FLUID MECHANICS
FLUID MECHANICS &
TURBO MACHINERY
CONTENTS
Unit Chapters Page No.
1 Fundamentals and Properties of Fluids 2 - 17
2 Fluid Statics 18 - 33
3 Fluid Kinematics 34 - 50
4 Fluid Dynamics 51 - 56
5A Laminary Flow 57 - 58
5B Turbulent Flow 59 - 61
6 Boundary Layer 62 - 65
7 Turbo Machinery 66 - 69
Copyright © Ascent Gate Academy 2013
All rights reserved.
No part of this publication may be reproduced, stored in a retrieval system,
or transmitted, in any form or by any means, electronic, mechanical,
photocopying, digital, rocording, or otherwise, without the prior
permission of the publishers.
Published at : Ascent Gate Academy
“Shraddha Saburi”, Near Gayatri Vidyapeeth,
Rajnandgaon (Chhattisgarh) Mob. 9993336391
www.ascentgateacademy.com © Copyright : Ascent Gate Academy 1
FLUID MECHANICS
1 FUNDAMENTALS AND PROPERITES OF FLUIDS
1. A Newtonian fluid fills the clearance between a shaft and a sleeve. When a force of 800 N is
applied to the shaft, parallel to the sleeve, the shaft attains a speed of 1.5 cm/s. if a force of
2.4 kN is applied instead, the shaft would move with a speed of.
(a) 1.5 cm/s (b) 13.5cm/s (c) 0.5 cm/s (d) 4.5 cm/s
2. The velocity profile for laminar flow of water between two parallel plates. shown in fig. is
given as u= 0.01 (1-10,000 y2), where u is in m/s and y in m, the viscosity of water may be
assumed to be 10-3 N.s/m2. The shear stress on the plates will be.
(a) 2.0N/m2. (b) 0.002N/m2. (c) 0.0N/m2. (d) 0.004N/m2.
3. A 100 N rectangular solid block slides down a 300 in clined plane, the plane is lubricated by a
2 mm thick film of oil of relative density 0.80 and viscosity 10 poise. if the contact area is
0.1m2, estimate the terminal velocity of the block.
(a) 0.5 m/sec
(b) 1.0 m/sec
(c) 1.5 m/sec
(d) none
4. An incompressible fluid (kinematic viscosity = 7.4 x 10-7 m2/s, specific gravity, 0.88) is held
between two parallel plates. If the top plate is moved with a velocity of 0.5 m/s while the
bottom one is held stationary, the fluid attains a linear velocity profile in the gap of 0.5 mm
between these plates ; the shear shtress is Pascal on the surface of bottom plate is :
[GATE-ME-04]
a) 0.651 x 10-3
b) 0.651
c) 6.51
d) 0.651 x 103
5. A journal bearing has a shaft diameter of 40 mm and a length of 40 mm. The shaft is rotating at
20 rad/s and the viscosity of the lubricant is 20 mPa-s. The clearnace is 0.020 mm. The loss of
torque due to the viscosity of the lubricant is approximately : [GATE-ME-08]
a) 0.040 Nm
b) 0.252 Nm
c) 0.400 Nm
d) 0.652 Nm
www.ascentgateacademy.com © Copyright : Ascent Gate Academy 2
FLUID MECHANICS
6. A cubic block of side ‘L’ and mass ‘M’ is dragged over an oil film across table by a string
connects to a hanging block of mass ‘m’ as shown is fig. The Newtonian oil film of thickness
‘h’ has dynamic voscitiy ‘µ’ and the flow condition is laminar. The acceleration due to gravity
is ‘g’ . The steady state velcity ‘V’ of block is : [GATE-PI-04]
Mgh
a) µ L2
Mgh
b) µ
mgh
c) µ L2
mgh
d) µ
7. Oil in a hydraulic cylinder is compressed from an initial volume 2m3 to 1.96m3. If the pressure
of oil in the cylinder change from 40 MPa to 80 MPa during compression, the bulk modulus of
elasticity of oil is :GATE-PI-07]
a) 1000 MPa b) 2000 MPa c) 4000 Mpa d) 8000 Mpa
8. A lightly loaded full journal bearing has journal diameter of 50 mm, bush bore of 50.50 mm and
bush legnth of 20 mm. If rotational speed of journal is 1200 rpm and average viscosity of
liqurid lubricant is 0.3 Pa-sec, the power (in W) will be [GATE-ME-10]
a) 37 b) 74 c) 118 d) 237
9. The velocity distribution near the solid wall at a section in a laminar flow is given by u = 5 sin
(5πy). If µ = 5 poise. The shear stress @ y = 0.05 m in N/m2.
(a) 39.27 (b) 27.76 (c) 38.9 (d) none
10. A pressure increase of 200 N/cm2 increases the density of water by 0.1%. The bulk modulus of
elasticity of water is equal to.
(a) 200 GN/m2. (b) 20 GN/m2. (c) 2 GN/m2. (d) 0.2 GN/m2.
11. The excess pressure (above atmospheric) inside a soap bubble of diameter 1 cm, by assuming
the surface tension of soap solution to be 0.04 N/m is.
(a) 32.0 N/m2. (b) 16.0 N/m2. (c) 160.0 N/m2. (d) 0.32 N/m2.
12. The capillary rise in a 3mm tube immersed in a liquid is 15mm. If another tube of dia 4 mm
immersed in the same liquid the capillary rise would be (in mm).
(a) 11.25 (b) 20.00 (c) 8.44 (d) 26.67
13. A spherical bubble of radius ‘R’ cm is blown in to 64 small bubbles of equal volume. In terms
of surface tension ‘σ’, the work required is.
(a) 12π R2σ (b) 16π R2σ (c) 4π R2σ (d) none.
www.ascentgateacademy.com © Copyright : Ascent Gate Academy 3
FLUID MECHANICS
Common Data question
Data for Q. 14 - 15 are given below. Solve the problems and choose the correct answers. A cylindri-
cal shaft of 100 mm dia. rotates about a vertical axis inside a fixed cylindrical tube of length 2 m and 106mm
internal dia. If the space between the tube and the shaft is filled by a lubricant of dynamic viscosity 2.0 poise.
The shaft is rotated at a speed of 240rpm. Assume linear variation of velocity across the gap.
14. The shear stress on the shaft in ‘Pa’ is
(a) 4.19 (b) 41.9 (c) 83.8 (d) 8.38
15. The power required to overcome the viscous resistance in ‘watt’ is.
(a) 6.6 (b) 66 (c) 3.3 (d) 33
16. For a fluid µ = 0.048 Pa-S, Sg = 0.913 for flow over solid plate, the velocity at a pt. 75 mm away
from surface is 1.125 m/s. Calculate shear stresses at the solid boundary & also at points
25 mm, 50 mm & 75 mm away from surface in normal direction, if velocity distribution across
the surface is
i) Linear, ii) Parabolic with vertex at pt. 75 mm away from surface.
17. A space 25 mm wide between two large plane surfaces is filled with glycerin. What force is
required to drag a very thin plate 0.75 sq metre in area between the surfaces at a speed of
0.5 m/s (i) if this plate remains equidistant from the two surfaces, (ii) if it is at a distance of
10 mm from one of the surface ? Take µ = 0.785 N-s/m2.
18. In a simple concentric shaft-bearing arrangement, the lubricant flows in the 2 mm gat between
the shaft and the bearing. The flow may be assumed to be a plane Couette flow with zero
pressure gradient. The diameter of the shaft is 100 mm and its tangential speed is 10 m/s. The
dynamic viscosity of the lubricant is 0.1 kg/m.s. The frictional resisting force (in Newton) per
100 mm length of the bearing is ____________. (GATE-ME-14)(S-1)
19. Which of the following statement are TRUE, when the cavitation parameter σ = 0 ?
(i) The local pressure is reduced to vapor pressure.
(ii) Cavitation starts
(iii) Boiling of liquid starts
(iv) Cavitations stops
(a) (i), (ii) and (iv)
(b) Only (ii) and (iii)
(c) Only (i) and (iii)
(d) (i), (ii) and (iii)
www.ascentgateacademy.com © Copyright : Ascent Gate Academy 4
FLUID MECHANICS
20.) Consider fluid flow between two infinite horizontal plates which are parallel (the gap between
them being 50 mm). The top plate is sliding parallel to the stationary bottom plate at a speed
of 3 m/s. The flow between the plates is sovely due to the motion of the top plate. The force
per unit area (magnitude) required to maintain the bottom plate stationary is __________
N/m2.
Viscosity of the fluid µ = 0.44 kg/m-s and density ρ = 888 kg/m3.
PRACTICE QUESTIONS :
1. A fluid is said to be Newtonian fluid when the shear stress is [GATE-ME-95]
a) directoly proportional to the velocity gradient
b) invesrsely proportional to the velocity gradient
c) independent of the velocity gradient d) none of the above
2. A fluid is one which can be defined as a substance that : [GATE-ME-96]
a) has that same shear stress at all points
b) can deform indefinitely under the action of the smallest shear force
c) has the small shear stress in all directions
d) is practically incompressible
3. The dimension of surface tension is : [GATE--ME-96]
a) ML-1 b) L2T-1 c) ML-1T-1 d) MT2
4. The dimension of surface tension is : P [GATE-PI-97]
a) N/m2 b) J/m 2 c) J/m2 d) W/m
5. If ‘P’ is the gauge pressure within a spherical droplet, then gauge pressure within a bubble of
the same fluid samd of same size will be : [GATE-ME-99]
P c) P d) 2P
a) 4 b)
6. Kinematic viscosity of air at 200 C is given to be 1.6 x 10-5 m2/s. Its kinematic viscosity at 700C
will be varying approximately : [GATE-ME-99]
a) 2.2 x 10-5 m2/s
b) 1.6 x 10-5 m2/s
c) 1.2 x 10-5 m2/s
d) 3.2 x 10-5 m2/s
7. The SI unit of kinematic viscosity (v) is : [GATE-ME-01]
a) m2/sec b) kg/m-sec c) m/sec2 d) m3/sec2
8. A body has a weight of 392 N at standard earth’sgravity of 9.8m/sec2. If a force of 800 N is
applied to the body. the value of acceleration moon are.
(a) 20 (b) 3.33
(c) 39.9 (d) 9.81
www.ascentgateacademy.com © Copyright : Ascent Gate Academy 5
FLUID MECHANICS
9. If the shear stress ‘t’ and shear rate (du/dy) relationship of a material is plotted with t on the
Y-axis and du/dy on the X-axis, the behaviour of an ideal fluid is exhibited by .
(a) a straight line passing through the origin and inclined to the X-axis.
(b) the positive X-axis
(c) the positive Y-axis
(d) a curved line passing through the origin.
10 The space between two parallel plates kept 3 mm apart is filled with an oil of dynamic viscosity
0.2Pa.s. The shear stress on the lower fixed plate, if the upper one is moved with a velocity of
1.5 m/sec is. V
(a) 500 N/m2. 3mm
(b) 100 N/m2.
(c) 150 N/m2.
(d) none τ
11. A liquid of density ρ and dynamic viscosity µ flowssteadily down an inclined plane in a thin
sheet of constant thickness t. Neglecting air friction the shear stress on the bottom surface due
to the liquid flow is (whereθ is the angle, the plane makes with the horizontal).
(a) ρ g t sinθ (b) ρ g t cosθ (c) µ √g/t (d) ρg
12. If the dynamic viscosity of a fluid is 0.5 poise and specific gravity is 0.5, then the kinematic
viscosity of that fluid in stokes is.
(a) 0.25 (b) 0.50 (c) 1.0 (d) none
13. At room temperature, the dynamic and kinematic viscosity of water .
(a) are both greater than that of air
(b) are both less than that of air
(c) are respectively greater than and less than that of air
(d) are respectively less than and greater than that of air.
14. At 200C, the bulk modulus of elasticity of kerosene is 1.43 x 109 Pa and its relative density0.804.
The velocity of propagation of sound in kerosene at this temperature is.
(a) 1225 m/sec
(b) 2225 m/sec
(c) 1335 m/sec
(d) 1885 m/sec
15. The work done in blowing a soap bubble of diameter 10cm is . Assume the surface tension of
soap solution = 0.050 N/m)
(a) 0.00157 N.m (b) 0.00314 N.m (c) 0.00628 N.m (d) none
16. Newton’s law of viscosity states that the shear stress in a fluid is proportional to :
a) The velocity of end fluid.
b) The time rate of change of velocity of the fluid
c) The rate of change of velocity of the fluid with the height of fluid film
d) The square of the velocity of the fluid.
www.ascentgateacademy.com © Copyright : Ascent Gate Academy 6
FLUID MECHANICS
IES Questions :
1. The shear stress developed in a lubricating 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/m2. (b) 19.62 N/m2. (c) 29.62 N/m2. (d) 40 N/m2.
2. In the phenomenon of cavitation, the characteristic fluid property involved is
(a) surface tension
(b) viscosity
(c) bulk modulus of elasticity
(d) vapor pressure
3. Pressure reaches a value of absolute zero.
(a) at a temperature fo - 273K
(b) under vaccum condition
(c) at the earth’s centre
(d) when molecular momentum of system becomes zero.
4. Assertion (A) : In general, viscosity in liquids increases and in gases it decreases with rise in
temperature.
Reason (R) : Viscosity is caused by intermolecular forces of cohesion and due transfer of
molecular momentum between fluid layers; of which in liquids he former and in gases the later
contribute the major part towards viscosity.
(a) Both A and R are true and R is the correct explanation of A
(b) Both A and R are true but R is Not the correct explanation of A
(c) A is true but R is false
(d) A is false but R is true.
5. The capillary rise at 200C in clean glass tube of 1mm diameter containing water is
approximately.
(a) 15 mm (b) 50 mm (c) 20 mm (d) 30 mm.
6. Match list - I (Type of fluid) with list II (Variation of shear stress) and select the correct answer.
List - I List - II
A. Ideal fluid - 1. Shear stress varies linearly with the rate of strain.
B. Newtonian fluid - 2. Shear stress does not vary linearly with the rate of strain.
C. Non- Newtonian fluid - 3. Fluid behaves like a solid until a minimum yield stress
beyond which it exhibits a linear relationship between shear
stress and the rate of srain
D. Bingham plastic - 4. Shear stress is zero.
Codes:
ABCD
(a) 3 1 2 4
(b) 4 2 1 3
(c) 3 2 1 4
(d) 4 1 2 3
www.ascentgateacademy.com © Copyright : Ascent Gate Academy 7
FLUID MECHANICS
7. Match list - I (Phenomena) with list - II (Causes) and select the the correct answer.
List - I List - II
A . Shock wave - 1. Surface tension
B. Flow seperation - 2. Vapor pressure
C. Capillary rise - 3. Compressibility
D. Cavitation - 4. Adverse Pressure gradient
Codes :
ABCD
(a) 3 1 2 4
(b) 4 2 1 3
(c) 3 4 1 2
(d) 4 1 2 3
8. Match the list - I (Rheological Equation) with List - II (types of fluids) and select the correct
answer.
List - I List - II
A. τ = µ (du / dy)n , n = 1 - 1. Bingham plastic
B. τ = µ (du / dy)n , n < 1 - 2. Dialtant fluid
C. τ = µ (du / dy)n , n > 1 - 3. Newtonian fluid
D. τ = τo + µ (du / dy)n , n = 1 - 4. Psudo-plastic fluid
Codes:
ABCD
(a) 3 2 4 1
(b) 4 1 2 3
(c) 3 4 2 1
(d) 4 2 1 3
9. An oil of specific gravity 0.9 has viscosity of 0.28 stokes at 380C. What will be its viscosity in
Ns/m2?
(a) 0.2520 (b) 0.0311 (c) 0.0252 (d) 0.0206
10. Consider the following statements.
1. Viscosity 2. Surface tension
3. Capillary 4. Vapour pressure
Which of the above properties can be attributed to the flow of jet of oil in an unbroken
stream ?
(a) 1 only (b) 2 only (c) 1 and 3 (d) 2 and 4
11. A vertical clean glass tube of uniform bore is used as a piezometer to measure the pressure of
liquid at a point. The liquid has a specific weight fo 15kN/m3 and a surface tension of
0.06 N/m in contact with air. If for the liquid, the angle of contact with glass is zero and the
capillary rise in the tube is not to exceed 2 mm, what is the required minimum diameter of the
tube?
(a) 6 mm (b) 8 mm (c) 10 mm (d) 12 mm
www.ascentgateacademy.com © Copyright : Ascent Gate Academy 8
FLUID MECHANICS
12. When the pressure on a given mass of liquid is increased from 3.0 MPa to 3.5 MPa, the density
of the liquid increases from 500 kg/m3 to 501 kg/m3. What is the average value of bulk
modulus of liquid over the given pressure range?
(a) 700 MPa (b) 600 MPa
(c) 500 MPa (d) 250 MPa
13. If the relationship between the shear stress and the rate of shear τ and the rate of shear strain
(du/dy) is expressed as. τ = µ (du/dy)n,then the fluid with exponent n > 1 is known as which
one of the following?
(a) Bingham plastic (b) Dilatant fluid
(c) Newtonian fluid (d) Pseudo plastic fluid
14. What are the dimensions of kinematic viscosity of a fluid?
(a) LT-2. (b) L2 T1. (c) ML-1T-1. (b) ML-2T-2.
15. In an experiment, the following shear stress- time rate of shear strain values are obtained for a
fluid:
Time rate of shear strain (1/s): 0234
Shear stress (kPa) : 0 1.4 2.6 4
How can be fluid be classified?
(a) Newtonian fluid (b) Bingham plastic (c) Pseudo plastic (d) Dilatant
16. What is the unit of dynamic viscosity of a fluid termed ‘poise’ equivalent to?
(a) dyne / cm2. (b) gm s / cm2. (c) dyne s/ cm2. (d) gm-cm / s.
17. What is the pressure difference between inside and outside of a droplet of water?
(a) 2 σ/d (b) 4 σ/d (c) 8 σ/d (d) 12 σ/d
Where σ is surface tension and d is the diameter of the droplet.
18. What is the pressure inside a soap bubble, over the atmospheric pressure if its diameter is 2 cm
and the surface tension is 0.1 N/M? (a) 4.0 N/m2.
(a) 0.4 N/m2. (d) 400.0 N/m2.
(c) 40.0 N/m2.
19. Which one of the following is correct?
The capillary rise or depression in a small diameter tube is
(a) directly proportional to the specific weight of the fluid.
(b) inversely proportional to the surface tension.
(c) inversely proportional to the diameter.
(d) directly proportional to the surface area.
20. Assertion (A) : A narrow glass tube when immersed into
mercury causes capillary depression, and when immersed into water causes capillary rise.
Reason (R) : Mercury is denser than water.
(a) Both A and R are true and R is the correct explanation of A
(b) Both A and R are true but R is Not the correct explanation of A
(c) A is true but R is false
(d) A is false but R is true.
www.ascentgateacademy.com © Copyright : Ascent Gate Academy 9
FLUID MECHANICS
21. What is the capillary rise in a narrow two dimensional slit of width ‘w’ ?
(a) Half of that in a capillary tube of diameter ’w’
(b) Two- third of that in a capillary tube of diameter ’w’
(c) one - third of that in a capillary tube of diameter ’w’
(d) one - fourth of that in a capillary tube of diameter ’w’
22. An incompressible fluid (kinematic viscosity, 7.4 x 10 m/s, specific gravity, 0.88) is held
between two parallel plates. If the top plate is moved with a velocity of 0.5 m/s while the
bottom one is held stationary, the fluid attains a linear velocity profile in the gap of 0.5 mm
between these plates; the shear stress in Pascals on the surface of top plate is .
(a) 0.651 x 10-3 (b) 0.651
(c) 6.51 (d) 0.651 x 103
23. For a Newtonian fluid.
(a) shear stress is proportional to shear strain
(b) rate of shear stress is proportional to shear strain.
(c) shear stress is proportional to rate of shear strain.
(d) rate of shear stress is proportional to rate of shear strain.
*************
“When firmness is sufficient, rashness is unnecessary”
FUNDAMENTALS AND PROPERITES OF FLUIDS :
1-d, 2-b, 3-b, 4-b, 5-a, 6-c, 7-b, 8-a, 9-b, 10-sol, 11-a, 12-a, 13-a, 14-sol, 15-b
PRACTICE QUES. : 1-a, 2-b, 3-d, 4-c, 5-d, 6-a, 7-a, 8-a, 9-b, 10-b, 11-a, 12-sol, 13-sol, 14-c,
15-b, 16-c IES Ques. : 1-b, 2-d, 3-b, 4-d, 5-d, 6-d, 7-c, 8-c, 9-c, 10-a, 11-b, 12-d, 13-b, 14-b, 15-d,
16-c, 17-b, 18-c, 19-c, 20-d, 21-a, 22-sol, 23-c.
www.ascentgateacademy.com © Copyright : Ascent Gate Academy 10
FUNDAMENTALS AND PROPERITES OF FLUIDS : CLASS WORK : 16-sol, 17-sol, 18-15.7, 19-d, 20-26.4
FLUID MECHANICS
2 FLUID STATICS
CLASS ROOM OBJECTIVE
1. If a Mohr circle is drawn for a fluid element inside a fluid body at rest, it would be.
(a) a circle not touching the origin
(b) a circle touching the origin
(c) a point on the normal stress axis
(d) a point on the shear stress axis
2. Normal stresses are of the same magnitude in all directions at a point in a fluid.
(a) only when the fluid is frictionless
(b) only when the fluid is at rest.
(c) only when the fluid has no shear stress
(d) in all cases of fluid motion
3. The left limb of the machine shown below is subjected to 100 kN load. The dia of left and right
limbs are 10 cm and 1 cm respectively. The load to be applied on right limb to keep the fluid at
same level is.
(a) 10 kN
(b) 1kN
(c) 100 kN
(d) none
4. The pressure in meteres of oil of specific gravity 0.8 equivalent to 80 m of water is.
(a) 64 m (b) 88 m (c) 80m (d) 100 m
5. A 6m deep tank contains 4m of water (at bottom) and 2m of oil of relative density 0.90 above
water. The pressure at the bottom of the tank in ‘KN/m2’ is (assume γw = 10kN/m3)
(a) 58 (b) 60 (c) 5.8 (d) 0.58
6. Which of the following pressure units represents the LEAST pressure ?
(a) milibar (b) mm of mercury
(c) N/mm2 (d) kgf/cm2
7. The specific weight of the ocean water may be taken to vary according to the expression.
γ = γ0 + C.√h
where γ0 = the specific weight at the sea level, and h is the depth below the sea surface. The
pressure @ depth ‘h’ in excess of γ0 is.
(a) 1 / 3 C.h (b) 2 / 3 C.h
(c) 1 / 3 C.h (d) none
www.ascentgateacademy.com © Copyright : Ascent Gate Academy 11
FLUID MECHANICS
8. The difference in pressure head measured by a mercury oil
differential manometer for a 8 cm difference of mercury level will be (specific gravity for oil is
0.8)
(a) 1m of oil (b) 1.024 m of oil
(c) 1.28 m of oil (d) 1.36 m of oil
9. A U-tube open at both ends and made of 8mm diameter glass tube has mercury in the bottom to
a height of 10cm above the horizontal limb. If 19cc of water is added to one of the limbs, the
difference in mercury levels at equilibrium is.
(a) 3.0 cm (b) 2.8 cm (c) 1.0 cm (d) 0
10. The cross - sectional area of limb of a U - tube manometer (shown in the fig is made 500
times larger than the other so that the pressure difference between the two limbs can be
determined by measuring ‘h’ on one limb of the manometer. Determine the percentage error
involved)
(a) 1 %
(b) 2 %
(c) 0.2 %
(d) none
11.
A pipe carrying water attached differential gauge deflection mercury gauge is 0.6 m, the (P - P)
is _____ in of water.
(a) 7.56 meters of water (b) 75.76 meters of water
(c) 8.16 meters of water (d) none
12.
What is the gauge pressure at P (in terms of oil column)
(a) 1.96 m (b) 1.87 m (c) 0.7 m (d) 2.2 m
© Copyright : Ascent Gate Academy 12
www.ascentgateacademy.com
FLUID MECHANICS
13. In the vertical limb shown, the rise (H) of mercury is
(a) 50 cm
(b) 76 cm
(c) 126 cm
(d) None
14. The pressure at ‘P’ of the bulb shown in
(a) 26 cm of Hg (abs)
(b) 50 cm of Hg (abs)
(c) 76 cm of Hg (abs)
(d) 102 cm of Hg (abs)
15. The pressure difference between points A and B for the set up shown in fig and in kPa is
(a) 9.26
(b) 10.54
(c) 10.65
(d) 11.66
16. The pressure diffference between points M and N for the
manometer shown in fig in cm of oil is.
(a) 13.84
(b) - 13.84
(c) 10.84
(d) - 10.84
17. Refer to fig. discharges the absolute pressure of gas A in the bulb.
(a) 771.3 mm Hg
(b) 752.65 mm Hg
(c) 767.35 mm Hg
(d) 748.8 mm Hg
www.ascentgateacademy.com © Copyright : Ascent Gate Academy 13
FLUID MECHANICS
18. The total pr. on a circular plate of 2m dia, immersed horizontally in water at a depth of 1m is .
(a) 1000 kg (b) 4000 kg
(c) 2000 kg (d) 3140 kg
19. A cylindrical tank of 2m diameter is laid with its axis horizontal and is filled with water just to
its top. The force on one of its end plates in kN, is .
(a) 123.0 (b) 61.51
(c) 30.81 (d) 19.58
20 The magnitude of hydrostatic pressure on one side of a circular surface, 1m area with centroid
1m below free water surface.
(a) depends on the orientation of the area
(b) is the product of specific wt. and vertical distance from free surface to the centre of pressure.
(c) 1000 kgf
(d) none of the above
21. The depth of centre of pressure on a rectangular plane surface of 6 m wide and 4 m depth
immersed vertically and its top edge touching the free surface of liquid, lies at.
(a) 2 m (b) 3m
(c) greater than 2 m but less than 4 m (d) greater than 3 m but less than 6 m
22. A rectangular plate 0.75 m x 2.4 m is immersed in a liquid of relative density 0.85 with its
0.75 m side horizontal and just at the water surface. If the plane of the plate makes an angle of
600 with the horizontal, the pressure force on one side of the plate, in kN, and centre of pressure
in m are.
(a) 15.6 & 1.39 (b) 7.8 & 1.2
(c) 24.0 & 1.39 (d) 18.0 & 1.2
23. A rectangular plate 30cm x 50cm is immersed vertically, in water with its longer side vertical.
The total force on one side of the plane is estimated as 17.6 kN. If the plate turned in the vertical
plane at its centered of gravity by 900 and if all the other factors remain the same, the total force
on one side of the plate would now be.
(a) 8.8 kN (b) 15.6 kN (c) 17.6 kN (d) 19.6 kN
24. A vertical gate 5 m high and 3 m wide closes horizontal tunnel running full with water. The
pressure at the bottom of the gate is 2 x 104 kg/sq m. The total pressure on the gate would be in kg.
(a) 192,000 (b) 250,000
(c) 262,500 (d) 225,000
25. A hollow hemispherical object of diameter D was immersed in water with its plane surface
coinciding with the free surface. The vertical component of force on the curved surface is given
by Fv = (b) 1 / 12 γπ D3.
(a) 3 / 8 γπ D3. (d) zero
(c) 1 / 24 γπ D3.
26. One end of a two dimensional water tank has the shape of a quadrant of a circle of radius 2 m .
When the tank is full, the vertical component of the force per unit length on the curved surface
will be. (b) 1000π kgf (c) 4000π kgf (d) 3000π kgf
(a) 250π kgf
www.ascentgateacademy.com © Copyright : Ascent Gate Academy 14
FLUID MECHANICS
27. In which one of the following arrangements would the vertical force on the cylinder due to
water be the maximum?
(a) (b)
(c) (d)
28. A sliding gate 3 m wide and 1.5 m high lies in a vertical plane and has a coefficient of friction
0.20 between itself and guides. If the gate weights 19.6 kN and if its upper edge is at a depth of 10 m.
determine the vertical force required to raise it? Neglect buoyancy effects on the gate.
29. A hinged gate of length 5m, inclined at 300 with the horizontal and with water mass on its left, is shown
in the figure below. Density of water is 1000 kg/m3. The minimum mass of the gate in kg per unit width
(perpendicular to the plane of paper), required to keep it closed is (GATE-ME-13)
(a) 5000 (b) 6600 (c) 7546 (d) 9623
30. A spherical ballon with a diameter of 10m, shown in the figure below is used for advertisements. The
ballon is filled with helium (RHe = 2.08 kJ/kg.K) at ambient conditions of 150C and 100 kPa.Assuming
no distrubances due to wind, the maximum allowable weight (in Newton) of ballon material and rope
requried to avoid the fall of the ballon (Rair = 289 kJ/kg.K) is ___________ (GATE-ME-14)
31. An inverted U-tube manometer is used to measure the pressure difference between two pipeAand B,
as shown in the figure. PipeAis carrying oil (Specific gravity = 0.8) and Pipe B is carrying water. The
densities of air and water are 1.16 kg/m3 and 1000 kg/m3, respectively. The pressure difference
between pipe A and B is __________ kPa.
Acceleration due to gravity g = 10 m/s2 (GATE-16-Set-1)
www.ascentgateacademy.com © Copyright : Ascent Gate Academy 15
FLUID MECHANICS
32. The large vessel shown in the figure containts oil and water.Abody is submerged at the interface of oil
and water such that 4.5 percent of its volume is in oil while the rest is in water. The density of the body
is _________ kg/m3.
The specific gravity of oil is 0.7 and density of water is 1000 kg/m3.
Acceleration due to gravityg = 10m/s2.
π22ρRρR2Rρ2 g2ggLLL1 −+ π
4
33. Considere a frictionless, massless and leak-proof blocking a rectangular hole of dimensions 2/R x L at
the bottom of an open tank as shown in the figure. The head of the plug has the shape of a
semi-cylinder of radius R. The tank is filled with a liquid of density ρ up to the tipe of the plug. The
gravitational acceleration is g. Neglect the effect of the atmospheric pressure.
The force F required to hold the plug in its positions is (GATE-16-Set-2)
(d)
(a) (b) (c)
www.ascentgateacademy.com © Copyright : Ascent Gate Academy 16
FLUID MECHANICS
34. A 2m x 2m square opening in a vertical wall is covered with a metallic plate of the same diemnsions as
shown in the figure below. Consider the acceleration due to gravity to be 10.0 m/s2. The force (in kN)
exerted by water on the plate is __________. (GATE-PI-16)
35. For a floating body, buoyant force acts at the (GATE-16-Set-1)
(a) centroid of the floating body
(b) center of gravity of the body
(c) centroid of the fluid vertically below the body
(d) centroid of the displaced fluid
Five Marks Questions
1. A cylinder of mass 10 kg and area of cross-section 0.1 m2 is tied down with string in a vessel
containing tow liquids as shown in Figure. Calculate gauge pressure on the cylinder bottom and the
tension in the string. Density of water = 1000 kg/m3. Specific gravity of A = 0.8. Specific gravity of
B (water) = 1.0. (GATE-ME-98)
*********************
Unit 2 : Fluid Statics (Class Work Ans.)
1-c, 2-c, 3-b, 4-d, 5-a, 6-a, 7-b, 8-c, 9-b, 10-c, 11-a, 12-d, 13-a, 14-b, 15-a, 16-b, 17-a, 18-d,
19- c, 20-c, 21-c, 22-a, 23-c, 24-c, 25-b, 26-b, 27-d, 28-115kN, 29-d, 30-3306, 31-2.2, 32-865,
33-a, 34-120, 35-d
www.ascentgateacademy.com © Copyright : Ascent Gate Academy 17
FLUID MECHANICS
2 FLUID STATICS
PRACTICE QUESTIONS :
1. The depth of a fluid is measured in vertical z-direction; x and y are the other two directions and
are mutually perpendicular. the static pressure variation in the fluid is given by (symbols have
the usual meaning).
(a) dp/dz = g (b) dp/dz = 0 (c) dp/dz =ρg (d) dp/dz = (-)ρg
2 If z is vertically upwards, ρ is the density and g gravitational acceleration (see fig) then the
pressure δP/δZ in fluid at rest due to gravity is given by.
(a) ρgz2/2 z
(b) −ρg
(c) −ρgz y
(d) ρg/z g
y
3 Surface tension is due to
(a) viscous forces
(b) cohesion
(c) adhesion
(d) the difference between adhesive and cohesive forces
4 Newton’s law of viscosity depends upon the
(a) stress and strain in a fluid (b) shear stress, pressure and velocity
(c) shear stress and rate of strain (d) viscosity and shear stress
5 If the surface tension of water of air interface is 0.073 N/m, the gauge pressure inside a rain
drop of 1mm diameter will be.
(a) 0.146 N/m2. (b) 73 N/m2. (c) 146 N/m2. (d) 292 N/m2.
6 Stability of a freely failing object is assured if the centre of
(a) buoyancy lies below its centre of gravity
(b) gravity coincides with its centre of buoyancy
(c) gravity lies below its metacentre
(d) buoyancy lies below its metacentre
7 Match list - I with List - II regarding a body partly submerged in a liquid and select the correct
answer using the codes given below.
List - I List - II
A. Centre of pressure- 1. Point of application of the weight of displace liquid.
B. Centre fo gravity - 2. Point about which the body starts oscillating when tilted by a small angle.
C. Centre of buoyancy - 3. Point of application of hydrostatic pressure force.
D. Metacentre - 4. Point of application of the weight of the body.
www.ascentgateacademy.com © Copyright : Ascent Gate Academy 18
FLUID MECHANICS
Codes:
ABCD
(a) 4 3 1 2
(b) 4 3 2 1
(c) 3 4 1 2
(d) 3 4 2 1
8 If a piece of metal having a specific gravity of 13.6 is placed in mercury of specific gravity 13.6,
then
(a) The metal piece will sink to the bottom
(b) The metal piece will simply float over the mercury with no immersion
(c) The metal piece will be immersed in mercury by half
(d) The whole of the metal piece will be immersed with its top surface just at mercury level.
9 A bucket of water hangs with a spring balance. If an iron piece is suspended into water from
another support without touching the sides of the bucket, the spring balance will show.
(a) an increased reading
(b) a decreased reading
(c) no change in reading
(d) increased or decreased reading depending on the depth of immersion
10 The least radius of gyration of a ship is 9 m and the metacentric height is 750mm. The time
period of oscillation of the ship is .
(a) 42.41 s (b) 75.4 s (c) 20.85 s (d) 85 s
11 Assertion (A) : If a boat, built with sheet metal on wooden frame, has an average density which
is greater than that of water, then the boat can float in water with its hollow face upward but will
sink once it overturns.
Reason (R): Buoyant force always acts in the upward direction
(a) Both A and R are true and R is the correct explanation of A
(b) Both A and R are true but R is Not the correct explanation of A
(c) A is true but R is false
(d) A is false but R is true.
12. A capillary tube is inserted in mercury kept in an open container Assertion (A) : The mercury
level inside the tube shall rise above the level of mercury outside.
Reason (R) : The cohesive force between the molecules of mercury is greater than the adhesive
force between mercury and glass.
(a) Both A and R are true and R is the correct explanation of A
(b) Both A and R are true but R is Not the correct explanation of A
(c) A is true but R is false
(d) A is false but R is true.
13. The following terms relate to floating bodies: Centre of gravity .......G, Metacentre .....M, Weight
of floating body...... W, Buoyant force..... FB. Match List - I and List - II and select the correct
answer.
www.ascentgateacademy.com © Copyright : Ascent Gate Academy 19
FLUID MECHANICS
List - I (Condition) List - II (Result)
A. G isabove M - 1. Stable equilibrium
B. G and M coincide - 2. Unstable equilibrium
C. G is below M - 3. Floating body
D. FB > W - 4. Neutral equilibrium
Codes:
AB CD
(a) 1 3 24
(b) 3 1 42
(c) 2 3 41
(d) 2 4 13
14. The manometer shown in the given fig. connects two pipes, carrying oil and water respectively.
From the fig, one.
(a) can conclude that the pressure in the pipes are equal.
(b) can conclude that the pressure in the oil pipe is higher.
(c) can conclude that the pressure in the water pipe is higher.
(d) cannot compare the pressure in the two pipes for want of sufficient data.
15. Consider the following statements:
The metacentric height of a floating body depends
1. directly on the shape of its water line area.
2. on the volume of liquid displaced by the body.
3. on the distance between the metacentre and the centre of gravity.
4. on the second moment of water - line area.
Of these statements
(a) 1 and 2 are correct (b) 2 and 3 are correct
(c) 3 and 4 are correct (d) 1 and 4 are correct
16. Assertion (A) : U- tube manometer connected to a venturimeter fitted in a pipeline can measure
the velocity through the pipe.
Reason (R) : U - tube manometer directly measures dynamic and static heads.
(a) Both A and R are individually true and R is the correct explanation of A.
(b) Both A and R true but R is not the correct explanation of A.
(c) A is true but R is false
(d) A is false but R is true
www.ascentgateacademy.com © Copyright : Ascent Gate Academy 20
FLUID MECHANICS
17. A differential manometer is used to measure the difference in pressure at points A and B in
terms of specific weight of water W. The specific gravities of the liquids X,Y and Z are respec
tively s1,s2, and s3, The correct difference is given by. PA PB
( )W W
(a) h3 s2 - h1 s1 + h2 s3 (b) h1 s1 + h2 s3 - h3 s2
(c) h3 s1 - h1 s2 + h2 s3 (b) h1 s1 + h2 s2 - h3 s3
18. A large metacentric height in vessel
(a) improves stability and makes periodic time of oscillation longer.
(b) improves stability and makes periodic time of oscillation shorter.
(c) has no effect on stability or the periodic time of oscillation
(d) improves stability and makes the periodic time of oscillation shorter.
19. In the fig. shown above, air is contained in the pipe and water is the manometer liquid. The
pressure at ‘A’ is approximately.
(a) 10.14 m of water absolute © Copyright : Ascent Gate Academy 21
(b) 0.2 m of water
(c) 1.2 m of water vaccum
(d) 4901 pa
www.ascentgateacademy.com
FLUID MECHANICS
20. The mercury manometer is fitted to a pipe. It is mounted on the delivery line of centrifugal
pump. One limb of the manometer is connected to the upstream side of the pipe at ‘A’ and the
other limb at ‘B’, just below the valve ‘V’ as shown in fig. The manometer reading ‘h’ varies
with different valve positions.
Assertion (A): with gradual closure of the valve, the magni tude of ‘h’ will go on
increasing and even a situation may arise when mercury will be sucked in by the water flowing
around ‘B’
Reason (R) : with the gradual closure of the valve, the pressure at ‘A’ will go on increasing.
(a) Both A and R are individually true and R is the correct
explanation of A.
(b) Both A and R true but R is not the correct explanation of A.
(c) A is true but R is false
(d) A is false but R is true.
21. A circular annular plate having outer and inner diameters of 1.4m and 0.6m respectively is
immersed in water with its plane making an angle of 600 with the horizontal. The centre of the
circular annular plate is 1.85 m below the free surface. The hydrostatic thrust on one side of the
plate is.
(a) 1975 N (b) 19.75 N
(c) 11.4 N (d) 22.8 N
22. Consider the following statements:
Filling up a part of the empty hold of a ship with ballasts will
1. reduce the metacentric height.
2. lower the position of the centre of gravity.
3. elevate the position of centre of gravity.
4. elevate the position of centre of buoyancy.
Of these statements
(a) 1, 3 and 4 are correct
(b) 1 and 2 are correct
(c) 3 and 4 are correct
(d) 2 and 4 are correct
www.ascentgateacademy.com © Copyright : Ascent Gate Academy 22
FLUID MECHANICS
23. A pipe flow system with flow direction is shown in above fig. The following table gives the velocities
and the corresponding areas.
4
1
23
Pipe No. Area (cm)2 Velocity (cm/s)
1. 50 10
2. 50 V2
3. 80 5
4. 70 5
The value of V2 is
(a) 2.5 cm/s (b) 5.0 cm/s (c) 7.5 cm/s (d) 10.0 cm/s
24. The normal stress is the same in all directions at a point in a fluid only when.
(a) The fluid is frictional
(b) The fluid is frictionless and incompressible.
(c) The fluid has zero viscosity and is at rest.
(d) One fluid layer has no motion relative to an adjacent layer.
25. The reading of gauge ‘A’ shown in the given fig. is
(a) -31.392 kPa (b) -1.962 kPa (c) 31.392 kPa (d) +1.962 kPa
26. A vertical sludge gate, 2.5m wide and weighing 500 kg is held in position due to horizontal
force of water on one side and associated friction force. When the water level drops down to 2m
above the bottom of the gate, the gate just starts sliding down.
The coefficient of friction between the gate and the supporting structure is.
(a) 0.20 (b) 0.10
(c) 0.05 (d) 0.02
www.ascentgateacademy.com © Copyright : Ascent Gate Academy 23
FLUID MECHANICS
27. A triangular dam of height h and base width b is fitted to its top with water as shown in the given
fig. The condition of stability is.
(a) b = h
(b) b = 2.6h
(c) b = √2h
(d) b = 0.625h
28. The pipe cross-sections and fluid flow rates are shown in the given fig. The velocity in the pipe
labelled as (A) is.
(a) 1.5 m/s (b) 3 m/s (c) 15 m/s (d) 30 m/s
29. Assertion (A): Depth of centre of pressure of any immersed surface is independent of the
density of liquid.
Reason (R) : Centre of area of immersed surface lies below the centre of pressure.
(a) Both A and R are true and R is the correct explanation of A
(b) Both A and R are true but R is not the correct explanation of A
(c) A is true but R is false (d) A is false but R is true.
30. Differential pressure head measured by mercury oil differential manometer (Specific gravity of
oil is 0.9) equivalent to a 600mm difference of mercury levels will nearly be.
(a) 7.62 m of oil (b) 76.2 m of oil (c) 7.34 m of oil (d) 8.47 m of oil
31. A U-tube manometer is connected to a pipeline Atmosphere
conveying water as shown in the given fig.
The pressure head of water in the pipeline is.
(a) 7.12 m water
(b) 6.56 50cm
56cm
(c) 6.0 m water 45cm
(d) 5.12 m Sp. G r.=1.0
Mercury
www.ascentgateacademy.com Sp. G r.= 13.6
© Copyright : Ascent Gate Academy 24
FLUID MECHANICS
32 Assertion (A): If a cube is placed in a liquid with two of its surface parallel tothe free surface of
the liquid, then the pressure on the two surfaces which are parallel tothe free surface, are the
same.
Reason (R) : Pascal’s law states that when a fluid is at rest, the pressure at any plane is the same
in all directions.
(a) Both A and R are individually true and R is the correct explanation of A.
(b) Both A and R true but R is not the correct explanation of A.
(c) A is true but R is false
(d) A is false but R is true.
33. A float of cubical shape has sides of 10cm. The float value just touches the valve seat to have
a flow area of 0.5 cm2 as shown in the given fig. If the pressure of water in the pipeline is 1 bar,
the rise of water level h in the tank to just stop the water flow will be.
(a) 7.5 cm
(b) 5.0 cm
(c) 2.5 cm
(d) 0.5 cm
34. A block of aluminium having mass of 12 kg is suspended by a wire and lowered until
submerged 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
35. 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 (d) 0.5
36. A barge 30m long and 10m wide has a draft of 3m when floating with its sides in vertical
position. If its centre of gravity is 2.5m above the bottom, the nearest value of metacentric
height is .
(a) 3.28 m (b) 2.78 m
(c) 1.78 m (d) 0
37. A cylindrical vessel having its height equal to its diameter is filled with liquid and moved
horizontally at an accelaration 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 (d) 0.75
www.ascentgateacademy.com © Copyright : Ascent Gate Academy 25
FLUID MECHANICS
38. Three immiscible liquids of specific densities ρ, ρ2 , ρ3 are kept in a jar. The height of the
liquids in the jar and at the piezometer fitted to the bottom of the jar are as shown in the given
fig, The ratio H/h is
(a) 4 3h p
(b) 3.5
(c) 3 1.5 h 2p H
(d) 2.5 h 3p
Y = x2
39. A dam is having a curved surface as shown in the fig. 4
y
20 m
→x
The height of the water retained by the dam is 20m, density of water is 1000 kg/m3. Assuming
g as 9.81 m/s2, the horizontal force acting on the dam per unit length is.
(a) 1.962 x 102N (b) 2 x 105N (c) 1.962 x 106N (d) 3.924 x 106N
40. Match List - I and List - II and select the correct answer:
List - I
A. Stable equilibrium of a floating body
B. Stable equilibrium of submerged body
C. Unstable equilibrium of a floating body
D. Unstable equilibrium of a submerged body
List - II
1. Centre of buoyancy below the centre of gravity
2. Metacentre above the centre of gravity
3. Centre of buoyancy above the centre of gravity
4. Metacentre below the centre of gravity.
Codes:
A B CD
(a) 4 3 21
(b) 2 3 41
(c) 4 1 23
(d) 2 1 43
www.ascentgateacademy.com © Copyright : Ascent Gate Academy 26
FLUID MECHANICS
41. The hydraulic means depth (where A = area and P = wetted perimeter) is given by
(a) P/A (b) P2/A (c) A/P (d) √A/P
42. Pressure drop of water flowing through a pipe (density 1000 kg/m3) between two points is
measured by using a vertical U-tube manometer . Manometer uses a liquid with density
2000 kg/m3. The difference height of manometric liquid in the two limbs or the manometer is
observed to be 10 cm. The pressure drop between the two points is:
(a) 98.1 N/m2 (b) 981 N/m2 .
(c) 1962 N/m2 (d) 19620 N/m2.
43. To measure the pressure head of the fluid of specific
gravity S flowing through a pipeline. A simple
micro-manometer containing a fluid of
specific gravity s1,is connected to it. The readings
are as indicated in the diagram. The pressure head
in the pipeline is.
(a) h1 S1 - hS - ∆h (S1- S)
(b) h1 S1 - hS + ∆h (S1- S)
(c) hS - h1 S1 - ∆h (S1- S)
(d) hS - h1 S1 + ∆h (S1- S)
44. consider the following statements about hydrostatic force on a submerged surface:
1. It remains the same even when the surface is turned.
2. It acts vertically even when the surface is turned. Which of these is / are correct?
(a) Only 1 (b) Only 2
(c) Both 1 and 2 (d) Neither 1 nor 2
45. The vertical component of force on a curved surface submerged in a static liquid is equal to the.
(a) Weight of liquid column above the C.G. of the curved surface.
(b) Weight of liquid above the curved surface.
(c) Product of pressure at C.G. multiplied by the area of the curved surface.
(d) Product of pressure at C.G. multiplied by the projected area of the curved surface.
46. The point of application of a horizontal force on curved surface submerged in liquid is.
www.ascentgateacademy.com © Copyright : Ascent Gate Academy 27
FLUID MECHANICS
47. The depth of centre of pressure for rectangular lamina immersed vertically in water up to
height ‘h’is given by.
(a) h/2 (b) h/4 (c) 2h/3 (d) 3h/2
48. Assertion (A) : For a vertically immersed surface, the depth of the centre of pressure is
independent of the density of the liquid.
Reason (R) : Centre of pressure lies above the centre of area of the immersed surface.
(a) Both A and R are true and R is the correct explanation of A
(b) Both A and R are true but R is not the correct explanation of A
(c) A is true but R is false
(d) A is false but R is true.
49. A mercury-water manometer has a gauge difference of 500mm (difference in elevation of
menisci). What will be the difference in pressure?
(a) 0.5 m (b) 6.3 m (c) 6.8 m (d) 7.3 m
50. A circular annular plate bounded by two concentric circles of diameter 1.2m and 0.8 m is
immersed in water with its plane making and angle of 45 wiht the horizontal. The centre of the
circle is 1.625 m below the free surface. What will be the total pressure force on the face of the
plate?
(a) 7.07 kN (b) 10.00 kN (c) 14.14 kN (d) 18.00 kN
51. A plate of rectangular shape having teh dimensions of 0.4 x 0.6 m is immersed in water with its
longer side vertical. the total hydrostatic thrust on one side of the plate is estimated as 18.3 kN.
All other conditions remaining the same, the plate is turned through 90 such that its longer side
remains vertical. What would be the total force on one face of the plate?
(a) 9.15 kN (b) 18.3 kN
(c) 36.6 kN (d) 12.2 kN
52. An open rectangular box of base 2m x 2m contains a liquid of specific gravity 0.80 up to a
height of 2.5m. If the box is imparted a vertically upward acceleration of 4.9 m/s2, what will the
pressure on the base of the tank ?
(a) 9.81 kPa (b) 19.62 kPa (c) 36.80 kPa (d) 29.40 kPa\
53. Match list - I (Measuring Devices) with list - II (Measured Parameter) and select the correct
answer using the codes given below.
List - I List - II
A. Pitot tube - 1. Flow static pressure
B. Micro-manometer - 2. Rate of flow (indirect)
C. Pipe bend meter - 3. Differential pressure
D. Wall pressure tap - 4. Flow stagnation pressure
Codes:
ABCD
(a) 1 3 2 4
(b) 4 3 2 1
(c) 1 2 3 4
(d) 4 2 3 1
www.ascentgateacademy.com © Copyright : Ascent Gate Academy 28
FLUID MECHANICS
54.
The balancing column shown in the above diagram contains 3 liquids of different densities
ρ1,ρ2 and ρ3. The liquid level of one limb is h1 below the top level and there is a diffrence of
h relative to that in the other limb.
What will be the expression of h ?
(a) ρ1 - ρ2 ρ2 - ρ3 (c) ρ1 - ρ3 (d) ρ1 - ρ2
ρ1 - ρ3 h1 (b) ρ1 - ρ3 h1 ρ2 - ρ3 h1 ρ2 - ρ3 h1
55. Which one of the following is the condition for stable equilibrium for a floating body?
(a) The metacenter coincides with the centre of gravity
(b) The metacentre is above the centre of gravity
(c) The metacentre is below the centre of gravity.
(d) The centre of buoyancy is below the centre of gravity.
56. Assertion (A): The buoyant force for a floating body passes through the centroid of the
displaced volume.
Reason (R) : The force of buoyancy is a vertical force & equal to the weight of fluid displaced.
(a) Both A and R are true and R is the correct explanation of A
(b) Both A and R are true but R is not the correct explanation of A
(c) A is true but R is false (d) A is false but R is true.
57. Which one of the following statements is correct? The pressure centre is
(a) The centroid of the pressure prism
(b) A point of the line of action the resultant force.
(c) at the centroid of the submerged area. (d) always above the centroid of the area.
58. A U-tube open at both ends and made of 8mm diameter glass tube has mercury up to a height of
10 cm in both the limbs. If 19cm3 of water is added to one of the limbs, what is the difference
in mercury levels in the two limbs at equilibrium?
(a) 4.5 mm (b) 1.0 cm (c) 2.8 cm (d) 3.2 cm
59. A breaker of water is falling freely under the influence of gravity. Point B is on the surface and
point C is vertically below B near the bottom of the breaker. If PB is the pressure at point B and
PC the pressure of point C, then which one of the following is correct?
(a) PB = PC. (b) PB < PC.
(c) PB > PC.
(d) Insufficient information to determine any of the above.
www.ascentgateacademy.com © Copyright : Ascent Gate Academy 29
FLUID MECHANICS
60. The standard atmospheric pressure is 762mm of Hg. At a specific location, the barometer reads
700mm of Hg. At this place, wha t does at absolute pressure of 380mm of Hg corresponds to?
(a) 320 mm of Hg vaccum (b) 382 mm of Hg vaccum
(c) 62 mm of Hg vaccum (d) 62 mm of Hg gauge
61. A manometer is made of a tube of uniform bore of 0.5cm2 cross-sectional area, with one limb
vertical and the other limb in clined at 30 to the horizontal. Both of its limbs are open to
atmosphere and initially, it is partly filled with a manometer liquid of specific gravity 1.25. if
then and additional volume of 7.5 cm3 of water is poured in the inclined tube, what is the rise
of the meniscus in the vertical tube?
(a) 4 cm (b) 7.5 cm (c) 12 cm (d) 15 cm
62. A homogeneous solid of any arbitrary shape floats upright in a homogeneous liquid with
immersed volume V and is in stable equilibrium. If the solid is overturned and made to float
upside down in a different homogeneous liquid with exactly same volume V above the liquid
surface, then the equilibrium.
(a) Would be stable (b) Would be neutral
(c) Would be unstable (d) May or may no be stable
63. A 25 cm of long prismatic homogenous solid floats in water with its axis vertical and 10 cm
projecting above water surface. If the same solid floats in some oil with vertical and 5 cm
projecting above the liquid surface, what is the specific gravity of the oil?
(a) 0.60 (b) 0.70 (c) 0.75 (d) 0.80
64. A semicircular plane area of diameter 1 m, is subjected to a uniform gas pressure of 420 kN/m.
what is the moment of thrust (approximately) on the are about its straight edge?
(a) 35 kNm (b) 41 kNm (c) 55 kNm (d) 82 kNm
65. A hydrometer weights 0.03 N and has a stem at the upper end which is cylindrical and 3mm in
diameter. It will float deeper in oil of specific gravity 0.75, than in alcohol of sp. gravity 0.8 by
how much amount?
(a) 10.7 mm (b) 43.3 mm (c) 33 mm (d) 36 mm
66. A wooden rectangular block of length of / is made to float in water with its axis vertical. The
centre of gravity of the floating body is 0.15/above the centre of buoyancy what is the specific
gravity of the wooden block?
(a) 0.6 (b) 0.65 (c) 0.7 (d) 0.75
67. If B is the centre of buoyancy, G is the centre of gravity and M is the metacentre of a floating
body, the body will be in stable equilibrium if.
(a) MG = 0 (b) M is below G (c) BG = 0 (d) M is above G
68. The metacentric height of a passenger ship is kept lower than that of a naval or a cargo ship
because .
(a) Apparent weight will increase
(b) Otherwise it will be in neutral equilibrium
(c) It will decreases the frequency of rolling.
(d) Otherwise it will sink and be totally immersed.
www.ascentgateacademy.com © Copyright : Ascent Gate Academy 30
FLUID MECHANICS
69. The pressue difference of two very light gases in two rigid vessels is being measured by a
vertical U-tube water filled manometer. The reading is found to be 10cm. what is the pressure
difference?
(a) 9.81 kPa (b) 0.0981 bar
(c) 98.1 Pa (d) 981 N/m2
70. A circular plate 1.5m diameter is submerged in water with its greatest and least depths below
the surface being 2 m and 0.75m respectively. What is the total pressure (approximately) on the
face of the plate?
(a) 12 kN (b) 16 kN
(c) 24 kN (d) None of the above
71. Whenever a plate is submerged at an angle with the direction of flow of liquid. it is subjected
to some pressure.What is the component of this pressure in the direction of flow of liquid,
known as?
(a) Stagnation pressure (b) Lift
(c) Drag (d) Bulk modulus
72. Resultant pressure of the liquid in case of and immersed body acts through which one of the
following?
(a) Centre of gravity (b) Centre of pressure
(c) Metacentre (d) Centre of buoyancy
73. The lower portion of a U-tube of uniform bore having both limbs vertical and open to
atmosphere, is initially filled with a liquid of specific gravity 3S. A lighter liquid of specific
gravity S is then poured into one of the limbs such that the length of column of lighter liquid is
X. What is the resulting movement of the meniscus of the heavier liquid in the other limb?
(a) X (b) X/2
(c) X/3 (d) X/6
74. What is the vertical component of pressure force on submerged curved surface equal to ?
(a) its horizontal component
(b) The force on a vertical projection of the curved surface.
(c) The product of the pressure at centroid and surface area.
(d) The force of liquid vertically above the curved surface up to the free surface
75. What is buoyant force?
(a) Lateral force acting on a submerged body.
(b) Resultant force acting on a submerged body.
(c) Resultant force due to water on a body.
(d) Resultant hydrostatic force on a body due to fluid surrounding it.
76. How is the metacentric height. GM expressed?
(a) GM = BG - (I/V) (b) GM = (V/I) - BG
(c) GM = (I/V) - BG (d) GM = BG - (V/I)
where, I = Moment of inertia of the plan of the floating body at the water surface. V = Volume
of the body submerged in water
BG = Distance between the centre of gravity (G) and the centre of buoyancy (B).
www.ascentgateacademy.com © Copyright : Ascent Gate Academy 31
FLUID MECHANICS
77. Stability of a floating body cab be improved by which of the following?
1. Making its width large
2. Making the draft small
3. Keeping the centre of mass low
4. Reducing its density
Select the correct answer using the code given below.
(a) 1, 2, 3 and 4 (b) 1, 2 and 3 only (c) 1 and 2 only (d) 3 and 4 only
78. Assertion (A) : The center of pressure for a vertical surface submerged in a liquid lies above
the centroid (centre of gravity) of the vertical suface.
Reason (R) : The distance of the centre of pressure from the free surface of the liquid for a
vertical surface submerged in a liquid is independent of the density of the liquid.
(a) Both A and R are true and R is the correct explanation of A
(b) Both A and R are true but R is not the correct explanation of A
(c) A is true but R is false
(d) A is false but R is true.
79. The distance from the centre of buoyancy to the metacentre is given by I/Vd, where Vd is the
volume of fluid displaced. What does I represent ?
(a) Moment of inertia of a horizontal section of the body taken at the surface of the fluid?
(b) Moment of inertia about its vertical centroidal axis.
(c) Polar moment of inertia.
(d) Moment of inertia about its horizontal centroidal axis.
80. A rectangular plate 0.75 m x 2.4 m is immersed in a liquid of relative density 0.85 with its
0.75m side horizontal and just at the water surface. if the plane of plate makes an angle of 600
with the horizontal, what is the approximate pressure force on one side of the plate ?
(a) 7.80 kN (b) 15.60 kN
(c) 18.00 kN (d) 24.00 kN
81. In an open U-tube containing mercury, kerosene of specific gravity 0.8 is poured into one of its
limbs so that the length of column of kerosene is about 40cm. The level of mercury column in
that limb is lowered approximately by how much?
(a) 2.4 cm (b) 1.2 cm
(c) 3.6 cm (d) 0.6 cm
82. A body weighs 30 N and 15 N when weighed under submerged conditions in liquids of relative
densities 0.8 and 1.2 respectively. What is the volume of the body?
(a) 12.50 l (b) 3.82 l (c) 18.70 l (d) 75.50 l
83. For floating bodies, how is the metacentric radius defined ?
(a) The distance between centre of gravity and the metacentre.
(b) Second moment of area of plane of floatation about centroidal axis perpendicular to plane
of rotation/ immersed volume.
(c) The distance between centre of gravity and the centre of buoyancy.
(d) Moment of inertia of the body about its axis of rotation/immersed volume.
www.ascentgateacademy.com © Copyright : Ascent Gate Academy 32
FLUID MECHANICS
84. What is the difference in pressure head, measured by a mercury -oil differential manometer for
a 20 cm difference of mercury level ? (Sp. gravity of oil = 0.8)
(a) 2.72 m of oil (b) 2.52 m of oil (c) 3.40 m of oil (d) 2.00 m of oil
85. A tank has in its side a very small horizontal cylinder fitted with a frictionless piston. The head
of liquid above the piston is h and the piston area a, the liquid having a specific weight γ .What
is the force that must be exerted on the piston to hold it in position against the hydrostatic
pressure? (b) γha (c) 2γha / 3 (d) γha / 2
(a) 2γha
86. What is the vertical distance of the centre of pressure below the centroid of the plane area ?
(a) IG (b) IG . sin θ IG . sin2 θ (d) IG . sin2 θ
(c)
A. h A. h A. h2
A. h
*****************
“It is a terrible thing to see and have no vision”
FLUID STATICS :
PRACTICE QUESTIONS
1-d, 2-b, 3-b, 4-c, 5-d, 6-c, 7-c, 8-d, 9-c, 10-c, 11-b, 12-d, 13-d, 14-b, 15-b, 16-a, 17-a, 18-d, 19-a, 20-a, 21-d, 22-d,
23-b, 24-d, 25-b, 26-b, 27-d, 28-d, 29-a, 30-d, 31-c, 32-d, 33-b, 34-d, 35-c, 36-c, 37-c, 38-c, 39-c, 40-b, 41-c, 42-b,
43-b, 44-c, 45-b, 46-b, 47-c, 48-c, 49-b, 50-b, 51-b, 52-d, 53-b, 54-c, 55-b, 56-b, 57-b, 58-c, 59-a, 60-a, 61-a, 62-d,
63-c, 64-a, 65-d, 66-c, 67-d, 68-c, 69-d, 70-c, 71-c, 72-b, 73-d, 74-d, 75-d, 76-c, 77-c, 78-d, 79-a, 80-b, 81-b, 82-b,
83-a, 84-c, 85-b, 86-c.
www.ascentgateacademy.com © Copyright : Ascent Gate Academy 33
FLUID MECHANICS
3 FLUID KINEMATICS
CLASS WORK QUESTIONS :
ONE MARK QUESTIONS
1. Existence of velocity potential implies that [GATE-ME-94]
a) Fluid is in continuum b) Fluid is irrotational
c) Fluid is ideal d) Fluid is compressible
2. A streamline and an equipotential line in a flow field [GATE-ME-11]
a) Are parallel to each other b) Are perpendicular to each other
c) Intersect at an acute angle d) Are identical
3. In a two-dimensional velocity field with velocities u and v along x and y directions
respectively, the convenctive acceleration along the x-directions is given by [GATE-ME-06]
a) u ∂u + v ∂u b) u ∂u + v ∂v c) u ∂v + ∂u d) ∂u + u ∂u
∂x ∂y ∂x ∂y ∂x v ∂y v ∂x ∂y
4. The velocity potential function for a source varies with the distance r as [GATE-ME-87]
1 1 c) er d) ln r
a) b)
r r2
5. A two-dimentional flow field has velocities along the x and y directions given by u = x2t and
v = -2xyt respectively, where t is time. The equation of streamlines is [GATE-ME-06]
a) x2y = constant b) xy2 = constant
c) x y = constant d) not possible to determine
→→
6. →
For a continuity equation given ∇.V = 0 to be valid,
V where is the velocity vector, which one
of the following is a necessary condition ? [GATE-ME-08]
a) Steady flow b) Irrotational flow c) Inviscid flow d) Incompressible flow
7. Circulation is defined as line intergral of tangential component of velocity about a __________
(fill in the blank).
[GATE-ME-94]
8. Streamlines, path lines and streak lines are virtually identical for [GATE-ME-94]
a) Uniform flow b) flow of ideal fluids c) Steady flow d) Non uniform flow
9. The velocity components in the x and y directions of a two dimentsional potential flow are
u and v, respectively.
Then ∂v is equal to [GATE-ME-05]
∂x
a) ∂u b) - ∂u c) ∂u d) - ∂v
∂x ∂x ∂y ∂y
www.ascentgateacademy.com © Copyright : Ascent Gate Academy 34
FLUID MECHANICS
10. In a steady flow through a nozzle, the flow velocity on the nozzle axis is given by v = uo
(1 + 3x / L), where x is the distance along the axis of the nozzle from its inlet plane and L is the
length of the nozzle. The time required for a fluid particle on the axis to travel from the inlet to
the exit plane of the nozzle is q [GATE-ME-07]
L L L L
a) uo b) ln 4 c) 4uo d) 2.5 uo
3uo
11. A fluid flow is represented by the velocity field → → ay → , where a constant. The equation
V= ax i + j
of stream line passing through a point (1, 2) is [GATE-ME-04]
a) x - 2y = 0 b) 2x - y = 0 c) 2x - y = 0 d) x + 2y = 0
r
12. For an incompressible flow field, V , which one of the followng conditions must be satisfied ?
(GATE-ME-14)(S-2)
a) b)
c) d)
13. A flow field which has only convective acceleration is (GATE-ME-14)(S-4)
a) a steady uniform flow b) an unsteady uniform flow
c) a steady non-uniform flow d) an unsteady non-uniform flow
14. If the fluid velocity for a potential flow is given by V(x,y) = u(x,y)i + v(x,y)j with usal notations, then the
( ( ) )ψ|∆−δuuvvψδ∆V2.122Vuvtr1xr/.−+cψVV=Vr)rψr20.=V∆2r|0=Vr0= 0
slope of potential line at (x, y) is (GATE-15)(Set-2)
v d)
a) u b)
15. The volumetric flow rate (per unit depth) between two streamlines having stream functions &
is (GATE-16)(Set-2)
a) b) ψ ψ 2 c) d)
1
16. A channel of width 450 mm branches into sub-channels having width 300 mm and 200 mm as shown
in figure. If the volumentric flow rate (taking unit depth) of an incompressible flow through the main
channel is 0.9 m3/s and the velocity in the sub-channel of width 200 mm is 3 m/s, the velocity in the
sub-channel of width 300 mm is ________.
Assume both inlet and oputlet to be at the same elevation.
www.ascentgateacademy.com © Copyright : Ascent Gate Academy 35
FLUID MECHANICS
17. For a certain two-dimensional incompressible flow, velocity field is given by . The
streamlines for this flow are given by the family of curves (GATE-16)(Set-3)
a) x2y2 = constant
b) xy2 = constant
c) 2xy - y2 = constant
d) xy = constant
TWO MARKS QUESTIONS
1. A leaf is caught in a whirlpool. At a given instant, the leaf is at a distance of 120 m from the
centre of the whirlpool. The whirlpool cane be described by the following velocity distribution
60 X 103 300 X 103
Vr = - 2πr m/s and V0 = 2πr m/s.
Where r (in meters) in the distance from the centre of the whirlpool. What will be the distance
of the leaf from the centre when it has moved through half a revolution ? [GATE-ME-05]
a) 48 m b) 64 m c) 120 m d) 142 m
2. Velocity vector of a flow fields is given as → = 2xy^i - x2z^j. The Vorticity vector at (1, 1,1) is
V
[GATE-ME-10]
a) 4 ^i -^j b) 4 ^i -^k c) ^i - 4^j d) ^i - 4^k
3. A Newtonian fluid has the following velocity field : [GATE-ME-88]
2xyiˆ − y2 ˆj
→ = x2 y ^i + 2 xy2z^j - yz3^k
V
The rate shear deformation ε at the point x = -2, y = -1 and z = 2 for the given flow is :
yz
a) -6 b) -2 c) -12 d) 4
4. You are asked to evaluate assorted fluid flows for their suitability in a given laboratory
application. The following three flow choices. Expressed in terms of the two-dimensional
velocity fields in the x - y plane, are made available. [GATE-ME-09]
P : u = 2y, v = - 3 x Q : u = 3xy , v = 0 R : u = -2x , v = 2y
Which flows should be recommended when the application requires the flow to be
incompressible and irrotational ?
a) P and R b) Q c) Q and R d) R
5. The velocity comoponents in the x and y directions are given by u = λxy3 - x2 y, v = xy2 - 3 y4.
4
The value of λ for a possible flow field involving an incompressible fluid is
[GATE-ME-95]
a) - 3 b) - 4 4 d) 3
4 3 c)
3
www.ascentgateacademy.com © Copyright : Ascent Gate Academy 36
FLUID MECHANICS
6. A velocity field is given as → = 3x2 y ^i - 6 xyz^k [GATE-ME-93]
V
Where x, y, z are in m and V m/s. Determine if
i) It represents an incompressible flow
ii) The flow is irrotational
iii) The flow is steady.
Statement for linked Questions (Q 7 & Q 8)
The gap between a moving circular plate and a stationary surface is being continuously
reduced, as the circular plate comes down at a uniform speed V towards the stationary bottom sur-
face, as shown in the figure. In the process, the fluid contained between the two plates flows out
radially. The fluid is assumed to be incompressible and inviscid. [GATE-ME-08]
7. The radial velocity V r, at any radius r, when the gap width is h , is
a) Vr b) V r = V r c) V r = 2Vh d) Vh
Vr = Vr =
2h h r
r
8. The radial component of the fluid acceleration at r = R is
a) 3V2R b) V2R c) V2R d) V2h
4h2 4h2 2h2 4h2
9. For a fluid flow through a divergent pipe of length L having inlet and outlet radii of R1 and R2
respectively and a constant flow rate of Q, assuming the velocity to be axial and uniform at any
cross-section, the acceleration at the exit is [GATE-ME-04]
2Q (R1 - R2) 2Q2 (R1 - R2) 2Q2 (R - R ) 2Q2 (R - R )
a) b) πLR 3 c) 12 d) 21
πLR2
π2LR25 π2LR 5
2 2
10. The stream function in a two dimensional flow field is given by Ψ = x2 - y2
The magnitude of the velocity at point (1, 1) is [GATE-ME-89]
A) 2 B) 2√ 2 C) 4 D) 8
www.ascentgateacademy.com © Copyright : Ascent Gate Academy 37
FLUID MECHANICS
11. Consider steady flow of water in a situation where two pipe lines (pipe 1 and pipe 2) combine
into a single pipe lien (pipe-3) as shown in the figure. The cross-sectional areas of all three
pipelines are constant. The following data is given : [GATE-PI-09]
Pipe number Area (m2) Velocity (m/s)
1 1 1
2 2 2
3 2.5 ?
Assuming the water properties and the velocities to be uniform across the cross section of the
inlets and the outlet , the exit velocity (in m/s) in pipe 3 is
a) 1 b) 1.5 c) 2 d) 2.5
12 Which combination of the following statements about steady incompressible forced vortex
flow is correct ? [GATE-ME-07]
P : Shear stress is zero at all points in the flow.
Q : Vorticity is zero at all pionts in the flow.
R : Velocity is directly propertional to the radius from the centre of the vortex.
S : Total mechanical energy per unit mass is constant in the entire flow field.
a) P and Q b) R and S c) P and R d) P and S
13. A closed cylinder having a radius R and height H is filled with oil of density ρ. If the cylinder is
rotated about its axis at an angular velocity of ω, then thrust at the bottom of the cylinder is
[GATE-ME-04]
a) π R2 ρgH b) π R2 + ρω2R2 c) π R2 (ρω2R2+ ρgH) d) π R2 ρω2R2 + ρgH
4 4
14. The 2 - D flow with, velocity → → →→ is [GATE-ME-01]
V = (x + 2y + 2) i + (4 - y) j
a) Compressible and irrotational
b) Compressible and not irrotational
c) Incompressible and irrotational
d) Incompressible and not irrotational
15. Consider the following statements regarding streamline(s) :
(i) It is a continuous line such that the tangent at any point on it shows the velocity vector at that point
(ii) There is no flow across streamlines
(iii) dx = dy = dz is the differential equation of a streamline, where u, v and w are velocities in
u vw
directions x, y and z respectively.
(iv) In an unsteady fow, the path of a particle is a streamline
Which one of the following combinations of the statements is true ? (GATE-ME-14) (Set-4)
a) (i), (ii), (iv)
b) (ii), (iii), (iv)
c) (i), (iii), (iv)
d) (i), (ii), (iii)
www.ascentgateacademy.com © Copyright : Ascent Gate Academy 38
FLUID MECHANICS
16. Consider a velocity field , where K is a constant. The vorticity , Ωz , is
(GATE-ME-14)(S-4)
a) -K b) K c) -K/2 d) K/2
17. Mathc the following pairs
a) P-IV, Q-I, R-II, S-III
b) P-IV, Q-III, R-I, S-II
c) P-III, Q-I, R-IV,S-II
d) P-III, Q-I, R-II, S-IV
18. The velocity field on an incompressible flow is given by
V = (a1x+a2y+a3z)i + (b1x+b2y+b3z)j + b(c21ixs+_c_Vu2arˆj_yy_+===_cxK_3(z2_x()+.kx2y,i−ˆ+y+2yyixˆ2 k)+ˆ2) y ˆj (GATE-15-Set-1)
where a1 = 2 and c3 = -4. The value of + y2
x2
19. For a two-dimensional fow, the velocity field is , where iˆ and are the
basis vectors in the x-y Cartesian coordinate system. Identify the CORRECT statements from below,
(1) The flow is incompressible (GATE-16-Set-3)
(2) The flow is unsteady
(3) y-component of acceleration,
(4) x-component of acceleration,
ax = −(x + y)
(x2 + y2)2
a) (2) and (3) b) (1) and (3) c) (1) and (2) d) (3) and (4)
FLUID KINAMATICS : CLASS ROOM OBJECTIVE (ANS)
One Mark : 1-b, 2-b, 3-a, 4-a, 5-b, 6-d, 7- closed contour in a fluid in a fluid flow, 8- c, 9-d, 10-b,
11-b, 12-a, 13-c, 14-b, 15-d, 16-1, 17-b
Two Marks : 1-b, 2-d, 3-c, 4-d, 5-d, 6-sol, 7-a, 8-c, 9-c, 10-b, 11-c, 12-b, 13-d, 14-d., 15-d, 16-a,
17-c, 18-2, 19-b
www.ascentgateacademy.com © Copyright : Ascent Gate Academy 39
FLUID MECHANICS
3 FLUID KINEMATICS
PRACTICE QUESTIONS :
Assignment
1 The flow of a liquid at constant rate in a conically tapered pipe is classified as (PSC ‘92’/AEE)
(a) steady, uniform flow (b) steady non uniform flow
(c) unsteady, uniform flow (d) unsteady, non uniform flow
2 Unsteady flow occurs when:
(a) the velocity at a point remains unchanged with time
(b) the flow fluctuates but the average values of flow parameters remain unchanged.
(c) the velocity at a given point varies with time.
(d) th e mass rate of fluid flow increase gradually wiht time.
3 One - dimensional flow is (PSC-92)
(a) steady uniform flow
(b) flow which neglects changes in a transverse direction.
(c) restricted to flow in a straight line
(d) none of these.
4 A three- dimensional flow is one in which:
(a) the flow region has a width, depth and length
(b) the velocity vector is inclined such that it can be resolved into three mutually perpendicular
directions.
(c) the fluid moves in straight paths parallel to the main direction of flow.
(d) the velocity distribution over parallel planes is identical throughout the flow region.
5 A water supply pipeline changes its alignment through a bend. When the flow in the pipeline is
increased by operating a valve, the flow in the bend is classified as :
(a) unsteady, uniform flow (b) unsteady,non uniform flow
(c) steady, uniform flow (d) steady, non-uniform flow
6 A stream line is a line
(a) which is normal to the velocity vector at every point
(b) which represents lines of constant velocity potential
(c) which is normal to the lines of constant stream function
(d) path traced by continously injected tracer at a point
7 A path line is
(a) mean direction of number of particles at the same instant of time.
(b) instantaneous picture of positions of all particles in the flow which passed a given point.
(c) trace made by a single particle over a period of time.
(d) path traced by continously injected tracer at a point.
www.ascentgateacademy.com © Copyright : Ascent Gate Academy 40
FLUID MECHANICS
8 In a flow visualization experiment, a continuous release rked particles is produced from a point
and the resulting line is.
(a) streamline (b) Pathline
(c) streak line (d) potential line
9 Stream lines, streak lines, path lines are all identical in case of
(a) uniform flow (b) non-uniform flow
(c) both (a) & (b) (d) none.
10 The given fig. represents flow of water past a body moving with velocity ‘V’ in a take.
(IES’94’)
(a) and equipotential line B
(b) a path line A ←V
(c) a streakline body
(d) a stream line
11 Match the following:
List - I List - II
A. Stream lines - 1.Tracing of motion of any one fluid particle
B. Streak lines - 2.Tracing of motion of different fluid particles
C. Path lines - 3. Identification of location of number of fluid particles
D. Equipotential lines - 4. Orthogonal to streak lines
- 5. Location of equal piezometric heads.
ABCD
(a) 3 2 1 4
(b) 4 1 2 3
(c) 2 3 1 5
(d) 4 1 3 2
12 In two- dimensional flow the equation of a streamline is given as .
(a) dy/u = dx/v (b) dx/u = dy/v
(c) dx/dt = u, dy/dt = v (d) u/dx = dy/v
13 In a two - dimensional flow u = kx and v = -ky, where k = a constant. The stream lines are
expressed by the equation.
(a) x / y = constant (b) x y = constant
(c) x + y = constant (d) x - y = constant
14 In a two - dimensional flow acceleration component in the X - direction is given by ax =
(a) ( ∂u / ∂t) + u (∂u / ∂x) + v (∂v / ∂y)
(b) u (∂u / ∂x) + v (∂v / ∂y).
(c) ( ∂u / ∂t) + u (∂u / ∂x) + v (∂u / ∂y)
(d) ( ∂u / ∂t) + v (∂u / ∂x) + u (∂v / ∂y)
15 Given the velocity field : V = (6 + 2xy + t2) i - (xy2 + 10 t) j + 25 k. The acceleration of a
particle at (3,0,2) at time t = 1 is ......................... units.
www.ascentgateacademy.com © Copyright : Ascent Gate Academy 41
FLUID MECHANICS
16 Normal acceleration in fluid flow situations exists only when
(a) the streamlines are straight and parallel (b) the flwo is two - dimensional
(c) the steamlines are curved (d) the flow is unsteady
17 The mean velocities at two ends of a stream tube 10cm a part are 2.5 m/s and 3 m/s and.
The convective tangential acceleration . (IES - 93)
(a) zero (b) 0.5 m/s2
(c) 13.75 m/s2
(d) not deteminable
Read the following data for question 18 and 19
A 2.0 m long conical diffuser 20 cm in diameter at the up stream end has 80 cm diameter at the
downstream end. At a certain instant the discharge through the diffuser is observed to be
200 L/s of water and is found to increase uniformly at a rate of 50 L/s per second at section
1.5 m from the upstream end.
18 The local acceleration in m/sec2 is .
(a) 1.5 (b) - 1.5 (c) 0.15 (d) - 015
19 The convective acceleration in m/sec2 is
(a) 0.33 (b) - 0.33
(c) 3.3 (d) - 3.3
Read the following data for question 20 and 21
A pipe 15 cm in a diameter carries an unsteady flow of an in compressible fluid. The pipe
terminates in a nozzle 7.5cm in diameter. The velocity and acceleration in pipe are 2 m/s and
0.5 m/s2
20 The velocity of the jet leaving the nozzle in m/sec is
(a) 2 (b) 4 (c) 6 (d) 8
21 The acceleration of the jet leaving the nozzle in m/sec2 is
(a) 0.5 (b) 1 (c) 1.5 (d) 2.0
22. The continuity equation in fluid mechanics is a mathematical statement embodying the prin
ciple of :
(a) conservation of energy (b) conservation of mass
(c) conservation of momentum (d) none of these
23 The velocity components in the ‘x’ and ‘y’ directions are given by u =λ xy3 - x2y, v = xy2 -
(3/4) y4: the value of ‘λ’ for a possible flow field is. (G-95)
(a) - (3 / 4) (b) - (4 / 3)
(c) (4 / 3) (d) 3
24 Which one of the following can be a set of velocity components of a two- dimensional flow?
(a) u = x + y and v = x2 + y2 (b) u = x + y and v = x - y
(c) u = x y and v = x/y (d) u = x2 + y2 , v = x2 - y2
25 Which of the following sets of velocity components represent physical fluid flow.
(a) U = x2 + z2 + 5; V = y2 + z; W = 3 x2 yz
(b) U = 2x2; V = 2xyz ; W = -4xz - xz2 + 5y2
(c) U = x2 + 2xy; V = 2x2 + 3z2; W = xy2 + 2xz
(d) none of the above.
www.ascentgateacademy.com © Copyright : Ascent Gate Academy 42
FLUID MECHANICS
26 If ‘U’ and ‘V’ are the components of velocity in the ‘x’ and ‘y’ directions of a flow given by
U = ax + by, V = cx + dy then the condition to be satisfied is.
(a) a + c = 0 (b) b + d = 0
(c) a + b + c = 0 (d) a + d = 0
27 The continuity equation for steady incompressible flow is
expressed in vector notation as. (b) 2. q = 0
(a) . q = 0 (d) 2 x q = 0
(c) x q = 0
28 A continuity equation for steady two dimensional compressible flow is
(a) ρ ∂u + ρ ∂v =0 (b) ρ ∂u + ρ ∂v =0
∂x ∂y ∂x ∂y
(c) ∂ (ρu) + ∂ (ρ v) = 0 (d) u ∂ρ + v∂ ρ =0
∂x ∂y ∂x ∂y
29 The relation that must hold for the flow to be irrotational is
(a) (∂u / ∂y) - (∂v / ∂x) = 0 (b) (∂u / ∂x) = (∂v / ∂y).
(c) (∂2u / ∂x2) + (∂2u / ∂y2) = 0 (d) (∂u / ∂y) = - (∂v / ∂x).
30 In a three dimensional motion of a fluid, the component of rotation about the x - axis, wx is.
(a) (1 / 2) (∂w / ∂y - ∂v / ∂z)
(b) (1 / 2) (∂u / ∂z - ∂w / ∂y)
(c) (1 / 2) (∂v / ∂x - ∂u / ∂y)
(b) (1 / 2) (∂v / ∂x - ∂w / ∂y)
31 If wz = component of rotation of a fluid about z - axis, the vorticity along that axis is usually
defined as Ez= (b) 2 wz
(d) {wz dz
(a) (1/2) wz
(c) ∂wz / x
32 Irrotational flow is characterized as the one in which:
(a) the fluid flow along a straight path
(b) the fluid does not rotate as it moves long
(c) the net rotation of fluid particles about their mass centers remains zero.
(d) the streamlines of flow are curved and closely spaced
(e) none of the above
33 The flow of water in a wash hand basin when it is being
emptied through a central opening, is an example of.
(a) free vortex (b) forced vortex
(c) rotational vortex (d) Rankine vortex
34 Which of the following velocity fields represent a possible fluid flow ?
(a) U = x, V = y (b) U = x2 , V = y2
(c) U = xy , V = x2y2 (d) U = x , V = - y
www.ascentgateacademy.com © Copyright : Ascent Gate Academy 43
FLUID MECHANICS
35 If flow conditions satisfy “ Laplace Equation “ then
(a) Flow is rotational
(b) Flow does not satisfy continuity equation
(c) Flow is irrotational but does not satisfy continuity equation
(d) Flow is irrrotational and satisfy continuity equation.
36 If q is the velocity vector in an irrotational flow then.
(a) div q = 0 (b) curi q = 0
(c) q = 0 (d) grad q = 0
37 The velocity components representing the irrotational flow is
(a) u = x + y, v = 2x - y
(b) u = 2x + 3y, v = -2y2 + x
(c) u = x2, v = -2xy
(d) u = -2x , v = 2y
38 A stream function in a two dimensional flow field is given by ψ = x2 - y2.
(a) 2 (b) 2 √2 (c) 4 (d) 8
39 Existence of velocity potential implies that
(a) fluid is in continuum
(b) fluid is irrotational
(c) fluid is ideal
(d) fluid is compressible
40 A velocity potential exists
(a) whenever the real fluid flow exists.
(b) when the flow is real and rotational
(c) when the flow satisfies the conditions of irrotational motion
(d) when the flow satisfies the equations of continuity
41 If a stream function ‘ψ’ exists, it implies that
(a) the function ‘ψ’ represents a possible flow field
(b) the flow is irrotational
(c) the flow is steady incompressible
(d) the potential function also exists.
42 For stream function ψ = 3x2 - y3 , the magnitude of velocity at the point (2,1) is (IES’99’)
(a) 12.37 (b) 12 (c) 13 (d) 13.5
PREVIOUS IES QUESTIONS :
1. The differential form of continuity equation for two dimensional flow of fluid may be written in
the following form in which u and v are velocities in the x and y-direction and is the density.
This is valid for
(a) compressible, steady flow.
(b) compressible, unsteady flow
(c) incompressible, unsteady flow
(d) incompressible, steady flow
www.ascentgateacademy.com © Copyright : Ascent Gate Academy 44
FLUID MECHANICS
2 Given that
u = velocity in the x - direction, v = velocity in the y - direction a two - dimensional flow in
x - y plane is irrotational if
(a) ∂u = ∂v (b) ∂u = ∂u
∂x ∂ ∂x ∂
y ∂v y
∂x ∂v
(c) ∂v = ∂u (d) = ∂
∂x ∂
3 Of the posysible irrotational flow functions given y the incorrrect relation is (where
below,
ψ = stream function and φ = velocity potential)
(a) ψ = xy (b) ψ = A(x2 - y2)
(c) φ = ur cosθ + u / r cos θ (d) φ = (r - 2/r) sinθ .
4 Which one of the following statements is true to two-dimensional flow of ideal fluids?
(a) Potential function exists if stream funciton exists.
(b) Stream function may or may not exist.
(c) Both potential function and stream function must exist for every flow.
(d) stream function will exist but potential function may or may not exist.
5 The curl of a given velocity field ( x V) indicates the rate of
(a) increase or decrease of flow at a point. (b) twisting of the lines of flow.
(c) deformation (d) translation
6 The general form of expression for the continous equation in a Cartesian coordinate system for
incompressible or compressible flow is given by.
(a) ∂u + ∂v ∂w = 0 (b) ∂ (ρu) + ∂ (ρ v) + ∂ (ρ w) =0
∂x ∂ ∂z ∂x ∂y ∂z
+
y (ρu) ∂ (ρ v) ∂ (ρ w)
∂ρ ∂ ∂x ∂y ∂z (ρ w)
(c) ∂t + + + =0 (d) ∂ρ + ∂ (ρu) + ∂ (ρ v) + ∂ ∂z =1
∂t ∂x ∂y
7 In a two - dimensional flow in x - y plane, if , ∂u = ∂ v then the fluid element will undergo
∂ ∂ x
(a) translation only. (by) translation and rotation
(c) translation and deformation (d) rotation and deformation
8 For an irrotational flow, the velocity potential lines and the streamlines are always.
(a) Parallel to each other (b) Coplanar
(c) Orthogonal to each other (d) inclined to the horizontal
9 Irrotational flow occurs when.
(a) flow takes place in a duct of uniform cross- section at constant mass flow rate.
(b) streamlines are curved.
(c) there is no net rotation of the fluid element about its mass centre
(d) fluid element does not undergo any change in size or shape
www.ascentgateacademy.com © Copyright : Ascent Gate Academy 45
FLUID MECHANICS
10 If the stream function is given by ψ = 3xy, then the velocity at a point (2,3) will be.
(a) 7.21 unit (b) 10.82 unit
(c) 18 unit (d) 54 unit
11 The area of 2 m long tapered duct decreases as A = (0.5 - 0.2x) where ‘x’ is the distance in
meters. At a given instant a discharge of 0.5m3/s is flowing in the duct and is found to increase
at a rate of 0.2 m/s. The local acceleration (in m3/s) at x = 0 will be.
(a) 1.4 (b) 1.0 (c) 0.4 (d) 0.667
12 Match list - I (Pipe flow) with list - II (Types of acceleration) and select the answer :
List - I List - II
A Flow at constant rate passing through - 1. Zero accelerationa bend.
B Flow at constant rate passing through - 2. Local and convetiveacceleration.
a straight uniform diameter pipe.
C. Gradually changing flow through a - 3. Convective acceleration
bend
D. Gradually changing flow through - 4. Local acceleration
a straight pipe.
13 A stream function is given by (x2 - y2). The potential function of the flow will be.
(a) 2 xy + f (x) (b) 2xy + constant
(c) 2 (x2 - y2) (d) 2xy + f (y).
14 A right circular cylinder is filled with a liquid upto its top level. it is rotated about its vertical
axis at such a speed that half the liquid spills out, then the pressure at the point of intersection
of the axis and bottom surface is.
(a) same as before rotation. (b) half of the value before rotation.
(c) quarter of the value before rotation. (d) equal to the atmospheric pressure.
15 The convective acceleration of fluid in the x - direction is given by.
(a) u ∂u + v ∂ v + ω ∂ w (b) ∂u + ∂v ∂ω
∂x ∂ ∂ z ∂t ∂t + ∂t
y
(c) u ∂u +u ∂ v +u ∂ (d) u∂u +v ∂v + ω ∂ u
∂x ∂ y ∂ωz ∂x ∂y ∂ z
16 The stream function in a 2-dimensional flow field is given by ψ= xy The potential function is.
(a) (x2 + y2) (b) (x2 - y2)
2 2
(c) xy (d) x2 y + y2 x
17 The critical depth of a rectangular channel of width 4.0m for a discharge fo 12 m3/s is , nearly
(a) 300 mm (b) 30 mm
(c) 0.972 m (d) 0.674 m
www.ascentgateacademy.com © Copyright : Ascent Gate Academy 46
FLUID MECHANICS
18 Assertion (A) : Stream lines are drawn in the flow field such that at a given instant of time they
are perpendicular to the direction of flow at every points in the flow field.
Reason (R) :Equation for a stream line in a two dimensional flow is given by.
Vx dy - Vy dx = 0.
(a) Both A and R are true and R is the correct explanation of A
(b) Both A and R are true but R is not the correct explanation of A
(c) A is true but R is false.
(d) A is false but R is true.
19 The velocity potential of a velocity field is given by φ = x2 - y2+ const. Its stream function will
be given by :
(a) - 2xy + constant (b) + 2xy + constant
(c) - 2 xy + f (x) (d) - 2xy + f (y)
20 A stream line is a line.
(a) which is along path of the particle
(b) which is always parallel to the main direction of flow.
(c) along which there is no flow.
(d) on which tangent drawn at any point gives the direction of velocity.
21 Which one of the following stream functions is a possible irrotational flow field?
(a) ψ = x3y (b) ψ = 2xy
(c) ψ = Ax2y2 (d) ψ = Ax + By2
22 Assertion (A) : Streamlines can cross one another if the fluid has higher velocity.
Reason (R) : At sufficiently high velocity, the Reynolds number is high and at sufficiently high
Reynolds numbers, the structure of the flow is of turbutlent type.
(a) Both A and R are true and R is the correct explanation of A
(b) Both A and R are true but R is not the correct explanation of A
(c) A is true but R is false.
(d) A is false but R is true.
23 The components of velocity in a two dimensional frictionless incompressible flow are
u = t2 + 3y and v = 3t + 3x. What is the approximate resultant total acceleration at the point
(3,2) and t = 2 ?
(a) 5 (b) 49 (c) 59 (d) 54
24 The stream function ψ = x3 - y3 is observed for a two dimensional flow field. what is the
magnitude of the velocity at point(1, -1) ?
(a) 4.24 (b) 2.83 (c) 0 (d) - 2.83
25 Which of the following functions represents the velocity potential in a two-dimensional flow of
an ideal fluid? (b) 4x2 - 3y2
(a) 2x + 3y (d) tan-1 (x/y)
(c) cos (x - y)
Select the correct answer using code given below
(a) 1 and 3 (b) 1 and 4 (c) 2 and 3 (d) 2 and 4
www.ascentgateacademy.com © Copyright : Ascent Gate Academy 47
FLUID MECHANICS
26 If for a flow, a stream function exists and satisfies the Laplace equation, then which one of the
following is the correct
statement?
(a) The continuity equation is satisfied and the flow is irrotational.
(b) The continuity equation is satisfied and the flow is rotational.
(c) The flow is irrotational but does not satisfy the continuity equation.
(d) The flow is rotational
27 For irrotational and incompressible flow, the velocity
potential and stream function are given by and , respectively
Which one of the following sets is correct?
(a) 2 φ = 0, 2ψ = 0 (b) 2 φ ≠ 0, 2ψ = 0
(c) 2 φ = 0, 2ψ ≠ 0 (d) 2 φ ≠ 0, 2ψ ≠ 0.
28 In a two-dimensional incompressible steady flow, the velocity component u = Aex is obtained.
What is the other component v of velocity ? (b) v = Aey
(a) v = Aexy (d) v = - Aeyx = f (y)
(c) v = - Aexy + f (x)
29 For a steady two-dimensional flow, the scalar components of the velocity field are Vx = -2x, Vy
= 2y, Vz = 0. What are the components of acceleration?
(a) ax = 0, ay = 0 (b) ax = 4x, ay = 0
(c) ax = 0, ay = 4y (d) ax = 4x, ay = 4y
30 Consider the following statements regarding a path line in fluid flow:
1 A path line is a line traced by a single particle over a time interval.
2. A path line shows the positions of the same particle at successive time instants.
31. A path line shows the instantaneous positions of a number of particle, passing through a
common point, at some previous time instants.
Which of the statements given above are correct ?
(a) Only 1 and 3 (b) Only 1 and 2
(c) Only 2 and 3 (d) 1 , 2 and 3
32 Which one of the following is the correct statement? Streamline, path line and streak line are
identical when the
(a) flow is steady.
(b) flow is uniform
(c) flow velocities do not change steadily with time
(d) flow is neither steady nor uniform.
∂2φ ∂2φ
33 The relation ∂x2 + ∂ y2 = 0 for an irrotational flow is known as which one of the following?
(a) Navier - Stokes equation. (b) Laplace equation
(c) Reynold’s equation (d) Euler’s equation
www.ascentgateacademy.com © Copyright : Ascent Gate Academy 48
FLUID MECHANICS
34 Which one of the following stream functions ψ is possible irrotational flow field?
(a) ψ = y2- x2 (b) ψ = A sin (xy)
(c) ψ = Ax2y2 (d) ψ = Ax + By2
35 Match list - I (Condition) with List - II (Regulating fact) and select the correct answer using the
code given below the lists .
List - I List - II
A. Existence of stream function - 1. Irrotational of flow
B. Existence of Velocity Potential - 2. Continuity of flow
C. Absence of temporal variations - 3. Uniform flow
D. Constant velocity - 4. Steady flow vector
Codes:
ABCD
(a) 4 3 2 1
(b) 2 1 4 3
(c) 4 1 2 3
(d) 2 3 4 1
36 Which property of mercury is the main reason for its use in barometers?
(a) High density (b) Negligible capillary effect
(c) Very low vapour pressure (d) Low compressibility
37 For steady incompressible flow. If the u-component of velocity is u = Aex. then what is the
v-component of velocity?
(a) A ey (b) A exy
(c) - A exy (d) - A ex
38 A velocity field is given by u = 3xy and v = 3/2 (x2-y2 ). What is the relevant equation of a
streamline?
(a) dx (x2-y2 ) (b) dx xy
= =
dy xy dy (x2-y2 )
(c) dx 2x y (d) dx (x2-y2 )
= (x2-y2 ) =
d y 2x y
dy
39 Two flows are specified as.
(a) u = y, v = - (3/2) x
(b) u = xy2 , v = x2y
Which one of the following can be conducted.
(a) Both flows are rotational.
(b) Both flows are irrotational.
(c) Flow A is rotational while flow B is irrotational.
(d) Flow A is irrotational while flow B is rotational.
www.ascentgateacademy.com © Copyright : Ascent Gate Academy 49
FLUID MECHANICS
40 A steady incompressible flow is given by:
u = 2x2 + y2 and v = - 4 xy
What is the convective acceleration along x - direction at point (1, 2) ?
(a) ax = 6 unit (b) ax = 24 unit
(c) ax = -8 unit (d) ax = -24 unit
41 The stream function in a flow field is given by ψ = 2xy. In the same flow field, what is the
velocity at a point (2, 1)?
(a) 4 unit (b) 5.4 unit
(c) 1.73 unit (d) 4.47 unit
42 Consider the following equations: 2. ∂u + ∂v =0
1. A1 v1 = A2 v2 ∂x ∂
(3. s∫ ρv.dA + c / ct v∫ρdV = 0( y
1∂ c
4. r ∂ r (rvr) + cz (Vz) = 0
Which of the above equations are forms of continuity equations ? (Where u , v are velocities
and V is volume)
(a) 1 only (b) 1 and 2
(c) 2 and 3 (d) 3 and 4
43 Assertion (A) : The local acceleration is zero in a steady motion.
Reason (R) : The convective component arises due to sthe fact that a fluid element experiences
different velocities at different locations.
Codes:
(a) Both A and R are individual true and R is the correct explanation of A
(b) Both A and R are individual true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
**********************
“All our dreams can come true,
if we have the courage to pursue them”
Answer’s Assignement:-
1 - b, 2 - c, 3 - b, 4 - b, 5 - b, 6 - d, 7 - c, 8 - c, 9 - d, 10 - b, 11 - c, 12 - b, 13 - b, 14 - c, 15 - 58.75 ,16
- c, 17 - c, 18 - -,19 - -, 20 - a, 21 - d, 22 - b, 23 - d, 24 - b, 25 - d, 26 - d, 27 - a, 28 - c, 29 - a, 30 - a,
31 - b, 32 - c, 33 - a, 34 - d, 35 - d, 36 - b, 37 - d, 38 - b, 39 - b, 40 - c, 41 - a, 42 - a,
Answer’s Previous IES Questions
1 - d, 2 - c, 3 - d, 4 - d, 5 - c, 6 - c, 7 - a, 8 - c, 9 - c, 10 - b, 11 - c, 12 - a, 13 - b, 14 - d, 15 - d ,16 - b,
17 - c, 18 - d,19 - b, 20 - d, 21 - b, 22 - d, 23 - c, 24 - a, 25 - a, 26 - a, 27 - a, 28 - c, 29 - d, 30 - b, 31
- a, 32 - a, 33 - b, 34 - a, 35 - b, 36 - c, 37 - c, 38 - c, 39 - c, 40 - c, 41 - d, 42 - b, 43 - b.
www.ascentgateacademy.com © Copyright : Ascent Gate Academy 50
The words you are searching are inside this book. To get more targeted content, please make full-text search by clicking here.
FM Objective Pdf
Discover the best professional documents and content resources in AnyFlip Document Base.
Search