance
with distance x from the leading edge of the ratio l1 / l2 is
the plate, along the free- stream flow
direction, as (A) 1/4 (B) 1

(A) x0.5 (B) x1.5 (C) 2 (D) 4

(C) x0.4 (D) x0.8

91. For a hydraulic lift with dimensions

shown in figure, assuming g = 10 m/s2, the 94. A disk turbine is used to stir a liquid
maximum diameter Dleft ( in m) that lifts a in a baffled tank. To design the agitator,
vehicle of mass 1000 kg using a force of experiments are performed in a lab-
100 N is _____(rounded off to two scale model with a turbine diameter of
decimal places). 0.05 m and a turbine impeller speed of
600 rpm. The liquid viscosity is 0.001 Pa
s while the liquid density 1000 kg/m3
the actual application has a turbine
diameter of 0.5 m, and impeller speed of
600 rpm, a negligible. If the power
required in the lab-scale model is Pi
and the estimated

power for the actual application is P2 then

the ratio P2/P1 is_____

(A) 103 (B) 104

92. A centrifugal pump is used to pump (C) 105 (D) 106

water (density 1000 kg/m3)from an inlet
pressure of 105 Pa to an exit pressure of 2 (Gate 2020)
x 105 Pa. The exit is at an elevation of 10 m
above the pump . the average velocity of
the fluid is 10 m/s. the cross-sectional area 95. Consider an incompressible flow of a
of the pipes at the pump inlet and outlet is constant property fluid over a smooth,
10-3 m2 and acceleration due to gravity is g
thin and wide flat plate. The free stream
= 10 m/s2 . Neglecting losses in the system
, the power (in watts) delivered by the flow parallel to the surface of the plate
pump is ____________ along its length and its velocity is
constant. Value of the Reynolds number at
a distance of 2.0 m from the leading edge
93. An incompressible Newtonian fluid of the plate is 8000. The flow within the
flow in pipe diameter Di at volumetric flow boundary layer at a distance of 0.1 m from
rate Q. Fluid with same properties flows in the leading edge of the plate is

THE GATE COACH, All Rights Reserved 97 |

GATE Previous Years Solved Papers The Gate Coach

(A) laminar Where τrx is the shear stress. If rc is 0.001

m, then the magnitude of yield stress for
(B) turbulent this Bingham Plastic (in Pa) is
(C) transitioning from laminar to (A) 1 (B) 5
turbulent
(C) 8 (D) 12
(D) inviscid

98. A U tube manometer contains two

96. Consider steady, laminar, fully manometric fluids of densities 1000 kg m-
developed flow of an incompressible 3 and 600 kg m-3. When both the limbs are
Newtonian fluid through two horizontal open to atmosphere, the difference
straight pipes, I and II, of circular cross between the two levels is 10 cm at
section. The volumetric flow rates in both equilibrium, as shown in the figure.
the pipes are the same. The diameter of
pipe II is twice the diameter of pipe I, i.e.,
dII = 2d1. The ratio of the shear stress at
the wall of pipe I to the shear stress at the
wall of pipe II is

(A) 0.5 (B) 2

(C) 4 (D) 8

97. A student performs a flow experiment The rest of the manometer is filled with air
with Bingham Plastic under fully of negligible density. The acceleration due
developed laminar flow conditions in a to gravity is 9.81 m s-2 and the
tube of radius 0.01 m with a pressure drop atmospheric pressure is 100 kPa. How
(∆P) of 10 kPa over tube length (L) of 1.0 much absolute pressure (in kPa) has to be
m. The velocity profile is flat for r < rc and applied on the limb ‘P’ to raise the fluid in
parabolic for r ≥ rc, as shown in the figure. the limb ‘Q’ by another 20 cm?

(A) 100.175 (B) 103.924

(C) 547.231 (D) 833.236

99. Liquid water is pumped at a

volumetric flow rate of 0.02 m3s-1 from
Consider r and x as the radial directions, Tank I to Tank II, as shown in the figure.
and the shear stress is finite as r
approaches zero. A force balance results in
the following equation

d  r rx   P 
r
dr L

THE GATE COACH, All Rights Reserved 98 |

GATE Previous Years Solved Papers The Gate Coach

Both the tanks are open to the

atmosphere. The total frictional head loss
for the pipe system is 1.0 m of water.

In addition, use the following data and

assumptions

 Density of water is 1000 kg m–3

 Acceleration due to gravity is 9.81
m s–2
 Efficiency of the pump is 100%
 The liquid surfaces in the tanks
have negligible velocities

The power supplied (in W) by the pump to

lift the water is _______________
(round off to 1 decimal place).

THE GATE COACH, All Rights Reserved 99 |