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GATE SOLVED PAPER - CEFLUID MECHANICS AND HYDRAULIC MACHINES

YEAR 2013 ONE MARK

Q. 1 For a 2-D flow field, the stream function y is given as y x23 2 2y = -^ h.

The magnitude of discharge occurring between the stream line passing through points (0, 3) and (3, 4) is(A) 6 units (B) 3 units

(C) 1.5 units (D) 2 units

Q. 2 Group I contains dimensionless parameter and Group II contains ratio

Group I Group II

P. Mach number 1. Ratio of inertial force and gravity force.

Q. Reynold number 2. Ratio of fluid velocity and velocity of sound.

R. Weber number 3. Ratio of inertial force and viscous force.

S. Froude number 4. Ratio of inertial force and surface tension force.

Correct match of the dimensionless parameter in Group I with Group II is(A) P-3, Q-2, R-4, S-1 (B) P-3, Q-4, R-2, S-1

(C) P-2, Q-3, R-4, S-1 (D) P-1, Q-3, R-2, S-4

Q. 3 For subcritical flow in an open channel, the control section for gradually varied flow profile is(A) at the downstream end (B) at the upstream end

(C) at both ends (D) at any intermediate section

YEAR 2013 TWO MARKS

Q. 4 A km2 pipe of . m0 2 diameter connects two reservoirs. The difference between the water levels in the reservoir is 8 m. The Darcy Weisbach friction factor of the pipe is 0.04. Accounting for frictional entry and exit losses. The velocity in the pipe in (m/sec) is(A) 0.63 (B) 0.35

(C) 2.52 (D) 1.25

Q. 5 The normal depth in a wide rectangular channel is increased by 10%. The % increase in discharge in the channel is(A) 20.1 (B) 15.4

(C) 10.5 (D) 17.2

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GATE SOLVED PAPER - CE FLUID MECHANICS AND HYDRAULIC MACHINES

YEAR 2012 ONE MARK

Q. 6 If a small concrete cube is submerged deep in still water in such a way that the pressure exerted on all faces of the cube is p , then the maximum shear stress developed inside the cube is(A) 0 (B) /p 2

(C) p (D) p2

Q. 7 A trapezoidal channel is 10.0 m wide at the base and has a side slope of 4 horizontal to 3 vertical. The bed slope is 0.002. The channel is lined with smooth concrete (Manning’s .n 0 012= ).The hydraulic radius (in m) for a depth of flow of 3.0 m is(A) 20.0 (B) 3.5

(C) 3.0 (D) 2.1

Q. 8 A rectangular open channel of width 5.0 m is carrying a discharge of 100 /m s3 . The Froude number of the flow is 0.8. The depth of flow (in m) in the channel is(A) 4 (B) 5

(C) 16 (D) 20

Q. 9 The circular water pipes shown in the sketch are flowing full. The velocity of flow (in m/s) in the branch pipe “R” is

(A) 3 (B) 4

(C) 5 (D)6

YEAR 2011 ONE MARK

Q. 10 For a given discharge, the critical flow depth in an open channel depends on(A) channel geometry only

(B) channel geometry and bed slope

(C) channel geometry, bed slope and roughness

(D) channel geometry, bed slope, roughness and Reynolds number

Q. 11 For a body completely submerged in a fluid, the centre of gravity (G ) and centre of Buoyancy (O ) are known. The body is considered to be in stable equilibrium if(A) O does not coincide with the centre of mass of the displaced fluid

(B) G coincides with the centre of mass of the displaced fluid

(C) O lies below G

(D) O lies above G

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Q. 12 The flow in a horizontal, frictionless rectangular open channel is supercritical. A smooth hump is built on the channel floor. As the height of hump is increased, choked condition is attained. With further increase in the height of the hump, the water surface will(A) rise at a section upstream of the hump

(B) drop at a section upstream of the hump

(C) drop at the hump

(D) rise at the hump

YEAR 2011 TWO MARKS

Q. 13 A single pipe of length 1500 m and diameter 60 cm connects two reservoirs having a difference of 20 m in their water levels. The pipe is to be replaced by two pipes of the same length and equal diameter ‘d ’ to convey 25% more discharge under the same head loss. If the friction factor is assumed to be the same for all the pipes, the value of ‘d ’ is approximately equal to which of the following options ?(A) 37.5 cm (B) 40.0 cm

(C) 45.0 cm (D) 50.0 cm

Q. 14 A spillway discharges flood flow at a rate of 9 /m s3 metre width. If the depth of flow on the horizontal apron at the toe of the spillway is 46 cm, the tail water depth needed to form a hydraulic jump is approximately given by which of the following options ?(A) 2.54 m (B) 4.90 m

(C) 5.77 m (D) 6.23 m

YEAR 2010 ONE MARK

Q. 15 A mild-sloped channel is followed by a steep-sloped channel. The profiles of gradually varied flow in the channel are(A) ,M S3 2 (B) ,M S3 3

(C) ,M S2 1 (D) ,M S2 2

Q. 16 The flow in a rectangular channel is subcritical. If width of the channel is reduced at a certain section, the water surface under no-choke condition will(A) drop at a downstream section

(B) rise at a downstream section

(C) rise at an upstream section

(D) not undergo any change

Q. 17 Match List-I (Devices) with List-II (Uses) and select the answer using the codes given below the lists :

List-I List-II

a. Pitot tube 1. Measuring pressure in a pipe

b. Manometer 2. Measuring velocity of flow in a pipe

c. Venturimeter 3. Measuring air and gas velocity

d. Anemometer 4. Measuring discharge in a pipe

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

YEAR 2010 TWO MARKS

Q. 18 For a rectangular channel section, Match List-I (Geometrical elements) with List-II (Proportions for hydraulicallys efficient section) and select the correct answer using the codes given below the lists :

List-I List-II

a. Top width 1. /y 2e

b. Perimeter 2. ye

c. Hydraulic Radius 3. y2 e

d. Hydraulic Depth 4. y4 e

ye is the flow depth corresponding to hydraulically efficient section.Codes : a b c d(A) 2 4 1 3(B) 3 1 4 2(C) 3 4 1 2(D) 3 4 2 1

Q. 19 The Froude number of flow in a rectangular channel is 0.8. If the depth of flow is 1.5 m, the critical depth is(A) 1.80 m (B) 1.56 m

(C) 1.36 m (D) 1.29 m

YEAR 2009 ONE MARK

Q. 20 Direct step method of computation for gradually varied flow is(A) applicable to non-prismatic channels

(B) applicable to prismatic channels

(C) applicable to both prismatic and non-prismatic channels

(D) not applicable to both prismatic and non-prismatic channels

YEAR 2009 TWO MARKS

Q. 21 Water flows through a 100 mm diameter pipe with a velocity of 0.015 m/sec. If the kinematic viscosity of water is 1.13 10 m sec6 2

#- , the friction factor of the

pipe material is(A) 0.0015

(B) 0.032

(C) 0.037

(D) 0.048

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Q. 22 A rectangular open channel of width 4.5 m is carrying a discharge of 100 m /sec.3 The critical depth of the channel is(A) 7.09 m (B) 17.0 m

(C) 2.16 m (D) 1.31 m

Q. 23 Water ( 9.879 )kN/mw3g = flows with a flow rate of 0.3 m sec3 through a pipe AB

of 10 m length and of uniform cross-section. The end B is above end A and the pipe makes an angle of 30c to the horizontal. For a pressure of 12 N/m2 at the end B, the corresponding pressure at the end A is(A) 12.0 kN/m2 (B) 17.0 kN/m2

(C) 56.4 kN/m2 (D) 61.4 kN/m2

YEAR 2008 ONE MARK

Q. 24 A person standing on the bank of a canal drops a stone on the water surface. He notices that the disturbance on the water surface is not travelling upstream. This is because the flow in the canal is(A) sub-critical (B) super-critical

(C) steady (D) uniform

YEAR 2008 TWO MARKS

Q. 25 The flow of water (mass density 100 kg/m3= and kinematic viscosity 10 m /s6 2= - in a commercial pipe, having equivalent roughness ks as 0.12 mm, yields an average shear stress at the pipe boundary 600 N/m2= . The value of /ks dl (dl being the thickness of laminar sub-layer) for this pipe is(A) 0.25 (B) 0.50

(C) 6.0 (D) 8.0

Q. 26 A river reach of 2.0 km long with maximum flood discharge of 10000m /s3 is to be physically modeled in the laboratory where maximum available discharge is 0.20 m /s3 . For a geometrically similar model based on equally of Froude number, the length of the river reach (m) in the model is(A) 26.4 (B) 25.0

(C) 20.5 (D) 18.0

Common Data For Questions. 27, 28 and 29 :A rectangular channel 6.0 m wide carries a discharge of 16.0 m /s3 under uniform flow condition with normal depth of 1.60 m. Minning’s ‘n’ is 0.015.

Q. 27 The longitudinal slope of the channel is(A) 0.000585 (B) 0.000485

(C) 0.000385 (D) 0.000285

Q. 28 A hump is to be provided on the channel bed. The maximum height of the hump without affecting the upstream flow condition is(A) 0.50 m (B) 0.40 m

(C) 0.30 m (D) 0.20 m

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Q. 29 The channel width is to be contracted. The minimum width to which the channel can be contracted without affecting the upstream flow condition is(A) 3.0 m (B) 3.8 m

(C) 4.1 m (D) 4.5 m

Statement For Linked Answer Q. 30 and 31 :An automobile with projected area 2.6 m2 is running on a road with a speed of 120 km per hour. The mass density and the kinematic viscosity of air are 1.2 kg/m3 and 1.5 10 m /s5 2

#- , respectively. The drag coefficient is 0.30.

Q. 30 The drag force on the automobile is(A) 620 N (B) 600 N

(C) 580 N (D) 520 N

Q. 31 The metric horse power required to overcome the drag force is(A) 33.23 (B) 31.23

(C) 23.23 (D) 20.23

YEAR 2007 ONE MARK

Q. 32 There is a free overfall at the end of a long open channel. For a given flow rate, the critical depth is less than the normal depth. What gradually varied flow profile will occur in the channel for this flow rate ?(A) M1 (B) M2

(C) M3 (D) S1

Q. 33 At two point 1 and 2 in a pipeline the velocities are V and 2V, respectively. Both the points are at the same elevation. The fluid density is r. The flow can be assumed to be incompressible, inviscid, steady and irrotational. The difference in pressures P1 and P2 at point 1 and 2 is(A) 0.5 V 2r (B) 1.5 V 2r(C) 2 V 2r (D) 3 V 2r

YEAR 2007 TWO MARKS

Q. 34 A horizontal water jet with a velocity of 10 m/s and cross sectional area of 10 mm2 strikes a flat plate held normal to the flow direction. The density of water is 1000 kg/m3. The total force on the plate due to the jet is

(A) 100 N (B) 10 N

(C) 1 N (D) 0.1 N

Q. 35 A 1:50 scale model of a spillway is to be tested in the laboratory. The discharge in the prototype is 100 kg/m3. The discharge to be maintained in the model test is(A) 0.057 m /s3 (B) 0.08 m /s3

(C) 0.57 m /s3 (D) 5.7 m /s3

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Q. 36 A triangle open channel has a vertex angle of 90c and carries flow at a critical depth of 0.30 m. The discharge in the channel is(A) 0.08 m /s3 (B) 0.11 m /s3

(C) 0.15 m /s3 (D) 0.2 m /s3

Q. 37 Flow rate of a fluid (density 1000 kg/m3= ) in a small diameter tube is 800 mm /s.3 The length and the diameter of the tube are 2 m and 0.5 mm, respectively. The pressure drop in 2 m length is equal to 2.0 MPa. The viscosity of the fluid is(A) 0.025 Ns/m2

(B) 0.012 Ns/m2

(C) 0.00192 Ns/m2

(D) 0.00102 Ns/m2

Q. 38 The flow rate in the rectangular open channel is 2.0 m /s3 per metre width. The channel bed slope is 0.002. The slope of ht cannel is classified as(A) Critical (B) Horizontal

(C) Mild (D) Steep

Statement For Linked Answer Q. 39 and 40 :A rectangular open channel needs to be designed to carry a flow of 2.0 m /s3 under uniform flow conditions. The Manning’s roughness coefficient is 0.018. The channel should be such that the flow depth is equal to half width, and the Froude number is equal to 0.5.

Q. 39 The bed slope of the channel to be provided is(A) 0.0012 (B) 0.0021

(C) 0.0025 (D) 0.0052

Q. 40 Keeping the width, flow depth and roughness the same, if the bed slope of the above channel is double, the average boundary shear stress under uniform flow conditions is(A) 5.6 N/m2 (B) 10.8 N/m2

(C) 12.3 N/m2 (D) 17.2 N/m2

YEAR 2006 ONE MARK

Q. 41 The necessary and sufficient condition for a surface to be called as a ‘free surface’ is(A) no stress should be acting on it

(B) tensile stress acting on it must be zero

(C) shear stress acting on it must be zero

(D) no print on it should be under any stress

Q. 42 A channel with a mild slope is followed by a horizontal channel and then by a sleep channel. What gradually varied flow profiles will occur ?(A) , ,M H S1 1 1 (B) , ,M H S2 2 2

(C) , ,M H S1 2 3 (D) , ,M H S1 2 2

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Q. 43 Identify the FALSE statement from the following. The specific speed of the pump increases with(A) increase in shaft speed

(B) increase in discharge

(C) decrease in gravitational acceleration

(D) increase in head

YEAR 2006 TWO MARKS

Q. 44 The velocity field for a flow is given by :( ) ( ) ( )V x y z i x y z j x y z k5 6 7 6 5 9 3 2 l= + + + + + + + +v v t t t and the density varies as

( )exp t20r r= - . In order that the mass is conserved, the value of l should be(A) 12- (B) 10-(C) 8- (D) 10

Q. 45 A hydraulic jump occurs in a rectangular, horizontal, frictonless channel. What would be the pre-jump depth if the discharge per unit width is 2 m /s/m3 and the energy loss is 1 m ?(A) 0.2 m (B) 0.3 m

(C) 0.8 m (D) 0.9 m

Q. 46 A very wide rectangular channel is designed to carry a discharge of 5 /m s3 per meter width. The design is based on the Manning’s equation with the roughness coefficient obtained from the grain size using Strickler’s equation and results in a normal depth of 1.0 m. By mistake, however, the engineer used the grain diameter in mm in the Strickler’s equation instead of in meter. What should be the correct normal depth?(A) 0.32 m (B) 0.50 m

(C) 2.00 m (D) 3.20 m

Q. 47 The flow of glycerin (kinematic viscosity 5 10v m /s4 2#= - ) in an open channel

is to be modeled in a laboratory flume using water ( 10v m /s6 2= - ) as the flowing fluid. If both gravity and viscosity are important, what should be the length scale (i.e. ratio of prototype to model dimensions) for maintaining dynamic similarity ?(A) 1 (B) 22

(C) 63 (D) 500

Q. 48 The thickness of the laminar boundary layer on a flat plate at a point A is 2 cm and at a point B, 1 m downstream of A from the leading edge of the plate ?(A) 0.50 m (B) 0.80 m

(C) 1.00 m (D) 1.25 m

Common Data For Questions. 49 and 50 :An upward flow of oil (mass density 800 kg/m3, dynamic viscosity 0.8 kg/m/s) takes place under laminar conditions in an inclined pipe of 0.1 m diameter as shown in the figure. The pressures at sections 1 and 2 are measured as 435p kN/m1

2= and 200p kN/m2

2= .

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Q. 49 The discharge in the pipe as equal to(A) 0.100 m /s3 (B) 0.127 m /s3

(C) 0.144 m /s3 (D) 0.161 m /s3

Q. 50 If the flow is reversed, keeping the same discharge and the pressure at section 1 is maintained as 435 kN/m2, the pressure at section 2 is equal to(A) 488 kN/m2 (B) 549 kN/m2

(C) 586 kN/m2 (D) 614 kN/m2

YEAR 2005 ONE MARK

Q. 51 An inert tracer is injected continuously from a point in an unsteady flow field. The locus of locations of all tracer particles at an instance of time represents(A) Streamline

(B) Pathline

(C) Streamtube

(D) Streakline

Q. 52 The reading of differential manometer of a Venturimeter, placed at 45c to the horizontal is 11 cm. If the Venturimeter is turned to horizontal position, the manometer reading will be

(A) zero (B) 2

11 cm

(C) 11 cm (D) 11 2 cm

Q. 53 A horizontal bed channel is followed by a steep bed channel as shown in the figure. The gradually-varied profiles over the horizontal and sleep beds are

(A) H2 and S2 respectively (B) H2 and S1 respectively

(C) H3 and S2 respectively (D) H3 and S1 respectively

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YEAR 2005 TWO MARKS

Q. 54 A stream function is given by :

Y 2 ( 1)x y x y2 2= + +The flow rate across a line joining points A(3,0) and B(0,2) is(A) 0.4 units (B) 1.1 units

(C) 4 units (D) 5 units

Q. 55 The circulation ' 'G around a circle of radius 2 units for the velocity field u x y2 3= + and v y2=- is(A) 6p- unit

(B) 12p- units

(C) 18p- units

(D) 24p- units

Q. 56 A tank and a deflector are placed on a frictionless trolley. The tank issues water jet (mass density of water 1000 kg/m3= ), which strikes the deflector and turns by 45c. If the velocity of jet leaving the deflector is 4 m/s and discharge is 0.1 m /s3 , the force recorded by the spring will be

(A) 100 N (B) 100 2 N

(C) 200 N (D) 200 2 N

Q. 57 Cross-section of an object (having same section normal to the paper) submerged into a fluid consists of a square of sides 2 m and triangle as shown in the figure. The object is hinged at point P that is one meter below the fluid free surface. If the object is to be kept in the position as shown in the figure, the value of 'X should be

(A) 2 3 (B) 4 3

(C) 4 m (D) 8 m

Q. 58 Critical depth at a section of a rectangular channel is 1.5 m. The specific energy at that section is(A) 0.75 m (B) 1.0 m

(C) 1.5 m (D) 2.25 m

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Q. 59 A partially open sluice gate discharge water into a rectangular channel. The tail water depth in the channel is 3 m and Froude number is /1 2 2 . If a free hydraulic jump is to be formed at downstream of the sluice gate after the vena contract a of the jet coming out from the sluice gate, the sluice gate opening should be (coefficient of contraction .C 0 9c = )(A) 0.3 m (B) 0.4 m

(C) 0.69 m (D) 0.9 m

Q. 60 A triangular irrigation lined canal carries a discharge of 25 m /s3 at bed slope

60001= . If the side slopes of the canal are 1:1 and

Manning’s coefficient is 0.018, the central depth of flow is equal to(A) 2.98 m (B) 3,62 m

(C) 4.91 m (D) 5.61 m

YEAR 2004 ONE MARK

Q. 61 The X component of velocity in a two dimensional incompressible flow is given by .u x1 5= . At the point ( , ) ( , )x y 1 0= , the y component of velocity v 0= . The equation for the y component of velocity is(A) v 0= (B) .v y1 5=(C) .v x1 5=- (D) .v y1 5=-

Q. 62 A frictionless fluid of density r flow through a bent pipe as shown below. If A is the cross sectional area and V is the velocity of flow, the forces exerted on segment 1 - 2 of the pipe in the x and y direction are, respectively,

(A) ;AV 02r (B) ;AV AV22 2r r

(C) ;0 0 (D) ; AV02

1 2r

Q. 63 In the inclined manometer shown in the figure below, the reservoir is large. Its surface may be assumed to remain at a fixed elevation. A is connected to a gas pipeline and the deflection noted on the inclined glass tube is 100 mm Assuming

30cq = and the manometric fluid as oil with specific gravity of 0.86, the pressure at A is

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(A) 43 mm water (vaccum) (B) 43 mm water

(C) 86 mm water (D) 100 mm water

Q. 64 For a pipe of radius, ,r flowing half full under the action of gravity, the hydraulic depth is

(A) r (B) r4p

(C) r2 (D) . r0 379

Q. 65 A wide channel is 1 m deep and has a velocity of flow, V , as 2.13 m/s. If a disturbance is caused, an elementary wave can travel upstream with a velocity of(A) 1.00 m/s

(B) 2.13 m/s

(C) 3.13 m/s

(D) 5.26 m/s

Q. 66 An aircraft is flying in level flight at a speed of 200 km/hr through air (density, . /kg m1 2 3r = , and viscosity 1.6 10 Ns/m5 2

#m = - ). The lift coefficient at this speed is 0.4 and the drag coefficient is 0.0065. The mass of the aircraft is 800 kg. The effective lift area of the aircraft is(A) 21.2 m2 (B) 10.6 m2

(C) 2.2 m2 (D) 1.1 m2

YEAR 2004 TWO MARKS

Q. 67 A velocity field is given as V yi xj2 3= +r t t where x and y are in metres. The acceleration of a fluid particle at ( , ) ( , )x y 1 1= in the x direction is(A) 0 (B) 5.00 m/s2

(C) 6.00 m/s2 (D) 8.48 m/s2

Q. 68 The velocity in m/s at a point in a two-dimensional flow is given as V yi xj2 3= +r t t

. The equation of the stream the passing through the point is(A) dx dy3 2 0- = (B) x y2 3 0+ =(C) dx dy3 2 0+ = (D) xy 6=

Q. 69 A fire protection system is supplied from a water tower with a bent pipe as shown in the figure. The pipe friction f is 0.03. Ignoring all minor losses, the maximum discharge, Q, in the pipe is

(A) 31.7 lit/sec (B) 24.0 lit/sec

(C) 15.9 lit/sec (D) 12.0 lit/sec

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Q. 70 A steady flow occurs in an open channel with lateral inflow of qm s3 per unit width as shown in the figure. The mass conservation equation is

(A) xq 0

22 = (B)

xQ 0

22 =

(C) xQ q 0

22 - = (D)

xQ q 0

22 + =

Q. 71 A steep wide rectangular channel takes off from a reservoir having an elevation of 101.2 m. At the entrance, the bottom elevation of the channel is 100 m. If the slope of the channel is increased by 4%, the discharge per unit length in the channel will be(A) 2.24 m /s2

(B) higher than 2.24 m /s2 by 4%

(C) higher than 2.24 m /s2 by 2%

(D) choked

Q. 72 The height of a hydraulic jump in the stilling pool of 1 : 25 scale model was observed to be 10 cm. The corresponding prototype height of the jump is(A) not determinable from the data given

(B) 2.5 m

(C) 0.5 m

(D) 0.1 m

Q. 73 A thin flat plate 0.5 m 0.7 m# in size settles in a large tank of water with a

terminal velocity of 0.12 m/s. The coefficients of drag .CR

1 328D

L

= for a laminar

boundary and ( )

.CR0 072

/DL

1 5= for a turbulent boundary layer, where RL is the plate Reynolds number. Assume 10 Ns/m3 2m = - and 1000 kg/m3r =

The submerged weight of the plate is(A) 0.115 N

(B) 0.0118 N

(C) 0.0231 N

(D) 0.0376 N

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Q. 74 The allowable Net Positive Sustion Head (NPSH) for a pump provided by the manufacturer for a flow of 0.05 m /s3 is 3.3 m. The temperature of water is 30 Cc (vapour pressure head absolute 0.44 m= ), atmosphere pressure is 200 kPa absolute and the heat loss from the reservoir to pump 0.3 Nm/N. The maximum height of the pump above the sustion reservoir is(A) 10.19 m (B) 6.89 m

(C) 6.15 m (D) 2.86 m

Common Data For Questions. 75 and 76 The laminar flow takes place between closely spaced parallel plates as shown in

figure below. The velocity profile is given by u Vhy= . The gap height, h , is 5 mm

and the space is filled with oil (specific gravity=0.86, viscosity 2 10 Ns/m4 2#m = -

). The bottom plate is stationery and the top plate moves with a steady velocity of 5V cm/s= . The area of the plate is 0.25 m2

Q. 75 The ratio of rotation of a fluid particle is given by

(A) ; hy0 2y 2w w= =- (B) ; h

y0y zw w= =-

(C) ;hy

hy

y zw w= = (D) ;hy 0y 2w w= =

Q. 76 The power required to keep the plate in steady motion is(A) 5 10 4

#- watts (B) 10 5- watts

(C) .2 5 10 5#

- watts (D) 5 10 5#

- watts

YEAR 2003 ONE MARK

Q. 77 For a two-dimensional irrotational flow, the velocity potential defined as ( )log x ye

2 2f = + . Which of the following is a possible stream function, y for this flow ?

(A) ( / )tan y x21 1-

(B) ( / )tan y x1-

(C) ( / )tan y x2 1- (D) ( / )tan x y2 1-

Q. 78 A flat plate is kept in an infinite fluid medium. The fluid has a uniform free-stream velocity parallel to the plate, peak the correct matching List-I and List-II List-Ia. Boundary layer thickness

b. Shear stress at the plate

c. Pressure gradient along the plate

List-II

1. Decreases in the flow direction

2. Increases in the flow direction

3. Remains unchanged

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Codes :

a b c(A) 1 2 3(B) 2 2 2(C) 1 1 2(D) 2 1 3

Q. 79 A laboratory model of a river is built to a geometric scale of 1:100. The fluid used in the model oil of mass density 900 kg/m3. The highest flood in the river is 10,000 m /s3 . The corresponding discharge in the model shall be(A) 0.095 m /s3 (B) 0.100 m /s3

(C) 0.105 m /s3 (D) 10.5 m /s3

YEAR 2003 TWO MARKS

Q. 80 A horizontal jet strikes a frictionless vertical plate (the plan view is shown in the figure). It is then divided into two parts, as shown in the figure. If the impact loss is neglected, what is the value of q ?

(A) 15c (B) 30c

(C) 45c (D) 60c

Q. 81 Two pipelines, one carrying oil (mass density 900 kg/m3) and the other water, are connected to a manometer as shown in figure. By what amount the pressure in the water pipe should be increased so that the mercury levels in both the limbs of the manometer become equal ? (mass density of mercury 13550 kg/m3= and

9.81g m/s2= )

(A) 24.7 kPa (B) 26.5 kPa

(C) 26.7 kPa (D) 28.9 kPa

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Q. 82 A solid sphere (diameter 6 mm) is rising through oil (mass density 900 kg/m3, dynamic viscosity 0.7 kg/ms) at a constant velocity of 1 cm/s. What is the specific weight of the material form which the sphere is made ? (Take 9.81g m/s2= )(A) 4.3 kN/m3 (B) 5.3 kN/m3

(C) 8.7 kN/m3 (D) 12.3 kN/m3

Q. 83 A hydraulic jump takes place in a triangular channel of vertex angle 90c, as shown in figure. The discharge is 1 m /s3 and the pre-jump depth is 0.5 m. What will be the post-jump depth ? (Take 981g m/s2= )

(A) 0.57 m

(B) 0.91 m

(C) 1.02 m

(D) 1.57 m

Common Data For Questions. 84 and 85 :A pipeline (diameter 0.3 m, length 3 km) carries water form point P to point R (see figure). The piezometric heads at P and R are to be maintained at 100 m and 80 m, respectively. To increase the discharge, a second pipe is added in parallel to the existing pipe form Q and R. The length of the additional pipe is also 2 km. Assume the friction factor, .f 0 04= for all pipes and ignore minor losses.

Q. 84 What is the increase in discharge if the additional pipe has same diameter (0.3 m) ?(A) 0% (B) 33%

(C) 41% (D) 67%

Q. 85 If there is no restriction on the diameter of the additional pipe, what would be the maximum increase in discharge theoretically possible from this arrangement ?(A) 0% (B) 50%

(C) 67% (D) 73%

Common Data For Questions. 86 and 87 :A very wide rectangular channel carries a discharge of 8 m /s3 per m width. The channel has a bed slope of 0.004 and Manning’s roughness coefficient, .n 0 015= . At a certain section of the channel, the flow depth is 1 m.

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Q. 86 What Gradually Varied Flow profile exists at this section ?(A) M2 (B) M3

(C) S2 (D) S3

Q. 87 At what distance from this section the flow depth will be 0.9 m ?(use the direct step method employing a single step.)(A) 65 m downstream (B) 50 m downstream

(C) 50 m upstream (D) 65 m upstream

YEAR 2002 ONE MARK

Q. 88 The force ‘F ’ required at equilibrium on the semi-cylindrical gate shown below is

(A) 9.81 kN (B) 0.0 kN

(C) 19.62 kN (D) None of these

Q. 89 Velocity distribution in a boundary layer flow over a plate is given by

/u um^ h .1 5 h =where, /yh d= ; y is the distance measured normal to the plate; d is the boundary layer thickness; and um is the maximum velocity at y d = . If the shear stress t , acting on the plate is given by

t . /K umm d= ^ h

Where, m is the dynamic viscosity of the fluid, K takes the value of(A) 0 (B) 1

(C) 1.5 (D) None of these

YEAR 2002 TWO MARKS

Q. 90 A pump can lift water at a discharge of . /m s0 15 3 to a head of m25 . the critical cavitation number cs ^ h for the pump is found to be 0.144. The pump is to be installed at a location where the barometric pressure is . m9 8 of water and the vapour pressure of water is . m0 30 of water. The intake pipe friction loss is . .m0 40 Using the minimum value of NPSH (Net Positive Suction Head), the

maximum allowable elevation above the sump water surface at which the pump can be located is(A) . m9 80

(B) . m6 20

(C) . m5 50

(D) None of these

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Q. 91 In a lined rectangular canal, the Froude number of incoming flow is 3.0. A hydraulic jump forms when it meets the pool of water. The depth of flow after the jump formation is . m1 51 . Froude number of flow after the hydraulic jump is(A) 0.30 (B) 0.71

(C) 0.41 (D) None of these

YEAR 2001 ONE MARK

Q. 92 In the Bernoulli’s equation, used in pipe flow, each term represents(A) Energy per unit weight (B) Energy per unit mass

(C) Energy per unit volume (D) Energy per unit flow length

YEAR 2001 TWO MARKS

Q. 93 A cm15 length of steel rod with relative density of 7.4 is submerged in a two layer fluid. the bottom layer is mercury and the top layer is water. The height of top surface of the rod above the liquid interface in ‘cm’ is(A) 8.24 (B) 7.82

(C) 7.64 (D) 7.38

Q. 94 In a 1/50 model of a spillway, the discharge was measured to be . / secm0 3 3 . The corresponding prototype discharge in / secm3 is(A) 2.0 (B) 15.0

(C) 106.0 (D) 5303.0

Q. 95 A trapezoidal channel with bottom width of m3 and side slope of 1 V : 1.5 H carries a discharge of . / secm8 0 3 with the flow depth of . m1 5 . The Froude Number of the flow is(A) 0.066 (B) 0.132

(C) 0.265 (D) 0.528

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ANSWER KEY

FLUID MECHANICS AND HYDRAULIC MACHINES

1 2 3 4 5 6 7 8 9 10

(B) (C) (A) (A) (D) (A) (D) (A) (B) (A)

11 12 13 14 15 16 17 18 19 20

(D) (B) (D) (C) (D) (A) (C) (C) (D) (B)

21 22 23 24 25 26 27 28 29 30

(D) (B) (D) (A) (D) (A) (A) (B) (C) (D)

31 32 33 34 35 36 37 38 39 40

(C) (B) (B) (C) (A) (B) (C) (D) (B) (D)

41 42 43 44 45 46 47 48 49 50

(C) (D) (D) (C) (B) (B) (C) (B) (B) (D)

51 52 53 54 55 56 57 58 59 60

(D) (C) (A) (C) (B) (D) (A) (D) (C) (D)

61 62 63 64 65 66 67 68 69 70

(D) (C) (B) (B) (D) (B) (D) (A) (B) (C)

71 72 73 74 75 76 77 78 79 80

(C) (B) (C) (C) (A) (C) (C) (D) (B) (B)

81 82 83 84 85 86 87 88 89 90

(A) (A) (C) (C) (D) (D) (C) (A) (B) (A)

91 92 93 94 95

(C) (A) (D) (D) (*)

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FLUID MECHANICS AND HYDRAULIC MACHINES - … chapter wise solved papers/ce/Fluid... · GATE SOLVED...

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Transcript of FLUID MECHANICS AND HYDRAULIC MACHINES - … chapter wise solved papers/ce/Fluid... · GATE SOLVED...