GATE-CH Previous Years Solved Paper
Fluid Mechanics and Mechanical Operations www.gatescore.in
GATE Previous Year Papers Solved by Team GATESCORE GATE SOLVED PAPER - CH FluidMechanicsandMechanicalOperations Year 2011 Q. 1
One Mark
Consider the following two cases of movement of particles. In case I, the particle moves along the positive Y -direction and in case II, the particle moves along the negative Y -direction. Which one of the following options corresponds to the correct directions of buoyancy acting on the particles?
(A) Positive Y -direction for both the case (B) Negative Y -direction for case I, positive Y -direction for case II (C) Negative Y -direction for both the cases (D) Positive Y -direction for case I, negative Y -direction for case II Q. 2
Match the pumps in Group I with the corresponding fluids in Group II. Group I
Group II
P. Gear pump
I.
Highly viscous liquid
Q. Peristaltic pump
II. Aqueous sterile liquid III. Slurry
(A) P-III, Q-I (B) P-II, Q-I (C) P-III, Q-II (D) P-I, Q-II Q. 3
In an orifice meter, if the pressure drop across the orifice is over estimated by 5%, then the percentage error in the measured flow rate is (A) +2.47 (B) 5 (C) –2.47 (D) –5
Year 2011 Q. 4
Two Marks
Two liquids (P and Q ) having same viscosity are flowing through a double pipe heat exchanger as shown in the schematic below.
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GATE Previous Year Papers Solved by Team GATESCORE GATE SOLVED PAPER - CH FluidMechanicsandMechanicalOperations
Densities of P and Q are 1000 kg/m3 and 800 kg/m3 respectively. The average velocities of the liquids P and Q are 1 m/s and 2.5 m/s respectively. The inner diameters of the pipes are 0.31 m and 0.1 m . Both pipes are 5 mm thick. The ratio of the Reynolds numbers Re p to ReQ is (A) 2.5 (B) 1.55 (C) 1 (D) 4 Q. 5
The particle size distributions of the feed and collected solids (sampled for same duration) for a gas cyclone are given below. Size range ^µm h
Weight of feed in the size range ^g h
Weight of collected solids in the size range ^g h
5-10
3.0
0.7
10-15
5.0
3.6
15-20
6.0
5.5
20-25
3.0
2.9
1-5
2.0
0.1
25-30 1.0 1.0 What is the collection efficiency (in percentage) of the gas cyclone? (A) 31 (B) 60 (C) 65 (D) 69 Q. 6
A liquid is flowing through the following piping network. The lengths of pipe sections P , Q , R and S shown in the schematic are equal. the diameters of the sections P and R are equal and the diameter of the section Q is twice that of S . The flow is steady and laminar. Neglecting curvature and entrance effects, the ratio of the volumetric flow rate in the pipe section Q to that in S is
(A) 16 (C) 2
Common
Data For
(B) 8 (D) 1
Questions 7 and 8 :
For a liquid flowing through a packed bed, the pressure drop per unit length of the bed ∆p is L
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GATE Previous Year Papers Solved by Team GATESCORE GATE SOLVED PAPER - CH FluidMechanicsandMechanicalOperations
2 150 µ f v 0 ^1 − εh 1.75 ρ f v 20 ^1 − εh ∆p = . + L ε3 φ S d p ε3 ^φ S d p h2
where, v 0 is the superficial liquid velocity, ε is the bed porosity, d p is average particle size, φ S is particle sphericity, ρ f is liquid density and µ f is liquid viscosity. Given, d p = 1 # 10−3 m , φ S = 0.8 , ρ f = 1000 kg/m3 , µ f = 1 # 10−3 kg/m -s Particle density ρ p = 2500 kg/m3 and acceleration due to gravity g = 9.8 m/s2 . Q. 7
When v 0 is 0.005 m/s and ε = 0.5 , which one of the following is the correct value for the ratio of the viscous loss to the kinetic energy loss? (A) 0.09 (B) 1.07 (C) 10.71 (D) 93
Q. 8
On further increasing v 0 , incipient fluidisation is achieved. Assuming that the porosity of the bed remains unaltered, the pressure drop per unit length (in Pa/m) under incipient fluidisation condition is (A) 3675 (B) 7350 (C) 14700 (D) 73501 Year 2010
Q. 9
The critical speed (revolution per unit time) of a ball moll of radius R, which uses balls of radius r is g (A) 1 2π Rr
(C) 1 2π
g R g r
(D) 1 2π
g R-r
(B) 1 2π
Q. 10
One Mark
The stream function in a xy -plane is given below ψ = 12 x2 y3 . The velocity vector for this stream function is (A) xy3 it - 32 x2 y2 tj (B) 32 x2 y2 it - xy3 tj (C) 32 x2 y2 it + xy3 tj (D) xy3 it + 32 x2 y2 tj
Q. 11
The height of a fluidized bed at incipient fluidization is 0.075 m and the corresponding voidage is 0.38. If the voidage of the bed increases to 0.5, then the height of the bed would be (A) 0.058 m (B) 0.061 m (C) 0.075 m (D) 0.093 m
Q. 12
A storage vessel exposed to atmosphere (absolute pressure = 10.3 m of water) has a diameter of 3 m and is initially filled with water to a height of 2 m . The pump draws water from the vessel and is located at an elevation of 5 m above the bottom of the vessel. The frictional head loss in the suction pipe is 2 m of
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GATE Previous Year Papers Solved by Team GATESCORE GATE SOLVED PAPER - CH FluidMechanicsandMechanicalOperations water. If the vapour pressure of the liquid at the temperature of operation is 3 m of water, then the available NPSH is
(A) 2.3 m (B) 5.3 m (C) 6.3 m (D) 8.3 m Q. 13
In Hagen-Poiseuille flow through a cylindrical tube, the radial profile of shear stress is (A) constant (B) cubic (C) parabolic (D) linear Year 2010
Q. 14
Two Marks
A hydrometer with stem cross-sectional area of 2.82 # 10-5 m2 is immersed in a very large vessel containing water as shown in the figure. The immersed volume is 15 # 10-6 m3 and the length of the stem about water surface is Lw . If the entire volume of water is replaced by a liquid with specific gravity 1.5 and if the length of the stem above the liquid surface is Lv then the difference, Ll - Lw is
(A) - 177 mm (B) 177 mm (C) - 266 mm (D) 266 mm Q. 15
The diameter of a drop of liquid fuel changes with time due to combustion t according to the relationship, D = D 0 b1 − tb l while burning, the drop falls at its terminal velocity under Stokes flow regime. The distance it will travel before complete combustion is given by D 2 ∆ρtb g D 02 ∆ρtb g (B) (A) 0 18µ 36µ (C)
D 02 ∆ρtb g D 02 ∆ρtb g (D) 108µ 54µ
Year 2009 Q. 16
One Mark
Under fully turbulent flow conditions, the frictional pressure drop across a packed
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GATE Previous Year Papers Solved by Team GATESCORE GATE SOLVED PAPER - CH FluidMechanicsandMechanicalOperations bed varies with the superficial velocity ^v h of the fluid as (A) v-1 (B) v 3/2 (C) v (D) v2 Q. 17
For a mixing tank operating in the laminar regime, the power number varies with the Reynolds number ^Reh as (A) Re-1/2 (B) Re1/2 (C) Re (D) Re-1
Year 2009 Q. 18
Two Marks
Two identical reservoirs, open at the top are drained through pipes attached to the bottom of the tanks as shown below. The two drain pipes are of the same length but of different diameters ^D1 > D2h.
Assuming the flow to be steady and laminar in both drain pipes, if the volumetric flow rate in the larger pipe is 16 times of that in the smaller pipe, the ratio D1 /D2 is (A) 2 (B) 4 (C) 8 (D) 16 Q. 19
The terminal settling velocity of a 6 mm diameter glass sphere (density = 2500 kg/m3 ) in a viscous Newtonian liquid (density = 1500 kg/m3 ) is 100 µm/s . If the particle Reynolds number is small and the value of acceleration due to gravity is 9.81 m/s2 , then the viscosity of the liquid (in Pa-s) is (A) 100 (B) 196.2 (C) 245.3 (D) 490.5
Statement For Linked
Answer
Q 20 and 21 :
A free jet of water is emerging from a nozzle (diameter 75 mm ) attached to a pipe
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GATE Previous Year Papers Solved by Team GATESCORE GATE SOLVED PAPER - CH FluidMechanicsandMechanicalOperations (diameter 225 mm ) as shown below
The velocity of water at point A is 18 m/s . Neglect friction in the pipe and nozzle. Use = 9.81 m/s2 and density of water = 1000 kg/m3 . Q. 20
The velocity of water at the tip of the nozzle (in m/s) is (A) 13.4 (B) 18.0 (C) 23.2 (D) 27.1
Q. 21
The gauge pressure (in kPa) at point B is (A) 80.0 (B) 100.0 (C) 239.3 (D) 367.6 Year 2008
Q. 22
One Mark
Three containers are filled with water up to the same height as shown. The pressures at the bottom of the containers are denoted as p1 , p2 and p 3 . Which one of the following relationships is true?
(A) p 3 > p1 > p2 (B) p2 > p1 > p 3 (C) p1 > p2 = p 3 (D) p1 = p2 = p 3 Q. 23
Losses for flow through valves and fittings are expressed in terms of (A) drag coefficient (B) equivalent length of a straight pipe (C) shape factor (D) roughness factor
Q. 24
Given a pipe of diameter D , the entrance length necessary; to achieve fully developed laminar flow is proportional to (N Re is Reynolds number).
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GATE Previous Year Papers Solved by Team GATESCORE GATE SOLVED PAPER - CH FluidMechanicsandMechanicalOperations D (A) DN Re (B) N Re D 2 (C) DN Re (D) 2 N Re Q. 25
Q. 26
For laminar flow conditions, the relationship between the pressure drop ^∆pc h across an incompressible filter cake and the specific surface area ^So h of the particles being filtered is given by which one of the following? (A) ∆pc is proportional to So (B) ∆pc is proportional to 1/So 2 (C) ∆pc is proportional to S o (D) ∆pc is proportional to 1/S o2 The power required for size reduction in crushing is 1 (A) proportional to surface energy of the material 1 (B) proportional to surface energy of the material (C) proportional to surface energy of the material (D) independent of the surface energy of the material Year 2008
Two Marks
Q. 27
A pump draws oil (specific gravity 0.8) from a storage tank and discharges it into an overhead tank. The mechanical energy delivered by the pump to the fluid is 50 J/kg . The velocities at the suction and the discharge points of the pump are 1 m/s and 7 m/s , respectively. Neglecting friction losses and assuming kinetic energy correction factor to be unity, the pressure developed by the pump (in kN/m2 ) is (A) 19.2 (B) 20.8 (C) 40 (D) 80
Q. 28
Match the following Group I with Group II and select the correct answer using the codes given below the lists. Group I P. Euler number
1. Viscous force/Inertial force
Q. Froude number
2. Pressure force/Inertial force
R. Weber number
3. Inertial force/Gravitational force
(A) P-1, Q-2, R-3 (C) P-3, Q-2, R-1 Q. 29
Group II
4. Inertial force/Surface tension force (B) P-2, Q-3, R-4 (D) P-4, Q-3, R-2
A steady flow field of an incompressible fluid is given by Vv = ^Ax + By h it − Ay tj , where A = 1 s−1 , B = 1 s−1 , and x , y are in metre. The magnitude of the acceleration (in m/s2 ) of a fluid particle at (1, 2) is (A) 1 (B) 2 (C) 5 (D) 10
Q. 30
Two identically sized spherical particles A and B having densities ρ A and ρ B , respectively; are settling in a fluid of density ρ . Assuming free settling under turbulent flow conditions, the ratio of the terminal settling velocities of particle
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GATE Previous Year Papers Solved by Team GATESCORE GATE SOLVED PAPER - CH FluidMechanicsandMechanicalOperations A to that of particle B is given by ^r B - rh ^r A - rh (A) (B) ^r B - rh ^r A - rh (C) Q. 31
^r A - rh ^r B - rh (D) ^r B - rh ^r A - rh
Consider the scale-up of a cylindrical baffled vessel configured to have the standard geometry (i.e., height = diameter). In order to maintain an equal rate of mass transfer under turbulent conditions for a Newtonian fluid, the ratio of the agitator speeds should be (Given N1 , D1 are agitator speed and vessel diameter before scale-up; N2 , D2 agitator speed and vessel diameter after scale-up) N1 = D 2 (A) N1 = D1 (B) N2 D2 N 2 D1 2
2
3 N1 = D 2 3 (C) N1 = c D1 m (D) N2 D2 N 2 c D1 m
Statement For Linked
Answer
Q 32 and 33 :
A siphon tube having a diameter of 2 cm draws water from a large open reservoir and discharges into the open atmosphere as shown in the figure. Assume incompressible fluid and neglect frictional losses. ^g = 9.8 m/s2h
Q. 32
MThe velocity (in m/s) at the discharge point is (A) 9.9 (B) 11.7 (C) 98 (D) 136.9
Q. 33
The volumetric flow rate (in L/s) of water at the discharge is (A) 3.11 (B) 3.67 (C) 30.77 (D) 42.99
Year 2007 Q. 34
One Mark
Consider a soap film bubble of diameter D . If the external pressure is p 0 and the surface tension of the soap film is σ , the expression for the pressure inside the
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GATE Previous Year Papers Solved by Team GATESCORE GATE SOLVED PAPER - CH FluidMechanicsandMechanicalOperations bubble is
(A) p 0 (B) p 0 + 2σ D (C) p 0 + 4σ (D) p 0 + 8σ D D Q. 35
In Tyler series, the ratio of the aperture size of a screen to that of the next smaller screen is (A) 1 (B) 2 2 (C) 1.5 (D) 2
Q. 36
Size reduction of coarse hard solids using a crusher is accomplished by (A) attrition (B) compression (C) cutting (D) impact
Q. 37
In constant pressure filtration, the rate of filtration follows the relation (V = filtrate volume, t = time, k and C = constants). dV = 1 (A) dV = kV + C (B) dt dt kV + C dV = kV 2 (C) dV = kV (D) dt dt
Q. 38
sticky materials are transported by (A) apron conveyor (C) belt conveyor
(B) screw conveyor (D) hydraulic conveyor
Year 2007 Q. 39
A pipeline system carries crude oil of density 800 kg/m3 . The volumetric flow rate at point 1 is 0.28 m3 /s . The cross sectional areas of the branches 1, 2 and 3 are 0.012, 0.008 and 0.004 m2 respectively. All the three branches are in a horizontal plane and the friction is negligible. If the pressures at the points 1 and 3 are 270 kPa and 240 kPa respectively, then the pressure at point 2 is
(A) 202 kPa (C) 284 kPa Q. 40
Two Marks
(B) 240 kPa (D) 355 kPa
The figure shows the idealized view of a return elbow or U bend, which is connected to two pipes by flexible hoses that transmit no force. Water with density 1000 kg/m3 flows at velocity of 10 m/s through the pipe, which has a uniform ID of 0.1 m . The gauge pressure at points 1 and 2 are 304 kPa and
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GATE Previous Year Papers Solved by Team GATESCORE GATE SOLVED PAPER - CH FluidMechanicsandMechanicalOperations 253 kPa respectively. The horizontal force F required to keep the elbow in position is
(A) 1574 N (B) 1970 N (C) 5942 N (D) 7533 N Q. 41
The figure shows a series-parallel configuration of three identical centrifugal pumps. The head increase ∆H across a single such pump varies with flow rate Q according to ∆H = a − bQ2 . The expression for the total head increase ∆H = H2 − H1 in terms of a and b and the total flow rate Q1 for this configuration is given by
(A) 2a - 5 bQ 12 (B) 2a - bQ 12 4 (C) 2a - 2bQ 12 (D) a - bQ 12 Q. 42
The pressure differential across a venturimeter, inclined at 45º to the vertical (as shown in the figure) is measured with the help of a manometer to estimate the flow rate of a fluid flowing through it. If the density of the flowing fluid is ρ and the density of the manometer fluid is ρ m , the velocity of the fluid at the throat can be obtained from the expression
2
2
(A) v 2 − v 1 = 2g
h ^r m − rh v 22 − v 12 = hr m + H sin 45º + H sin 45º (B) r 2g r
2 2 hr v 22 − v 12 = h ^r m − rh (C) v 2 − v 1 = m (D) 2g r 2g r
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GATE Previous Year Papers Solved by Team GATESCORE GATE SOLVED PAPER - CH FluidMechanicsandMechanicalOperations
Q. 43
In the Stokes regime, the terminal velocity of particles for centrifugal sedimentaion is given by ut = ω2 r ^ρ p − ρh d p2 /18 µ
where, ω : angular velocity; r : distance of the particle from the axis of rotation; ρ p : density of the particle; ρ : density of the fluid; d p : diameter of the particle and µ : viscosity of the fluid. In a bowl centrifugal classifier operating at 60 rpm with water ^µ = 0.001 kg/m−sh , the time taken for a particle (d p = 0.0001 m , specific gravity = 2.5 ) in second to traverse a distance of 0.05 m from the liquid surface is
(A) 4.8 (C) 6.8
Statement For Linked Q. 44
(B) 5.8 (D) 7.8
Answer
Q 44 and 45 :
A fluidized bed ( 0.5 m dia, 0.5 m high) of spherical particles (diameter = 2000 µm , specific gravity = 2.5 ) uses water as the medium. The porosity of the bed is 0.4. The Ergun equation for the system is 2 ∆p/L = 4 # 105 vmf + 1 # 107 v mf (SI unit, vmf in m/s) ∆p/L (SI unit) at minimum fluidization condition is ^g = 9.8 m/s2h.
(A) 900 (B) 8820 (C) 12400 (D) 17640 Q. 45
The minimum fluidization velocity (mm/s) is (A) 12.8 (B) 15.8 (C) 24.8 (D) 28.8
Q. 46
A tube of diameter D and length L is initially filled with a liquid of density ρ and viscosity µ . It is then pushed out by the application of a constant force F to the plunger as shown in the figure. Assuming laminar flow and pseudo steady state, the time required to expel one-half of the liquid out of the tube is
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GATE Previous Year Papers Solved by Team GATESCORE GATE SOLVED PAPER - CH FluidMechanicsandMechanicalOperations
(A)
3 πµL2 3 πµD2 (B) F F
(C)
6πµL2 6 πµDL (D) F F
Year 2006 Q. 47
One Mark
Match the following for a centrifugal pump with impeller speed n . Group I P. Capacity
1.
Proportional to n
Q. Head
2.
Proportional to n2
3.
Proportional to n3 (B) P-1, Q-3 (D) P-1, Q-2
(A) P-2, Q-1 (C) P-2, Q-3 Q. 48
Group II
The magnitude of the force (in newton) required to hold a body of volume 0.05 m3 and mass 40 kg in water (density 1000 kg/m3 ) at a depth of 0.1 m is ^g = 9.81 m/s2h. (A) 0 (B) 98.1 (C) 490.5 (D) 882.9 Year 2006
Two Marks
Q. 49
A liquid is pumped at the flow rate Q though a pipe of length L. The pressure drop of the fluid across the pipe is ∆p . Now a leak develops at the mid-point of the length of the pipe and the fluid leaks at the rate of Q/2. Assuming that the friction factor in the pipe remains unchanged, the new pressure drop across the pipe for the same inlet flow rate ^Q h will be (A) ^1/2h ∆p (B) ^5/8h ∆p (C) ^3/4h ∆p (D) ∆p
Q. 50
In a laminar flow through a pipe of radius R, the fraction of the total fluid flowing through a circular cross-section of radius R/2 centred at the pipe axis is (A) 3/8 (B) 7/16 (C) 1/2 (D) 3/4
Q. 51
A bed fluidized by water is used for cleaning sand contaminated with salt. The particles of sand and salt have the same shape and size but different densities ( ρ sand = 2500 kg/m3 and ρ salt = 2000 kg/m3 ). If the initial volume fraction of the salt in the mixture is 0.3 and if the initial value of the minimum fluidization velocity ^vmf h is 0.9 m/s , find the final value of the v mf (in m/s) when the sand
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GATE Previous Year Papers Solved by Team GATESCORE GATE SOLVED PAPER - CH FluidMechanicsandMechanicalOperations is washed free of the salt. Assume that the bed characteristics (bed porosity and solid surface area per volume) do not change during the operation and that the pressure drop per unit length is directly proportional to the fluid velocity. (A) 0.70 (B) 0.90 (C) 1.00 (D) 1.46 Q. 52
Two spherical particles have the same outer diameter but are made of different materials. The first one (with material density ρ 1 ) is solid, whereas the second (with material density ρ 2 ) is a hollow sphere with the inner shell diameter equal to half the outer diameter. If both the spheres have the same terminal velocity in any fluid, then the ratio of their material densities, r 2 /r 1 is (A) 1 (B) 8/7 (C) 2 (D) 8
Q. 53
A filtration is conducted at constant pressure to recover solids from dilute slurry. To reduce the time of filtration, the solids concentration in the feed slurry is increased by evaporating half the solvent. If the resistance of the filter medium is negligible, the filtration time will be reduced by a factor of (A) 1 (B) 2 (C) 4 (D) 8
Statement For Linked
Answer
Q 54 and 55 :
A continuous grinder obeying the Bond crushing law grinds a solid at the rate of 1000 kg/h from the initial diameter of 10 mm to the final diameter of 1 mm . Q. 54
If the market now demands particles of size 0.5 mm the output rate of the grinder (in kg/h) for the same power input would be reduced to (A) 227 (B) 474 (C) 623 (D) 856
Q. 55
In order to restore the output back to 1000 kg/h , an additional grinder was installed. The two grinders can be operated either in series (configuration-1) or parallel (configuration-2). Compare the two configurations in terms of the additional power consumption over the case above. (A) Configuration-1 consumes less power than configuration-2 (B) Configuration-2 consumes less power than configuration-1 (C) Both configurations consume the same power (D) Configuration-2 consumes less or more power than configuration-1 depending on how the feed is distributed between the two grinders in configuration-2 (the parallel configuration).
Q. 56
The liquid surface in a cylindrical bucket of radius R rotating about its axis acquires a parabolic profile given by the equation y = a + br 2 , where y is height of the liquid surface from the bottom of the bucket at a radial distance r from the bucket axis. If the liquid has density ρ , then the mass of the liquid in the bucket is
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GATE Previous Year Papers Solved by Team GATESCORE GATE SOLVED PAPER - CH FluidMechanicsandMechanicalOperations 2 2 (A) πρR2 c a + bR m (B) πρR2 ca + bR m 2 2
(C) πρR2 a (D) πρR2 ^a + bR2h Year 2005 Q. 57
One Mark
Match the following types of fluid (in Group I) with their respective constitutive relations (in Group II), where, τ is the stress and γo is the strain rate. Group I P. Pseudoplastic
1.
Group II τ = µγo
Q. Bingham plastic
2.
τ = τ 0 + Kγo
3.
n τ = K γo ; n < 1
4.
n τ = K γo ; n > 1
(A) P-1, Q-4 (C) P-2, Q-3
(B) P-4, Q-1 (D) P-3, Q-2
Q. 58
The critical speed of the ball mill of radius R, which contains balls of radius r is proportional to (A) ^R - r h-0.5 (B) ^R - r h-1 (C) ^R - r h (D) ^R - r h2
Q. 59
If the frequency of the stirrer in a mixing tank is increased by a factor of 2 while all other parameters are kept constant, by what factor is the power requirement increased at high Reynolds number? (A) 4 (B) 8 (C) 16 (D) 32 Year 2005
Q. 60
Two Marks
A dam of width 50 m is used to hold water in a reservoir. If the water height is 10 m from the bottom of the dam, what is the total force F acting on the dam due to the water? Assume g = 10 m/s2 , and the fluid density is 1000 kg/m3 . (A) F = 12.5 # 106 N (B) F = 25 # 106 N (C) F = 50 # 106 N (D) F = 5 # 106 N
Q. 61
The relation between the stress τ and the strain rate ^dux /dy h for the rapid flow of a granular material is given by τ = B ^dux /dy h2 , where B is a constant. If M , L and T are the mass, length and time dimension respectively, what is the dimension of the constant B ? (A) 6ML-1 T-1@ (B) 6ML-1 T-2@ (C) 6MT-1@ (D) 6ML-1@
Statement For Linked
Answer
Q 62 and 63 :
Two tanks A and B of cross-sectional area 1 m2 each, contain a fluid of density 1000 kg/m3 and viscosity 1 kg/ms . The tanks are connected by a pipe of diameter 0.02 m and length
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GATE Previous Year Papers Solved by Team GATESCORE GATE SOLVED PAPER - CH FluidMechanicsandMechanicalOperations 1 m , and a check valve at the bottom. Assume that the flow is laminar and there is no friction in the check valve. In the initial state, the height of the fluid in the tank A is 6 m and the height of the fluid in tank B is 2 m (as shown in the figure below). The check valve is opened and the fluid flows from tank A to tank B till the levels in the two tanks are equal in the final state. Assume g = 10 m/s2 in the calculations.
Q. 62
What is the average fluid velocity in the pipe as soon as the valve is opened? (A) 0.25 m/s (B) 0.5 m/s (C) 1 m/s (D) 2 m/s
Q. 63
What is the total energy loss between the initial and final states due to the fluid flow? (A) 2 # 10 4 J (B) 16 # 10 4 J (C) 8 # 10 4 J (D) 4 # 10 4 J
Q. 64
A centrifuge of diameter 0.2 m in a pilot plant rotates at a speed of 50 Hz in order to achieve effective separation. If this centrifuge is scaled up to a diameter of 1 m in the chemical plant and the same separation factor is to be achieved, what is the rotational speed of the scaled up centrifuge? (A) 15 Hz (B) 22.36 Hz (C) 30 Hz (D) 44.72 Hz
Q. 65
What is the terminal velocity in m/s, calculated from Stokes law for a particle of diameter 0.1 # 10-3 m , density 2800 kg/m3 settling in water of density 1000 kg/m3 and viscosity 10-3 kg/ms ? (Assume g = 10 m/s2 ) (A) 2 # 10-2 (B) 4 # 10-3 (C) 10-2 (D) 8 # 10-3 Year 2004
Q. 66
One Mark
The equivalent diameter for flow through a rectangular duct of width B and height H is HB (A) HB (B) 2 ^H + B h ^H + B h 4HB (C) 2HB (D) ^H + B h ^H + B h
Q. 67
What is the force required (in newton) to hold a spherical balloon stationary in water at a depth of H from the air-water interface? The balloon is of radius 0.1 m and is filled with air.
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GATE Previous Year Papers Solved by Team GATESCORE GATE SOLVED PAPER - CH FluidMechanicsandMechanicalOperations 4 πg 0.1 πgh (B) 3 4 0.1 πgh 0.04 πgH (C) (D) 8 3 (A)
Q. 68
Match the systems in Group I with equipment used to separate them in Group II. Group I
Group II
P. Gas - solid
1. Filter press
Q. Liquid - liquid
2. Cyclone 3. Decanter 4. Thickener
(A) P-1, (B) P-2, (C) P-3, (D) P-4,
Q-2 Q-3 Q-4 Q-1
Q. 69
For a cyclone of diameter 0.2 m with a tangential velocity of 15 m/s at the wall, the separation factor is (A) 2250 (B) 1125 (C) 460 (D) 230
Q. 70
For a particle settling in water at its terminal settling velocity, which of the following is true? (A) Buoyancy = Weight + Drag (B) Weight = Buoyancy + Drag (C) Drag = Buoyancy + Weight (D) Drag = Weight
Q. 71
In constant pressure filtration, (A) resistance decreases with time (B) rate of filtration is constant (C) rate of filtration increases with time (D) rate of filtration decreases with time Year 2004
Two Marks
Q. 72
Viscosity of water at 40cC lies in the range of (A) 1 # 10-3 - 2 # 10-3 kg/m -s (B) 0.5 # 10-3 - 1 # 10-3 kg/m -s (C) 1–2 kg/m -s (D) 0.5 - 1 kg/m -s
Q. 73
For the manometer setup shown in the figure, the pressure difference pA - pB is given by
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GATE Previous Year Papers Solved by Team GATESCORE GATE SOLVED PAPER - CH FluidMechanicsandMechanicalOperations
Q. 74
(A) ^r H - r airh gH (B) ^r H - r L h gH (C) ^r H − r L h gH + ^r L − r airh g (L − H) (D) ^r H − r L h gL + ^r L − r airh gH
A conical tank with a bottom opening of cross-sectional area A is filled with water and is mounted on supports as shown in the figure. What is the force F with which plate X must be pushed up to prevent water from leaking? Assume that the density of air is negligible as compared to the density of water ρ L .
(A) ρ L Vg (B) ρ L AHg (C) ρ L Vg/2 (D) ρ L Vg/3 Q. 75
Three piping networks as shown in the figure are placed horizontally. They are made using identical pipe segments and are subjected to the same pressure drop across them. Assuming no pressure losses at junctions, the flow rates across the three networks are related as
(A) 1 :
3 : 2 (B) 1:2:3
(C) 1 : 2 : 2 (D) 1: 2 : 2 Q. 76
To keep the power input constant for a stirred vessel operating under fully developed turbulent flow conditions (constant power number), if the impeller
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GATE Previous Year Papers Solved by Team GATESCORE GATE SOLVED PAPER - CH FluidMechanicsandMechanicalOperations diameter is increased by 20% , the impeller speed should be decreased by a factor of (A) ^1.2h3/2 (B) ^1.2h3/5 (C) ^1.2h2/3 (D) ^1.2h5/3 Q. 77
A centrifugal filtration unit operating at a rotational speed of ω has inner surface of the liquid (density ρ L ) located at a radial distance R from the axis of rotation. The thickness of the liquid film is δ and no cake is formed. The initial pressure drop during filtration is (A) b 1 l ω2 R2 ρ L (B) b 12 l ω2 δ2 ρ L 2 (C) b 1 l ω2 δρ L ^2R + δ h (D) b 12 l ω2 Rρ L ^R + 2δ h 2
Q. 78
v mf is the minimum fluidisation velocity for a bed of particles. An increase in the superficial gas velocity from, 2v mf to 2.5v mf results in (all velocities are smaller than the entrainment velocity of the particles) no change in (A) drag on particles (B) drag on column walls (C) the bed height (D) the bed voidage
Q. 79
The Kozney-Carman equation, rewritten in terms of non-dimensional numbers ∆p gives e ρu2 o proportional to ^L/D p h Re (B) (A) Re ^D p /L h ^L/D p h R e2 (C) (D) 2 Re ^D p /L h The cumulative mass fraction of particles smaller than size d j for a collection of Ni particles of diameter di and mass mi ^i = 1, 2, 3, ..., 3h is given by
Q. 80
j
/
Ni d i3
/
3 i
=1 (A) i 3 i=1 j
i
(C)
/
/N m d i
i
3 i
i=1 (B) j Ni d Ni mi d i3
/N m d
i=1 3
j
i
/
2 i
i=1 j
/N m d i
i
i
i=1 3
(D) 2 Ni mi d i Ni mi di
i=1
Year 2003
/
i=1
One Mark
Q. 81
A lubricant 100 times more viscous than water would have a viscosity (in Pa-s) (A) 0.01 (B) 0.1 (C) 1 (D) 10
Q. 82
The velocity profile for a Bingham plastic fluid flowing (under laminar conditions) in a pipe is (A) parabolic (B) flat (C) flat near the wall and parabolic in the middle (D) parabolic near the wall and flat in the middle
Q. 83
Energy requirement (per unit mass of material crushed/ground) is highest for (A) jaw crusher
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GATE Previous Year Papers Solved by Team GATESCORE GATE SOLVED PAPER - CH FluidMechanicsandMechanicalOperations (B) rod mill (C) ball mill (D) fluid energy mill Year 2003 Q. 84
Two Marks
A pipe has a porous section of length L as shown in the figure. Velocity at the start of this section is v 0 . If fluid leaks into the pipe through the porous section at a volumetric rate per unit area q ^x/L h2 , what will be the axial velocity in the pipe at any x ? Assume incompressible one dimensional flow, i.e., no gradients in the radial direction
3 (A) vx = v 0 + q x2 LD 3 (B) vx = v 0 + 1 q x 2 3 L 3 (C) vx = v 0 + 2q x LD 3 (D) vx = v 0 + 4 q x2 3 LD
Q. 85
A centrifugal pump is used to pump water through a horizontal distance of 150 m and then raised to an overhead tank 10 m above. The pipe is smooth with an ID of 50 mm . What head (of water) must the pump generate at its exit ^E h to deliver water at a flow rate of 0.001 m3 /s ? The Fanning friction factor f is 0.0062.
(A) 10 (B) 11 (C) 12 (D) 20
Q. 86
m m m m
The pressure differential across a vertical venturimeter (shown in figure) is measured with the help of a mercuty manometer to estimate flow rate of water
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GATE Previous Year Papers Solved by Team GATESCORE GATE SOLVED PAPER - CH FluidMechanicsandMechanicalOperations flowing through it. The expression for the velocity of water at the throat is
2 2 r v 22 − v 12 = h ^r m − r w h (A) v 2 − v 1 = h m (B) 2g rw 2g rw 2 ^r m − r w h v 22 − v 12 = h ^r m − r w h (C) v 2 = H + h (D) 2g rw 2g rm
Statement For Linked
Answer
Q 87 and 88 :
A bed of spherical particles (specific gravity 2.5) of uniform size 1500 µm is 0.5 in diameter and 0.5 m high. ln the packed bed state, the porosity may be taken as 0.4. Ergun’s equation for the above particle-fluid system (in SI units) is given below 2 (SI units) ∆p/L = 375 # 103 vOM + 10.94 # 106 V OM Q. 87
If water is to be used as the fluidizing medium, the minimum fluidization velocity, vOM is (A) 12 mm/s (B) 16 mm/s (C) 24 mm/s (D) 28 mm/s
Q. 88
In actual operation, the above bed has a height = 1 m . What is the porosity of the fluidized bed? (A) 0.2 (B) 0.5 (C) 0.7 (D) 0.8
Q. 89
The basic filtration equation is given as dt = µ αCV + R , b ml dV A∆p A where V is volume of the filtrate, A is the filtration area; α is specific cake resistance, µ is viscosity of the filtrate, and C is the concentration of solids in the feed slurry. In a 20 min constant rate filtration, 5 m3 of filtrate was obtained. If this is followed by a constant pressure filtration, how much more time in minutes will it take for another 5 m3 of filtrate to be produced? Neglect filter medium resistance, Rm ; assume incompressible cake. (A) 10 (B) 20 (C) 25 (D) 30 Year 2002
Q. 90
One Mark
With increasing flow rate, the hydraulic efficiency of a centrifugal pump (A) monotonically decreases (B) decreases and then increases
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GATE Previous Year Papers Solved by Team GATESCORE GATE SOLVED PAPER - CH FluidMechanicsandMechanicalOperations (C) remains constant
(D) increases and then decreases
Q. 91
For flow past a flat plate, if x is the distance along the plate in the direction of flow, the boundary layer thickness is proportional to 1 (A) x (B) x 1 (C) x (D) x
Q. 92
For turbulent flow of an incompressible fluid through a pipe, the flow rate Q is proportional to ^∆p hn , where ∆p is the pressure drop. The value of exponent n is (A) 1 (B) 0 (C) < 1 (D) > 1
Q. 93
If d p is the equivalent diameter of a non-spherical particle, Vp its volume and S p its surface area, then its sphericity φ s is defined by 6Vp V (B) (A) φ s = φs = p dp Sp dp Sp 6 dp Sp d S (C) φ s = (D) φs = p p Vp Vp
Q. 94
Arrange the following size reduction equipment in the decreasing order of the average particle size produced by each of them. (A) jaw crusher, ball mills, fluid energy mills (B) ball mills, jaw crusher, fluid energy mills (C) fluid energy mills, jaw crusher, ball mills (D) fluid energy mills, ball mills, jaw crusher Year 2002
Two Marks
Q. 95
The drag coefficient for a bacterium moving in water at 1 mm/s will be of the following order of magnitude (assume size of the bacterium to be 1 micron and kinematic viscosity of water to be 10-6 m2 /s ) (A) 24000 (B) 24 (C) 0.24 (D) 0.44
Q. 96
A gas (density = 1.5 kg/m3 , viscosity = 2 # 10−5 kg/m -s) flowing through a packed bed (particle size = 0.5 cm , porosity = 0.5 ) at a superficial velocity of 2 m/s causes a pressure drop of 8400 Pa/m . The pressure drop for another gas with density of 1.5 kg/m3 and viscosity of 3 # 10-5 kg/ms , flowing at 3 m/s will be (A) 8400 Pa/m (B) 18900 Pa/m (C) 12600 Pa/m (D) 16800 Pa/m
Q. 97
What is the critical rotational speed in rev/s. for a ball mill of 1.2 m diameter charged with 70 mm diameter balls? (A) 0.5 (B) 1.0 (C) 2.76 (D) 0.66
Q. 98
A sand mixture was screened through a standard 10-mesh screen. The mass fraction of the oversize material in feed, overflow and underflow were found to be 0.38, 0.79 and 0.22 respectively. The screen effectiveness based on the oversize is
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GATE Previous Year Papers Solved by Team GATESCORE GATE SOLVED PAPER - CH FluidMechanicsandMechanicalOperations (A) 0.50 (C) 0.68 Year 2001
(B) 0.58 (D) 0.62 One Mark
Q. 99
The power number for a stirred tank becomes constant at high Reynolds number. In this limit, the variation of power input with impeller rotational speed ^N h is proportional to (A) N 0 (B) N1 (C) N 2 (D) N3
Q. 100
The operation of a rotameter is based on (A) variable flow area (B) rotation of a turbine (C) pressure drop across a nozzle (D) pressure at a stagnation point
Q. 101
Applying a pressure drop across a capillary results in a volumetric flow rate Q under laminar flow conditions. The flow rate for the same pressure drop, in a capillary of the same length but half the radius is Q Q (A) (B) 2 4 Q Q (C) (D) 8 16 Year 2001
Two Marks
Q. 102
A Bingham fluid of viscosity µ = 10 Pa-s and yield stress τ 0 = 10 kPa is sheared between flat parallel plates separated by a distance 10-3 m . The top plate is moving with a velocity of 1 m/s . The shear stress on the plate is (A) 10 kPa (B) 20 kPa (C) 30 kPa (D) 40 kPa
Q. 103
The energy required per unit mass to grind limestone particles of very large size to 100 µm is 12.7 kWh/ton. An estimate (using Bond’s law) of the energy to grind the particles from a very large size to 50 µm is (A) 6.25 kW-h/ton (B) 9.0 kW-h/ton (C) 18 kW-h/ton (D) 25.4 kW-h/ton Year 2000
Q. 104
Q. 105
Q. 106
One Mark
For a sphere falling in the constant drag coefficient regime, its terminal velocity depends on its diameter d as (A) d (B) d 2 (C) d (D) 1/d In a fully turbulent flow ^Re > 105h in a pipe of diameter d for a constant pressure gradient, the dependence of volumetric flow rate of an incompressible fluid is (A) d (B) d2 (C) d 2.5 (D) d4 In the laminar boundary layer flow over a flat plate, the ratio ^δ/x h varies as (A) Re (B) Re
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GATE Previous Year Papers Solved by Team GATESCORE GATE SOLVED PAPER - CH FluidMechanicsandMechanicalOperations 1 (C) 1 (D) Re Re (Where, δ is the boundary layer thickness and x is the distance from the leading edge in the direction of flow). Q. 107
For laminar flow of a shear thinning liquid in a pipe, if the volumetric flow rate is doubled, the pressure gradient will increase by a factor of (A) 2 (B) <2 (C) > 2 (D) 1/2 Year 2000
Q. 108
Two Marks
The sphericity of a solid particle of cubical shape is π 1/3 a6k (A) π (B) π 1/2 π (C) a 6 k (D) 3
Q. 109
A 30% (by volume) suspension of spherical sand particles in a viscous oil has a hindered settling velocity of 4.44 µm/s . If the Richardson-Zaki hindered settling index is 4.5, then the terminal velocity of a sand grain is (A) 0.9 µm/s (B) 1 µm/s (C) 22.1 µm/s (D) 0.02 µm/s
Q. 110
A 1 m high bed made up of 2 mm particles is to be fluidised by an oil (density 900 kg/m3 ; viscosity 0.01 Pa-s) If at the point of incipient fluidisation, the bed voidage is 39% and the pressure drop across the bed is 10 kPa, then the density of particles is (A) 2571 kg/m3 (B) 3514 kg/m3 (C) 4000 kg/m3 (D) 4350 kg/m3
Q. 111
A free jet of water of cross-sectional area 0.01 m2 and a velocity of 20 m/s strikes a plate and then flows in the plane parallel to the plate as shown in the figure below. The horizontal component of the force of the support is
(A) 200 N (C) 2000 N
(B) 400 N (D) 4000 N
**********
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GATE Previous Year Papers Solved by Team GATESCORE GATE SOLVED PAPER - CH FluidMechanicsandMechanicalOperations ANSWER KEY Fluid Mechanics and Mechanical Operations 1
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