Download GATE 2015 XE B Engineering Sciences Question Paper

Download Graduate Aptitude Test in Engineering (GATE) 2015 XE B Engineering Sciences Question Paper

GATE 2015 FLUID MECHANICS ? XE-B
XE-B 1/6
B : FLUID MECHANICS
Q. 1 ? Q. 9 carry one mark each.
Q.1
The gap between two concentric cylinders, each of height h, is filled with an oil. The
torque required to rotate the inner cylinder at an angular velocity of against the fixed
outer cylinder is T. The diameter of the inner cylinder is d and < < d. The dynamic
viscosity of the oil is given by
(A)
(B)
(C)
(D)



Q.2 Water is retained against a sluice gate in the form of a circular segment as shown in the
figure. If and are the density of water and gravitational acceleration respectively, the
upward force exerted by the gate on the water per unit depth perpendicular to the plane of
the figure is

(A) ?
s in 2 (B) cos
?
sin

(C) cos ?
sin (D) cos
?
sin



Q.3
A two-dimensional velocity field is given by ?
= 10( ? ) ? + 2 ?, where ? and ?
are the unit vectors in the directions of the rectangular Cartesian coordinates x and y,
respectively. If the flow is incompressible, the constant should be
(A) ?10 (B) 0 (C) 5 (D) 10

Q.4
Let ?
and denote the velocity vector and temperature in a flow field. The rate of change
of temperature experienced by a fluid particle as it is passes through the point (x
1
, y
1
, z
1
) at
a time t
1
is 2.5
o
C/s. The rate of change of temperature at a time t
1
at the point (x
1
, y
1
, z
1
) is
4.8
o
C/s. The quantity ?
. ?
?
at (x
1
, y
1
, z
1
) and t
1
in
o
C/s is _____


FirstRanker.com - FirstRanker's Choice
GATE 2015 FLUID MECHANICS ? XE-B
XE-B 1/6
B : FLUID MECHANICS
Q. 1 ? Q. 9 carry one mark each.
Q.1
The gap between two concentric cylinders, each of height h, is filled with an oil. The
torque required to rotate the inner cylinder at an angular velocity of against the fixed
outer cylinder is T. The diameter of the inner cylinder is d and < < d. The dynamic
viscosity of the oil is given by
(A)
(B)
(C)
(D)



Q.2 Water is retained against a sluice gate in the form of a circular segment as shown in the
figure. If and are the density of water and gravitational acceleration respectively, the
upward force exerted by the gate on the water per unit depth perpendicular to the plane of
the figure is

(A) ?
s in 2 (B) cos
?
sin

(C) cos ?
sin (D) cos
?
sin



Q.3
A two-dimensional velocity field is given by ?
= 10( ? ) ? + 2 ?, where ? and ?
are the unit vectors in the directions of the rectangular Cartesian coordinates x and y,
respectively. If the flow is incompressible, the constant should be
(A) ?10 (B) 0 (C) 5 (D) 10

Q.4
Let ?
and denote the velocity vector and temperature in a flow field. The rate of change
of temperature experienced by a fluid particle as it is passes through the point (x
1
, y
1
, z
1
) at
a time t
1
is 2.5
o
C/s. The rate of change of temperature at a time t
1
at the point (x
1
, y
1
, z
1
) is
4.8
o
C/s. The quantity ?
. ?
?
at (x
1
, y
1
, z
1
) and t
1
in
o
C/s is _____


GATE 2015 FLUID MECHANICS ? XE-B
XE-B 2/6
Q.5
In a simple Couette flow apparatus, the gap ? between the parallel plates is filled with a
liquid of density and dynamic viscosity , and one plate is dragged at a velocity of U
parallel to itself, while the other plate is fixed. The magnitude of vorticity at any point in
the flow is
(A)
(B) 0
(C)


(D)



Q.6
An open glass capillary tube of 2 mm bore is lowered into a cistern containing mercury
(density = 13600 kg/m
3
) as shown in the figure. Given that the contact angle between
mercury and glass = 140
o
, surface tension coefficient = 0.484 N/m and gravitational
acceleration = 9.81 m/s
2
, the depression of mercury in the capillary tube below the free
surface in the cistern, in mm, is _____


Q.7
Consider a combined forced-free vortex. The central region with radius R and angular
velocity is the forced vortex and the rest is the free vortex. The pressure at the edge of
the combined vortex is p
o
. If the density of the fluid is ?, the pressure at the center of the
combined vortex is
(A) o
?
(B) o
?
(C) o
+

(D) o
+


Q.8 The following is true at the point of separation of a boundary layer:
(A) Transition occurs from laminar to turbulent flow
(B) The flow relaminarizes from turbulent regime
(C) The shear stress vanishes
(D) The relation between stress and rate of strain ceases to be linear

Q.9 A certain fluid flow phenomenon is described by Reynolds, Weber and Ohnesorge
numbers. The Weber and Ohnesorge numbers are defined as We =
2
, and Oh =
,
respectively, where is the surface tension, is the density, is the dynamic viscosity, U
is the velocity and L is the characteristic dimension. If Re denotes the Reynolds number,
which of the following relations is true?

(A) We= O h Re
2
(B) We = Oh
Re
2
(C) We=Oh
Re (D) We= O h R e

FirstRanker.com - FirstRanker's Choice
GATE 2015 FLUID MECHANICS ? XE-B
XE-B 1/6
B : FLUID MECHANICS
Q. 1 ? Q. 9 carry one mark each.
Q.1
The gap between two concentric cylinders, each of height h, is filled with an oil. The
torque required to rotate the inner cylinder at an angular velocity of against the fixed
outer cylinder is T. The diameter of the inner cylinder is d and < < d. The dynamic
viscosity of the oil is given by
(A)
(B)
(C)
(D)



Q.2 Water is retained against a sluice gate in the form of a circular segment as shown in the
figure. If and are the density of water and gravitational acceleration respectively, the
upward force exerted by the gate on the water per unit depth perpendicular to the plane of
the figure is

(A) ?
s in 2 (B) cos
?
sin

(C) cos ?
sin (D) cos
?
sin



Q.3
A two-dimensional velocity field is given by ?
= 10( ? ) ? + 2 ?, where ? and ?
are the unit vectors in the directions of the rectangular Cartesian coordinates x and y,
respectively. If the flow is incompressible, the constant should be
(A) ?10 (B) 0 (C) 5 (D) 10

Q.4
Let ?
and denote the velocity vector and temperature in a flow field. The rate of change
of temperature experienced by a fluid particle as it is passes through the point (x
1
, y
1
, z
1
) at
a time t
1
is 2.5
o
C/s. The rate of change of temperature at a time t
1
at the point (x
1
, y
1
, z
1
) is
4.8
o
C/s. The quantity ?
. ?
?
at (x
1
, y
1
, z
1
) and t
1
in
o
C/s is _____


GATE 2015 FLUID MECHANICS ? XE-B
XE-B 2/6
Q.5
In a simple Couette flow apparatus, the gap ? between the parallel plates is filled with a
liquid of density and dynamic viscosity , and one plate is dragged at a velocity of U
parallel to itself, while the other plate is fixed. The magnitude of vorticity at any point in
the flow is
(A)
(B) 0
(C)


(D)



Q.6
An open glass capillary tube of 2 mm bore is lowered into a cistern containing mercury
(density = 13600 kg/m
3
) as shown in the figure. Given that the contact angle between
mercury and glass = 140
o
, surface tension coefficient = 0.484 N/m and gravitational
acceleration = 9.81 m/s
2
, the depression of mercury in the capillary tube below the free
surface in the cistern, in mm, is _____


Q.7
Consider a combined forced-free vortex. The central region with radius R and angular
velocity is the forced vortex and the rest is the free vortex. The pressure at the edge of
the combined vortex is p
o
. If the density of the fluid is ?, the pressure at the center of the
combined vortex is
(A) o
?
(B) o
?
(C) o
+

(D) o
+


Q.8 The following is true at the point of separation of a boundary layer:
(A) Transition occurs from laminar to turbulent flow
(B) The flow relaminarizes from turbulent regime
(C) The shear stress vanishes
(D) The relation between stress and rate of strain ceases to be linear

Q.9 A certain fluid flow phenomenon is described by Reynolds, Weber and Ohnesorge
numbers. The Weber and Ohnesorge numbers are defined as We =
2
, and Oh =
,
respectively, where is the surface tension, is the density, is the dynamic viscosity, U
is the velocity and L is the characteristic dimension. If Re denotes the Reynolds number,
which of the following relations is true?

(A) We= O h Re
2
(B) We = Oh
Re
2
(C) We=Oh
Re (D) We= O h R e

GATE 2015 FLUID MECHANICS ? XE-B
XE-B 3/6
Q. 10 ? Q. 22 carry two marks each.

Q.10
A rectangular boat 6 m wide and 15 m long (dimension perpendicular to the plane of the
figure) has a draught of 2 m. The side view of the boat is as shown in the figure. The centre
of gravity G of the boat is at the free surface level. The metacentric height of the boat in m
is

(A) ?1.0 (B) 0.5 (C) 1.5 (D) 2.0

Q.11
Water drains out into atmosphere from a small orifice located at the bottom of a large open
tank. If the initial height of the water column is H, the time taken to empty the tank is
proportional to
(A) /
(B)
(C) / (D)

Q.12
Consider a two-dimensional velocity field given by ?
= ? ? ?, where ? and ? are the
unit vectors in the directions of the rectangular Cartesian coordinates x and y, respectively.
A fluid particle is located initially at the point (?1, 1). Its position after unit time is
(A) (?2,?2) (B) (1,?1) (C) (1,1) (D) (3,?1)

Q.13
The figure shows a reducing area conduit carrying water. The pressure p and velocity V
are uniform across sections 1 and 2. The density of water is 1000 kg/m
3
. If the total loss of
head due to friction is just equal to the loss of potential head between the inlet and the
outlet, then V
2
in m/s will be _____





FirstRanker.com - FirstRanker's Choice
GATE 2015 FLUID MECHANICS ? XE-B
XE-B 1/6
B : FLUID MECHANICS
Q. 1 ? Q. 9 carry one mark each.
Q.1
The gap between two concentric cylinders, each of height h, is filled with an oil. The
torque required to rotate the inner cylinder at an angular velocity of against the fixed
outer cylinder is T. The diameter of the inner cylinder is d and < < d. The dynamic
viscosity of the oil is given by
(A)
(B)
(C)
(D)



Q.2 Water is retained against a sluice gate in the form of a circular segment as shown in the
figure. If and are the density of water and gravitational acceleration respectively, the
upward force exerted by the gate on the water per unit depth perpendicular to the plane of
the figure is

(A) ?
s in 2 (B) cos
?
sin

(C) cos ?
sin (D) cos
?
sin



Q.3
A two-dimensional velocity field is given by ?
= 10( ? ) ? + 2 ?, where ? and ?
are the unit vectors in the directions of the rectangular Cartesian coordinates x and y,
respectively. If the flow is incompressible, the constant should be
(A) ?10 (B) 0 (C) 5 (D) 10

Q.4
Let ?
and denote the velocity vector and temperature in a flow field. The rate of change
of temperature experienced by a fluid particle as it is passes through the point (x
1
, y
1
, z
1
) at
a time t
1
is 2.5
o
C/s. The rate of change of temperature at a time t
1
at the point (x
1
, y
1
, z
1
) is
4.8
o
C/s. The quantity ?
. ?
?
at (x
1
, y
1
, z
1
) and t
1
in
o
C/s is _____


GATE 2015 FLUID MECHANICS ? XE-B
XE-B 2/6
Q.5
In a simple Couette flow apparatus, the gap ? between the parallel plates is filled with a
liquid of density and dynamic viscosity , and one plate is dragged at a velocity of U
parallel to itself, while the other plate is fixed. The magnitude of vorticity at any point in
the flow is
(A)
(B) 0
(C)


(D)



Q.6
An open glass capillary tube of 2 mm bore is lowered into a cistern containing mercury
(density = 13600 kg/m
3
) as shown in the figure. Given that the contact angle between
mercury and glass = 140
o
, surface tension coefficient = 0.484 N/m and gravitational
acceleration = 9.81 m/s
2
, the depression of mercury in the capillary tube below the free
surface in the cistern, in mm, is _____


Q.7
Consider a combined forced-free vortex. The central region with radius R and angular
velocity is the forced vortex and the rest is the free vortex. The pressure at the edge of
the combined vortex is p
o
. If the density of the fluid is ?, the pressure at the center of the
combined vortex is
(A) o
?
(B) o
?
(C) o
+

(D) o
+


Q.8 The following is true at the point of separation of a boundary layer:
(A) Transition occurs from laminar to turbulent flow
(B) The flow relaminarizes from turbulent regime
(C) The shear stress vanishes
(D) The relation between stress and rate of strain ceases to be linear

Q.9 A certain fluid flow phenomenon is described by Reynolds, Weber and Ohnesorge
numbers. The Weber and Ohnesorge numbers are defined as We =
2
, and Oh =
,
respectively, where is the surface tension, is the density, is the dynamic viscosity, U
is the velocity and L is the characteristic dimension. If Re denotes the Reynolds number,
which of the following relations is true?

(A) We= O h Re
2
(B) We = Oh
Re
2
(C) We=Oh
Re (D) We= O h R e

GATE 2015 FLUID MECHANICS ? XE-B
XE-B 3/6
Q. 10 ? Q. 22 carry two marks each.

Q.10
A rectangular boat 6 m wide and 15 m long (dimension perpendicular to the plane of the
figure) has a draught of 2 m. The side view of the boat is as shown in the figure. The centre
of gravity G of the boat is at the free surface level. The metacentric height of the boat in m
is

(A) ?1.0 (B) 0.5 (C) 1.5 (D) 2.0

Q.11
Water drains out into atmosphere from a small orifice located at the bottom of a large open
tank. If the initial height of the water column is H, the time taken to empty the tank is
proportional to
(A) /
(B)
(C) / (D)

Q.12
Consider a two-dimensional velocity field given by ?
= ? ? ?, where ? and ? are the
unit vectors in the directions of the rectangular Cartesian coordinates x and y, respectively.
A fluid particle is located initially at the point (?1, 1). Its position after unit time is
(A) (?2,?2) (B) (1,?1) (C) (1,1) (D) (3,?1)

Q.13
The figure shows a reducing area conduit carrying water. The pressure p and velocity V
are uniform across sections 1 and 2. The density of water is 1000 kg/m
3
. If the total loss of
head due to friction is just equal to the loss of potential head between the inlet and the
outlet, then V
2
in m/s will be _____





GATE 2015 FLUID MECHANICS ? XE-B
XE-B 4/6
Q.14
A fluid enters a control volume through an inlet port (denoted with subscript 'i') and leaves
through two outlet ports (denoted with subscripts 'o,1' and 'o,2') as shown in the figure. The
velocities may be assumed to be uniform across the ports. The rate of change of mass in the
control volume in kg/s, at the instant shown in the figure, is _____


Q.15
The total discharge of water through a lawn sprinkler shown in the figure is one liter per
minute. The velocity of the jet at each end, relative to the arm, is 2?/30 m/s. The density of
water is 1000 kg/m
3
and the length of each arm is 0.1 m. If the frictional torque of the pivot
is ?/36 mN.m, the rotational speed, in revolutions per minute, of the sprinkler is _____


Q.16 Consider a two-dimensional potential flow field with the radial and tangential velocity
components, r
=
and ?
=
, respectively, where m and k are constants. The stream
function is such that it increases along the direction of traverse of a line in the flow field if
the flow is from left to right across that line. The stream function
for this flow field, with
= 0 at r = a and ? = 0, is
(A)
+
ln
(B)
?
ln


(C)
+
ln
(D)
?
ln






FirstRanker.com - FirstRanker's Choice
GATE 2015 FLUID MECHANICS ? XE-B
XE-B 1/6
B : FLUID MECHANICS
Q. 1 ? Q. 9 carry one mark each.
Q.1
The gap between two concentric cylinders, each of height h, is filled with an oil. The
torque required to rotate the inner cylinder at an angular velocity of against the fixed
outer cylinder is T. The diameter of the inner cylinder is d and < < d. The dynamic
viscosity of the oil is given by
(A)
(B)
(C)
(D)



Q.2 Water is retained against a sluice gate in the form of a circular segment as shown in the
figure. If and are the density of water and gravitational acceleration respectively, the
upward force exerted by the gate on the water per unit depth perpendicular to the plane of
the figure is

(A) ?
s in 2 (B) cos
?
sin

(C) cos ?
sin (D) cos
?
sin



Q.3
A two-dimensional velocity field is given by ?
= 10( ? ) ? + 2 ?, where ? and ?
are the unit vectors in the directions of the rectangular Cartesian coordinates x and y,
respectively. If the flow is incompressible, the constant should be
(A) ?10 (B) 0 (C) 5 (D) 10

Q.4
Let ?
and denote the velocity vector and temperature in a flow field. The rate of change
of temperature experienced by a fluid particle as it is passes through the point (x
1
, y
1
, z
1
) at
a time t
1
is 2.5
o
C/s. The rate of change of temperature at a time t
1
at the point (x
1
, y
1
, z
1
) is
4.8
o
C/s. The quantity ?
. ?
?
at (x
1
, y
1
, z
1
) and t
1
in
o
C/s is _____


GATE 2015 FLUID MECHANICS ? XE-B
XE-B 2/6
Q.5
In a simple Couette flow apparatus, the gap ? between the parallel plates is filled with a
liquid of density and dynamic viscosity , and one plate is dragged at a velocity of U
parallel to itself, while the other plate is fixed. The magnitude of vorticity at any point in
the flow is
(A)
(B) 0
(C)


(D)



Q.6
An open glass capillary tube of 2 mm bore is lowered into a cistern containing mercury
(density = 13600 kg/m
3
) as shown in the figure. Given that the contact angle between
mercury and glass = 140
o
, surface tension coefficient = 0.484 N/m and gravitational
acceleration = 9.81 m/s
2
, the depression of mercury in the capillary tube below the free
surface in the cistern, in mm, is _____


Q.7
Consider a combined forced-free vortex. The central region with radius R and angular
velocity is the forced vortex and the rest is the free vortex. The pressure at the edge of
the combined vortex is p
o
. If the density of the fluid is ?, the pressure at the center of the
combined vortex is
(A) o
?
(B) o
?
(C) o
+

(D) o
+


Q.8 The following is true at the point of separation of a boundary layer:
(A) Transition occurs from laminar to turbulent flow
(B) The flow relaminarizes from turbulent regime
(C) The shear stress vanishes
(D) The relation between stress and rate of strain ceases to be linear

Q.9 A certain fluid flow phenomenon is described by Reynolds, Weber and Ohnesorge
numbers. The Weber and Ohnesorge numbers are defined as We =
2
, and Oh =
,
respectively, where is the surface tension, is the density, is the dynamic viscosity, U
is the velocity and L is the characteristic dimension. If Re denotes the Reynolds number,
which of the following relations is true?

(A) We= O h Re
2
(B) We = Oh
Re
2
(C) We=Oh
Re (D) We= O h R e

GATE 2015 FLUID MECHANICS ? XE-B
XE-B 3/6
Q. 10 ? Q. 22 carry two marks each.

Q.10
A rectangular boat 6 m wide and 15 m long (dimension perpendicular to the plane of the
figure) has a draught of 2 m. The side view of the boat is as shown in the figure. The centre
of gravity G of the boat is at the free surface level. The metacentric height of the boat in m
is

(A) ?1.0 (B) 0.5 (C) 1.5 (D) 2.0

Q.11
Water drains out into atmosphere from a small orifice located at the bottom of a large open
tank. If the initial height of the water column is H, the time taken to empty the tank is
proportional to
(A) /
(B)
(C) / (D)

Q.12
Consider a two-dimensional velocity field given by ?
= ? ? ?, where ? and ? are the
unit vectors in the directions of the rectangular Cartesian coordinates x and y, respectively.
A fluid particle is located initially at the point (?1, 1). Its position after unit time is
(A) (?2,?2) (B) (1,?1) (C) (1,1) (D) (3,?1)

Q.13
The figure shows a reducing area conduit carrying water. The pressure p and velocity V
are uniform across sections 1 and 2. The density of water is 1000 kg/m
3
. If the total loss of
head due to friction is just equal to the loss of potential head between the inlet and the
outlet, then V
2
in m/s will be _____





GATE 2015 FLUID MECHANICS ? XE-B
XE-B 4/6
Q.14
A fluid enters a control volume through an inlet port (denoted with subscript 'i') and leaves
through two outlet ports (denoted with subscripts 'o,1' and 'o,2') as shown in the figure. The
velocities may be assumed to be uniform across the ports. The rate of change of mass in the
control volume in kg/s, at the instant shown in the figure, is _____


Q.15
The total discharge of water through a lawn sprinkler shown in the figure is one liter per
minute. The velocity of the jet at each end, relative to the arm, is 2?/30 m/s. The density of
water is 1000 kg/m
3
and the length of each arm is 0.1 m. If the frictional torque of the pivot
is ?/36 mN.m, the rotational speed, in revolutions per minute, of the sprinkler is _____


Q.16 Consider a two-dimensional potential flow field with the radial and tangential velocity
components, r
=
and ?
=
, respectively, where m and k are constants. The stream
function is such that it increases along the direction of traverse of a line in the flow field if
the flow is from left to right across that line. The stream function
for this flow field, with
= 0 at r = a and ? = 0, is
(A)
+
ln
(B)
?
ln


(C)
+
ln
(D)
?
ln






GATE 2015 FLUID MECHANICS ? XE-B
XE-B 5/6
Q.17
A steady, two-dimensional, inviscid and incompressible flow field is described in
rectangular Cartesian coordinates as = and = ? , where and are the
components of the velocity vector in the x and y directions, respectively. Gravity acts along
the negative y-direction. The pressure distribution, with the reference pressure taken as zero
at the origin, with usual notation, is given by
(A) ?
( + + ) ? (B) ?
( ? + ) ?

(C) ?
( + ) ? (D) ?
( ? ) ?


Q.18
A cylinder of radius 0.1 m rotating clockwise about its own axis at an angular velocity of
100/? radians per second is placed in a cross-stream of air flowing at a velocity of 10 m/s
from left to right. The density of air is 1.2 kg/m
3
. The lift force per unit length of the
cylinder in N/m is _____


Q.19
The velocity profile in turbulent flow through a pipe is approximated as
= / ,
where max
is the maximum velocity, R is the radius and y is the distance measured normal
to the pipe wall towards the centerline. If av
denotes the average velocity, the ratio
is
(A)
(B)
(C)
(D)


Q.20
A steel sphere (density = 7900 kg/m
3
) of diameter 0.1 m is dropped from rest in water
(density = 1000 kg/m
3
). The gravitational acceleration is 9.81 m/s
2
. Assuming that the drag
coefficient is constant and equal to 1.33, the terminal velocity attained by the sphere in m/s
is _____


FirstRanker.com - FirstRanker's Choice
GATE 2015 FLUID MECHANICS ? XE-B
XE-B 1/6
B : FLUID MECHANICS
Q. 1 ? Q. 9 carry one mark each.
Q.1
The gap between two concentric cylinders, each of height h, is filled with an oil. The
torque required to rotate the inner cylinder at an angular velocity of against the fixed
outer cylinder is T. The diameter of the inner cylinder is d and < < d. The dynamic
viscosity of the oil is given by
(A)
(B)
(C)
(D)



Q.2 Water is retained against a sluice gate in the form of a circular segment as shown in the
figure. If and are the density of water and gravitational acceleration respectively, the
upward force exerted by the gate on the water per unit depth perpendicular to the plane of
the figure is

(A) ?
s in 2 (B) cos
?
sin

(C) cos ?
sin (D) cos
?
sin



Q.3
A two-dimensional velocity field is given by ?
= 10( ? ) ? + 2 ?, where ? and ?
are the unit vectors in the directions of the rectangular Cartesian coordinates x and y,
respectively. If the flow is incompressible, the constant should be
(A) ?10 (B) 0 (C) 5 (D) 10

Q.4
Let ?
and denote the velocity vector and temperature in a flow field. The rate of change
of temperature experienced by a fluid particle as it is passes through the point (x
1
, y
1
, z
1
) at
a time t
1
is 2.5
o
C/s. The rate of change of temperature at a time t
1
at the point (x
1
, y
1
, z
1
) is
4.8
o
C/s. The quantity ?
. ?
?
at (x
1
, y
1
, z
1
) and t
1
in
o
C/s is _____


GATE 2015 FLUID MECHANICS ? XE-B
XE-B 2/6
Q.5
In a simple Couette flow apparatus, the gap ? between the parallel plates is filled with a
liquid of density and dynamic viscosity , and one plate is dragged at a velocity of U
parallel to itself, while the other plate is fixed. The magnitude of vorticity at any point in
the flow is
(A)
(B) 0
(C)


(D)



Q.6
An open glass capillary tube of 2 mm bore is lowered into a cistern containing mercury
(density = 13600 kg/m
3
) as shown in the figure. Given that the contact angle between
mercury and glass = 140
o
, surface tension coefficient = 0.484 N/m and gravitational
acceleration = 9.81 m/s
2
, the depression of mercury in the capillary tube below the free
surface in the cistern, in mm, is _____


Q.7
Consider a combined forced-free vortex. The central region with radius R and angular
velocity is the forced vortex and the rest is the free vortex. The pressure at the edge of
the combined vortex is p
o
. If the density of the fluid is ?, the pressure at the center of the
combined vortex is
(A) o
?
(B) o
?
(C) o
+

(D) o
+


Q.8 The following is true at the point of separation of a boundary layer:
(A) Transition occurs from laminar to turbulent flow
(B) The flow relaminarizes from turbulent regime
(C) The shear stress vanishes
(D) The relation between stress and rate of strain ceases to be linear

Q.9 A certain fluid flow phenomenon is described by Reynolds, Weber and Ohnesorge
numbers. The Weber and Ohnesorge numbers are defined as We =
2
, and Oh =
,
respectively, where is the surface tension, is the density, is the dynamic viscosity, U
is the velocity and L is the characteristic dimension. If Re denotes the Reynolds number,
which of the following relations is true?

(A) We= O h Re
2
(B) We = Oh
Re
2
(C) We=Oh
Re (D) We= O h R e

GATE 2015 FLUID MECHANICS ? XE-B
XE-B 3/6
Q. 10 ? Q. 22 carry two marks each.

Q.10
A rectangular boat 6 m wide and 15 m long (dimension perpendicular to the plane of the
figure) has a draught of 2 m. The side view of the boat is as shown in the figure. The centre
of gravity G of the boat is at the free surface level. The metacentric height of the boat in m
is

(A) ?1.0 (B) 0.5 (C) 1.5 (D) 2.0

Q.11
Water drains out into atmosphere from a small orifice located at the bottom of a large open
tank. If the initial height of the water column is H, the time taken to empty the tank is
proportional to
(A) /
(B)
(C) / (D)

Q.12
Consider a two-dimensional velocity field given by ?
= ? ? ?, where ? and ? are the
unit vectors in the directions of the rectangular Cartesian coordinates x and y, respectively.
A fluid particle is located initially at the point (?1, 1). Its position after unit time is
(A) (?2,?2) (B) (1,?1) (C) (1,1) (D) (3,?1)

Q.13
The figure shows a reducing area conduit carrying water. The pressure p and velocity V
are uniform across sections 1 and 2. The density of water is 1000 kg/m
3
. If the total loss of
head due to friction is just equal to the loss of potential head between the inlet and the
outlet, then V
2
in m/s will be _____





GATE 2015 FLUID MECHANICS ? XE-B
XE-B 4/6
Q.14
A fluid enters a control volume through an inlet port (denoted with subscript 'i') and leaves
through two outlet ports (denoted with subscripts 'o,1' and 'o,2') as shown in the figure. The
velocities may be assumed to be uniform across the ports. The rate of change of mass in the
control volume in kg/s, at the instant shown in the figure, is _____


Q.15
The total discharge of water through a lawn sprinkler shown in the figure is one liter per
minute. The velocity of the jet at each end, relative to the arm, is 2?/30 m/s. The density of
water is 1000 kg/m
3
and the length of each arm is 0.1 m. If the frictional torque of the pivot
is ?/36 mN.m, the rotational speed, in revolutions per minute, of the sprinkler is _____


Q.16 Consider a two-dimensional potential flow field with the radial and tangential velocity
components, r
=
and ?
=
, respectively, where m and k are constants. The stream
function is such that it increases along the direction of traverse of a line in the flow field if
the flow is from left to right across that line. The stream function
for this flow field, with
= 0 at r = a and ? = 0, is
(A)
+
ln
(B)
?
ln


(C)
+
ln
(D)
?
ln






GATE 2015 FLUID MECHANICS ? XE-B
XE-B 5/6
Q.17
A steady, two-dimensional, inviscid and incompressible flow field is described in
rectangular Cartesian coordinates as = and = ? , where and are the
components of the velocity vector in the x and y directions, respectively. Gravity acts along
the negative y-direction. The pressure distribution, with the reference pressure taken as zero
at the origin, with usual notation, is given by
(A) ?
( + + ) ? (B) ?
( ? + ) ?

(C) ?
( + ) ? (D) ?
( ? ) ?


Q.18
A cylinder of radius 0.1 m rotating clockwise about its own axis at an angular velocity of
100/? radians per second is placed in a cross-stream of air flowing at a velocity of 10 m/s
from left to right. The density of air is 1.2 kg/m
3
. The lift force per unit length of the
cylinder in N/m is _____


Q.19
The velocity profile in turbulent flow through a pipe is approximated as
= / ,
where max
is the maximum velocity, R is the radius and y is the distance measured normal
to the pipe wall towards the centerline. If av
denotes the average velocity, the ratio
is
(A)
(B)
(C)
(D)


Q.20
A steel sphere (density = 7900 kg/m
3
) of diameter 0.1 m is dropped from rest in water
(density = 1000 kg/m
3
). The gravitational acceleration is 9.81 m/s
2
. Assuming that the drag
coefficient is constant and equal to 1.33, the terminal velocity attained by the sphere in m/s
is _____


GATE 2015 FLUID MECHANICS ? XE-B
XE-B 6/6
Q.21
An inclined venturimeter connected to an inverted manometer is shown in the figure. The
cross-sectional areas at the inlet and the throat are 2 ? 10
?3
m
2
and 2 ? 10
?4
m
2
,
respectively. The densities of water and oil are 1000 kg/m
3
and 800 kg/m
3
, respectively.
The gravitational acceleration is 9.81 m/s
2
. If the discharge of water through the
venturimeter is 5 ? 10
?4
m
3
/s, neglecting viscous effects and assuming uniform velocities
across the inlet and the throat, the manometer reading h, in m, will be _____



Q.22
A plane jet of water with volumetric flow rate 0.012 m
3
/s and cross-sectional area 6 ? 10
?4

m
2
strikes a stationary plate inclined at angle ? and leaves as two streams, as shown in the
figure. The ratio of the discharge through section 2 to that through section 3 is 3:1. The
velocities may be considered uniform across the cross-sections and the effects of friction
may be neglected. The density of water is 1000 kg/m
3
. Ignoring the effects of gravity, the
magnitude of the normal force exerted on the plate, in N, is _____




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