GATE MCQ MECHANICAL ENGINEERING by NODIA VOLUME 1. ENGINEERING MECHANICS 1. Equilibrium of Forces 2. Structure 3. Friction 4. Virtual Work 5. Kinematics of Particle 6. Kinetics of Particles 7. Plane Kinematics of Rigid body 8. Plane Kinetics of Rigid body STRENGTH OF MATERIALS 1. Stress and Strain 2. Axial Loading 3. Torsion 4. Shear Force and Bending Moment 5. Transformation of Stress and Strain 6. Design of Beams and Shafts 7. Deflection of Beams and Shafts 8. Column 9. Energy Methods THEORY OF MACHINES 1. Analysis of Plane Mechanism 2. Velocity and Acceleration 3. Dynamic Analysis of Slider - Crank and Cam 4. Gear – Trains 5. Fly Wheel 6. Vibration MACHINES DESIGN 1. Static and Dynamic Loading 2. Joints 3. Shaft and Shaft Components 4. Spur Gears 5. Bearings 6. Clutch and Brakes
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GATE MCQ MECHANICAL ENGINEERING by NODIA
VOLUME 1.
ENGINEERING MECHANICS
1. Equilibrium of Forces 2. Structure 3. Friction 4. Virtual Work 5. Kinematics of Particle 6. Kinetics of Particles 7. Plane Kinematics of Rigid body 8. Plane Kinetics of Rigid body
STRENGTH OF MATERIALS
1. Stress and Strain 2. Axial Loading 3. Torsion 4. Shear Force and Bending Moment 5. Transformation of Stress and Strain 6. Design of Beams and Shafts 7. Deflection of Beams and Shafts 8. Column 9. Energy Methods
THEORY OF MACHINES
1. Analysis of Plane Mechanism 2. Velocity and Acceleration 3. Dynamic Analysis of Slider - Crank and Cam 4. Gear – Trains 5. Fly Wheel 6. Vibration
MACHINES DESIGN
1. Static and Dynamic Loading 2. Joints 3. Shaft and Shaft Components 4. Spur Gears 5. Bearings 6. Clutch and Brakes
VOLUME 2
FLUID MECHANICS
1. Basic Concepts and Properties of Fluids 2. Pressure and Fluid Statics 3. Fluid Kinematics & Bernouli Equation 4. Flow Analysis Using Control Volumes 5. Flow Analysis Using Differential Method 6. Internal Flow 7. External Flow 8. Open Channel Flow 9. Turbo Machinery
HEAT TRANSFER 1. Basic Concepts & Modes of Heat-Transfer 2. Fundamentals of Conduction 3. Steady Heat Conduction 4. Transient Heat Conduction 5. Fundamentals of Convection 6. Free and Force Convection 7. Radiation Heat Transfer 8. Heat Exchangers
THERMODYNAMICS 1. Basic Concepts and Energy Analysis
2. Properties of Pure Substances
3. Energy Analysis of Closed System
4. Mass and Energy Analysis of Control Volume
5. Second Law of Thermodynamics
6. Entropy
7. Gas Power Cycles
8. Vapor and Combined Power Cycles
9. Refrigeration and Air Conditioning
VOLUME 3
Manufacturing Engineering
1. Engineering materials and Heat treatment
2. Metal casting
3. Forming process
4. Sheet metal working
5. Joining
6. Machining and machine tool operations
7. Non‐traditional machiching process
8. Metrology and Inspection
9. Computer Integrated Manufacturing
Industrial Engineering 1. Production Planning and Control
FM 6.1 Consider a fully developed laminar pipe flow. If the pipe diameter is reduced by half while the flow rate and pipe length are held constant, the head loss will be(A) Increase by a factor of 2 (B) Increase by a factor of 4
(C) Increase by a factor of 16 (D) Remains same.
FM 6.2 Consider a flow through a 15 m long horizontal pipe at the laminar transition point. The fluid is oil with 890 /kg m3r = and 0.07 /kg m sm -= . If the power delivered to the flow is 1 hp, the flow rate will be(A) 2420 /cm s3 (B) 4840 /cm s3
(C) 3630 /cm s3 (D) 484 /cm s3
FM 6.3 Glycerin at 40 Cc with 1252 /kg m3r = and 0.27 /kg m sm -= is flowing through a 5 cm diameter horizontal smooth pipe with an average velocity of 3.5 /m s. What will be the pressure drop per unit length of the pipe ?(A) 121 kPa (B) 1.21 kPa
(C) 12.1 kPa (D) 0.121 kPa
Common Data For Q. 4 and 5Water at 15 Cc ( 999.1 /kg m3r = ) is flowing steadily in a 45 m long and 4 cm diameter horizontal pipe made of stainless steel at a rate of 8 10 /m s3 3
#- . The
friction factor .f 0 01573= .
FM 6.4 What will be the head loss ?(A) 36.6 m (B) 3.66 m
(C) 366.0 m (D) 0.366 m
FM 6.5 The pumping power requirement to overcome pressure drop is(A) 1.5 kW (B) 4.5 kW
(C) 3 kW (D) 6.0 kW
Common Data For Q. 6 and 7A light liquid 950 /kg m3r =^ h flows through a horizontal smooth tube of diameter 5 cm at an average velocity of 10 /m s. The fluid pressure measured at 2 m intervals along the pipe is as given below:
( )mx 0 2 4 6
( )kPap 304 255 226 200
FM 6.6 The wall shear stress in the fully developed section of the pipe is (A) 163 Pa (B) 325 Pa
FM 6.7 What will be the overall friction factor ?(A) 0.000183 (B) 0.183
(C) 0.00183 (D) 0.0183
FM 6.8 The piston shown in figure below is pushed steadily by a force F , which causes flow rate of 0.15 /cm sv 3=o through the needle. If fluid has 900 /kg m3r = and
0.002 /kg m sm -= , the force F will be
(A) 2.0 N (B) 3.6 N
(C) 1.35 N (D) 4.0 N
FM 6.9 A compressor that draws in air ( 1.149 / , 1.802 10 / )kg m kg m s3 5r m # -= = - from the outside, through an 12 m long, 20 cm diameter duct. The compressor takes in air at a rate of 0.27 /m s3 . If the friction factor is to be 0.0211, the useful power used by the compressor to overcome the frictional losses in the duct is(Disregarding any minor losses)
(A) 14.5 W (B) 15.4 W
(C) 51.4 W (D) 41.5 W
FM 6.10 In fully developed laminar flow in a circular pipe, the velocity at . R0 5 (midway between the wall surface and the center-line) is(A) u2 max (B) . u0 5 max
(C) . u0 75 max (D) Not changed
(where umax is the maximum velocity)
FM 6.11 The velocity profile in fully developed laminar flow in a circular pipe of inner radius 4 cmR = in /m s is given by
( )u r 1Rr4 2
2
= -c m
The maximum velocity in the pipe and the volume flow rate respectively, are(A) 4 / ,m s 0.01005 /m s3 (B) 0.01005 / ,m s 4 /m s3
(C) 0.01005 / ,m s3 4 /m s (D) 4 / ,m s3 0.01005 /m s
FM 6.12 Consider a flow between two smooth parallel horizontal plates of 3 cm apart. If the fluid is 10SAE oil and 2 /m sV = 870 / 0.104 /kg m and kg ms3r m= =^ h, the head loss per meter is(A) 0.430 /m m (B) 0.487 /m m
(C) 0.325 /m m (D) 0.163 /m m
FM 6.13 Consider laminar flow of a fluid through a rectangular concrete channel with the smooth surfaces of friction factor ( / )Ref 58= . If the average velocity of the fluid is doubled, the change in the head loss of fluid in percentage is (Assume the flow regime remains same)(A) Decrease by 50% (B) Increase by 50%
(C) Increase by 100% (D) Decrease by 100%
FM 6.14 Water at 20 Cc flows from a tank by the pressurized air at a rate of 60 /m h3 as shown in figure below. If coefficient of friction .f 0 0136= , what gage pressure p1 is needed to drive the pipe flow ?
(A) 2.38 MPa (B) 1.2 MPa
(C) 0.238 MPa (D) 0.12 MPa
FM 6.15 A single 6 cm diameter tube consists of seven 2 cm diameter smooth thin tubes packed tightly as shown in figure below. Air at about 20 Cc and 1 atm (
1.2 /kg m3r = , 1.8 10 /kg m s5m # -= - ), flows through this system at 150 /m h3 . What will be the pressure drop per meter length of the pipe ? (Take .f 0 0250= )
(A) 202.5 Pa (B) 90 Pa
(C) 270 Pa (D) 27.0 Pa
FM 6.16 Oil with a density of 850 /kg m3 and kinematic viscosity of 6 10 /m s4 2#
- flows in a 5 mm diameter and 40 m long horizontal pipe, from a storage tank open to the atmosphere. If the height of the liquid level above the center of the pipe is 3 m and the flow is fully developed laminar, the flow rate of oil through the pipe is(A) 1.8 10 /m s8 6 3
FM 6.17 A fluid flows through two horizontal pipes of equal length which are connected together to form a pipe of length l2 . The flow is fully developed laminar and the pressure drop for the first pipe is 1.44 times greater than for the second pipe. If the diameter of the first pipe is D , the diameter D3 of the second pipe is(A) . D1 64 (B) 1.37D
(C) . D1 095 (D) . D1 92
FM 6.18 A capillary viscometer measures the time of t 6D = seconds required for a 8 cm3 of water at 20 Cc to flow through a D diameter glass tube as shown in figure below. If 12 cmL = , 2 cml = and flow is laminar with no entrance and exit losses, the capillary diameter D will be (Take 0.001 /kg m sm -= )
(A) . mm1 5 (B) 15 mm
(C) 0.15 mm (D) 0.015 mm
FM 6.19 Oil with 894 /kg m3r = and 2.33 /kg m sm -= , flows at 0.5 /m s through 300 m long and 40 cm diameter cast iron pipe. Neglect minor losses. The pumping power required to overcome the pressure losses, is(A) 0.45 kW (B) 5. kW0
(C) 4 kW5 (D) 4.5 kW
FM 6.20 SAE 30 oil at 20 Cc . /kg m s0 29m -=^ , /kg m891 3r = h flows upward in a 3 cm diameter pipe through a pump from A to B at a rate of 3 /kg s as shown in figure below. At %100 efficiency, what pump power is required ?
(A) 4.8 kW (B) 4 kW
(C) 0.63 kW (D) 3.5 kW
FM 6.21 Oil with 910 /kg m3r = and 0.01 /kg m sm -= flows through a 1.2 m- diameter pipe at a rate of 3 /m s3 . The pressure drop along the pipe and friction factor are
7.6 MPa and .0 0157 respectively. If the pump is %88 efficient, the power required and the length of the pipe respectively, are(A) 26 ,136.5MW km (B) 19.5 , 182MW km
(C) 19.5 , 136.5MW km (D) 26 ,182MW km
FM 6.22 The pump adds 25 kW to the water as shown in figure and causes a flow rate of 0.04 /m s3 . For either case .f 0 016= and neglect minor losses. What will be the flow rate expected when the pump is removed from the system ?
(A) 0.0289 /m s3 (B) 2.89 /m s3
(C) 0.289 /m s3 (D) 0.00289 /m s3
FM 6.23 Consider the pitot-static pressure arrangement as shown in figure below. Air at 20 Cc is flowing through the pitot tube 1.2 /kg m3r =^ , 1.8 10 /kg m s5m # -= -
h and the manometer fluid is colored water at 20 Cc 998 /kg m3r =^ , 0.001 /kg m sm -= h. If the friction factor of the flow is .f 0 0175= and .V V0 85avg CL= , the pipe volume flow rate and the wall shear stress respectively, are
(A) 0.109 /m s3 , 1.7 Pa (B) 0.109 /m s3 , 1.233 Pa
(C) 0.128 /m s3 , 1.233 Pa (D) 0.128 /m s3 , 1.7 Pa
FM 6.24 Glycerin at 20 Cc ( 1260 /kg m3r = , 1.50 /N s m2m -= ) flows upward in a vertical 75 mm diameter pipe with a centerline velocity of 1.0 /m s. The head loss and pressure drop in a 10 m length of the pipe respectively, are(A) 8.2 m, 225 kPa (B) 0.11 m, 125 kPa
(C) 6.75 m, 207 kPa (D) 3.43 m, 166 kPa
Common Data For Q. 25 and 26Oil ( 876 /kg m3r = and 0.24 /kg m sm -= ) is flowing through a 1.5 cm diameter pipe that discharges into the atmosphere at 98 kPa. The absolute pressure 15 m before the exit is measured to be 145 kPa.
FM 6.25 If the pipe is horizontal, the flow rate of oil through pipe is(A) 1.62 10 /m s5 3
#- (B) 162 10 /m s5 3
#-
(C) 16.2 10 /m s5 3#
- (D) 162 10 /m s4 3#
-
FM 6.26 The flow rate of oil through the pipe, if the pipe is inclined at 8c upward from the horizontal, is(A) 100 10 /m s5 3
#- (B) 1.00 10 /m s5 3
#-
(C) 0. 10 /m s10 5 3#
- (D) 10.0 10 /m s5 3#
-
FM 6.27 Consider two types of drinking straws, one with a square cross-sectional shape and the other type the typical round shape. The amount of material in each straw and the length of the perimeter of the cross section of each shape are same . Assume the drink is viscous enough to ensure laminar flow and neglect gravity. What is the ratio of the flow rates v
vsquare
round
oo
_ i through the straws for a given pressure drop ? (For square cross section .Ref 56 9h = and for round shape Ref 64h = ).(A) 0.183 (B) 0.55
(C) 5.5 (D) 1.83
FM 6.28 Water flows from tank A to tank B with the valve closed as shown in figure. If the friction factor is .0 02 for all pipes and all minor losses are neglected, what will be the flow rate into tank B when the valve is opened to allow water to flow into tank C also ?
(A) 0.180 /m s3 (B) 0.00180 /m s3
(C) 0.0180 /m s3 (D) 1.80 /m s3
FM 6.29 Water at 20 Cc flows through a multiple parallel-plate passages heat exchanger as shown in figure below. The available pressure drop is 2 kPa and plate walls are hydraulically smooth. If the desired total flow rate is 0.25 /m s3 , the appropriate number of passages are .f 0 028=^ h
FM 6.30 Oil at 20 Cc ( 888.1 / , 0.8374 / )kg m kg m s3r m -= = is flowing through a vertical glass funnel as shown in figure. The funnel consists of 20 cm high cylindrical reservoir and a 1 cm diameter, 20 cm high pipe. The funnel is always maintained full by the addition of oil from the tank. Neglect entrance losses. What will be the ratio of the actual flow rate through the funnel to the maximum flow rate for the “Frictionless” case ?
(A) 43.91 (B) 0.0232
(C) 2.32 (D) 0.232
FM 6.31 Water at 20 Cc flows upward through an inclined 6 cm diameter pipe at 4 /m s is shown in figure. A mercury manometer has a reading of 135 mmh = . The pipe length between points (1) and (2) is 5 m and point (2) is 3 m higher than point (1). What will be the friction factor of the flow ?
(A) 0.114 (B) 0.07
(C) 0.025 (D) 0.044
FM 6.32 Viscous oil ( . . 0.85S G = , 0.10 Pa sm -= ) flows from tank A to tank B through the six rectangular slots as shown in figure below. If minor losses are negligible and the total flow rate is 30 /mm s3 , the pressure in tank A will be (Take f 3250= )
FM 6.33 A 2 mm diameter and 20 cm long straw delivers the water at 10 Cc with a rate of 3 /cm s3 . If the flow is vertically up, what will be the axial pressure gradient
/p x2 2 ?(Take 1.307 10 /kg m s3m # -= - , 1000 /kg m3r = )(A) 2 /kPa m (B) 10 /kPa m
(C) 4 /kPa m (D) 20 /kPa m
FM 6.34 A tank of water has a 1.5 cm diameter hole at the bottom, where water discharges to the atmosphere. The water level is 3 m above the outlet. Disregarding the effect of the kinetic energy correction factor. If the entrance of the hole is sharp edged, the flow rate of water through the hole is (loss coefficient KL for sharp-edged .0 5= )(A) 1.11 10 /m s3 3
#- (B) 111 10 /m s3 3
#-
(C) 11.1 10 /m s3 3#
- (D) .111 10 /m s0 3 3#
-
FM 6.35 Water at a rate of 0.04 /m s3 , flows in a 0.12 m diameter pipe that contains a sudden contraction to a 0.06 m diameter pipe. If the loss coefficient .K 0 40L = , the pressure drop across the contraction section is(A) 99.75 kPa (B) 33 kPa
(C) 166.25 kPa (D) 133 kPa
FM 6.36 The water pipe system shown in figure below consists of 1200 m long cast-iron .f 0 0315=^ h pipe of 5 cm diameter, two 45c and four 90c flanged long-radius
elbows, a fully open flanged globe valve and a sharp exit into a reservoir. The minor losses coefficient for the pipe system is as follows
45c long-radius elbow : .K 0 2, 90c long-radius elbow : 0.K 3, Open flanged globe valve : .K 8 5, Sharp exit valve : .K 1 0,If the elevation at point 1 is 400 m, what gage pressure is required at point 1 to deliver 0.005 /m s3 of water at 20 Cc ( 0.001 / skg mm -= ) into the reservoir ?(A) .54 MPa4 (B) 3. MPa46
(C) . MPa1 43 (D) .4 MPa6
FM 6.37 Kerosine is to be withdrawn from a 15 cm high kerosine tank by drilling a well rounded 3 cm diameter hole with negligible loss at the bottom surface and attaching a horizontal 90c bend of negligible length. The kinetic energy correction factor is 1.05. What will be the flow rate of water through the bend, respectively
if (a) the bend is a flanged smooth bend and (b) the bend is miter bend without vanes ?
(A) 8.08 / ,L s 4.78 /L s (B) 4.78 / ,L s 6.03 /L s
(C) 6.03 / ,L s 4.78 /L s (D) 8.08 / ,L s 6.03 /L s
FM 6.38 A horizontal pipe has an sudden expansion from 6 cmD1 = to 12 cmD2 = . The water is flowing at 10 /m s and 300 kPap1 = in the small section and the flow is turbulent. If the kinetic energy correction factor to be 1.06 at both inlet and outlet, the downstream pressure is
(A) 300 kPa (B) 278 kPa
(C) 377 kPa (D) 322 kPa
FM 6.39 A 4.5 m diameter tank is initially filled with water 2 m above the centre of a sharp edged 15 cm diameter orifice. The tank water surface is open to the atmosphere and the orifice drains to the atmosphere. Neglecting the effect of the kinetic energy correction factor. The time required to empty the tank is (loss coefficient for sharp edge .K 0 5L = )
(A) 9.6 min1 (B) . min26 4
(C) . min0 264 (D) . min2 64
Common Data For Linked Answer Q. 40 and 41Water at 20 Cc flows through a 10 cm diameter smooth pipe which contains an orifice plate with 5 cm-diameter. The measured orifice pressure drop is 75 kPa. Discharge coefficient 0.605Cd = and non- recoverable head loss coefficient 1.8K = .
FM 6.40 What will be the flow rate in /m hr3 ?(A) 54 (B) 50
(C) 60 (D) 209
FM 6.41 What will be the non recoverable head loss ?(A) 33.4 kPa (B) 6.9 kPa
(C) 52. kPa4 (D) 26.4 kPa
Common Data For Linked Answer Q. 42 and 43Water at 20 Cc ( 9 8 / , 1.002 10 / )kg m kg m s9 3 3r m # -= = - flows through a 50 cm diameter pipe. The flow rate of water is measured with an orifice meter to be 0.25 /m s3 . The diameter ratio b and discharge coefficient Cd are .0 60 and .0 61 respectively.
FM 6.42 The pressure difference indicated by orifice meter is(A) 1.9 kPa (B) 19.0 kPa
(C) 14 kPa6 (D) 14.6 kPa
FM 6.43 What will be the head loss ?(A) 2.207 m (B) 2.0421 m
(C) 0.7734 m (D) 0.940 m
FM 6.44 A 5 cm diameter smooth pipe contains an orifice plate of .0 6b = and it is monitored by a mercury manometer /kg m13550 3r =^ h as shown in figure below. What will be the h when the flow rate is 0.334 /minm3 ?(Take .C 0 613d = )
(A) 75.75 cm (B) 7.52 cm
(C) 57 cm (D) 1.72 cm
FM 6.45 Air at 20 Cc ( 1.204 / )kg m3r = flows at high speed through a venturi-meter monitored by a water manometer as shown in figure below. If 40 cmh = , what will be the maximum mass flow rate of air that venturi can measure ? (Take discharge coefficient .C 0 98d = )
FM 6.46 Consider the flow of air at high speed through a venturi monitored by a mercury manometer 13550 /kg mHg
3r =^ h as shown in figure below. Discharge coefficient Cd and Expansion factor Y for this flow are .0 985 and .0 76 respectively. The upstream conditions are 150 kPa and 353 K. If 37 cmh = , the mass flow rate for flow to be compressible is
(A) 0.40 /kg s (B) 3.23 /kg s
(C) 7.27 /kg s (D) 0.90 /kg s
FM 6.47 Ethanol at 20 Cc /kg m789 3r =^ , 0.0012 /kg m sm -= h flows through a 5 cm diameter smooth pipe at a rate of 7 /m hr3 . Three piezometer tubes are installed as shown in figure below. If the pipe contains a thin plate orifice of diameter
3 cmd = , the piezometer levels h2 and h3 will be .Take K 1 5=^ and .f 0 023= h
FM 6.48 Consider the parallel-pipe system as shown in figure below. The SAE 10 oil at 20 Cc 870 /kg m3r =^ and 0.104 /kg m sm -= h is flowing laminarly through the pipe system with pressure drop 21 kPap p1 2- = . What will be the total flow rate between 1 and 2 ?
(A) 0.0005 /m s3 (B) 0.0022 /m s3
(C) 0.0027 /m s3 (D) 0.0032 /m s3
FM 6.49 Consider the parallel-pipe system of two identical length and material pipe as shown in figure below. The diameter of pipe A is half of the diameter of pipe B
. If the friction factor to be same in both case and disregarding minor losses, the flow rates in pipes A and B would be
(A) Remains same
(B) Flow rate of A increased by a factor of 0.177.
(C) Flow rate of B increased by a factor of 0.177.
(D) Flow rate of A decreased by a factor of 0.177.
Common Data For Linked Answer Q. 50 and 51Three pipes of same material .f 0 0275=^ h are laid in parallel with these dimensions:
Pipe 1 : 900 mL1 = 10 cmd1 =
Pipe 2 : 800 mL2 = 12 cmd2 =
Pipe 3 : 600 mL3 = 8 cmd3 =The total flow rate is 0.056 /m s3 of water at 20 Cc .
FM 6.50 The flow rate in each pipe is (A) 0.0166 /m sv1
3=o , 0.0277 /m sv23=o , 0.0116 /m sv3
3=o
(B) 0.0166 /m sv13=o , 0.0116 /m sv2
3=o , 0.0277 /m sv33=o
(C) 0.0277 /m sv13=o , 0.0166 /m sv2
3=o , 0.0116 /m sv33=o
(D) 0.0116 /m sv13=o , 0.0166 /m sv2
3=o , 0.0277 /m sv33=o
FM 6.51 The pressure drop across the system will be(A) 56 kPa (B) 55 kPa
(C) 550 kPa (D) 137.5 kPa
FM 6.52 For the Series -Parallel system of pipes shown in figure below, each pipe is 8 cmdiameter cast iron ( .f 0 0022, ) and the pressure drop 750 kPap p1 2- = . If the minor losses are neglected, what will be the resulting flow rate for water at 20 Cc ?
FM 6.53 Water at 80 Cc ( 3.65 10 /m s7 2n #= - ) flows with an average velocity of 2 /m s through a 120 mm diameter pipe. If the pipe wall roughness is small enough so that it does not protrude through the laminar sublayer and the pipe is to be considered as smooth ( .f 0 0125= ), what will be the largest roughness allowed to classify this pipe as smooth ?(A) 23.1 mm
(B) 0.0231 mm
(C) 0.00231 mm
(D) 0.231 mm
FM 6.54 The three water-filled tanks are connected by pipes as shown in figure. If minor losses are neglected, the flow rate in /m s3 in each pipe is
(A) .v 0 01441 =o , .v 0 02842 =o , .v 0 01413 =o
(B) .v 0 01411 =o , .v 0 01442 =o , .v 0 02843 =o
(C) .v 0 02841 =o , .v 0 01412 =o , .v 0 01443 =o
(D) .v 0 02841 =o , .v 0 01442 =o , .v 0 01413 =o
FM 6.55 A highly viscous liquid flows under the action of gravity from a large container through a small diameter pipe in laminar flow as shown in figure below. Disregarding entrance effects and velocity heads, the variation of fluid depth in the tank with time, is
(A) 32 lnk hH
b l (B) lnk hH64 b l
(C) lnk hH128 b l (D) lnk h
Hb l
where kgdLD
4
2
n=
FM 6.56 A triangular passages ( 52.9/ )Ref = of heat exchanger with 60 cmL = and an isosceles triangle cross section of side length 2 cma = and included angle 80cb = is shown in figure below. If the oil 870 / , 0.104 /kg m kg ms3r m= =^ h at 20 Cc flows at 2 /m s, the pressure drop will be
FM 6.57 An oil ( . . 0.87S G = and 2.2 10 /m s4 2n #= - ) flows at a rate of 4 10 /m s4 3#
- through a vertical pipe as shown in figure. The manometer reading h will be
(A) 18.5 m- (B) 13.87 m
(C) 13.87 m- (D) 18.5 m
FM 6.58 The water velocity at several locations along a cross section of 5 cm radius pipe is given in table below.
,cmr , /m sV
0 6.4
1 6.1
2 5.2
3 4.4
4 2.0
5 0.0
What will be the flow rate of water ?(A) 0.297 /m s3 (B) 0.0297 /m s3
(C) 2.97 /m s3 (D) 29.7 /m s3
FM 6.59 Oil ( 8900 /N m3g = , 0.10 /N s m2m -= ) flows through a 23 mm diameter horizontal tube as shown in figure. A differential U-tube manometer is used to measure the
FM 6.60 The water at 20 Cc flows from the tank as shown figure below, through the 3 cm long horizontal plastic pipe attached to the bottom of the tank. What time it will take to empty the tank completely, assuming the entrance to the pipe is well-rounded with negligible loss ? (Take the friction factor of the pipe to be 0.022.)
Since the flow is vertically downwards, so 90cq =- and
p p pinlet outletD = - ( )p gh p ghatm cylinder atm cylinderr r= + - =(because at inlet total pressure becomes patm and pressure due to oil in cylinder
ghcylinderr and at exit atmospheric pressure patm is there)
Therefore vactualo ( )sin
Lgh gL D
128cylinder
4
mr r q p= -
( )
Lg h L D
128cylinder
4
mr p= +
( 90 ) 1sin c- =-
. .. . ( . . ) ( . )
128 0 8374 0 20888 1 9 81 0 20 0 20 0 01 4
# #
# # # #p= +
5.1 10 /m s6 3#= -
So, the ratio of actual flow rate through the funnel to the maximum flow rate is
vv
max
actualoo
..
2 20 105 1 10
4
6
#
#= -
- 0.0232=
FM 6.31 Option (C) is correct.By moving through the manometer, we obtain the pressure change between points (1) and (2).
p gh gh g zw m w1 r r r D+ - - p2=or p p1 2- gh gh g zm w wr r r D= - + gh g zm w wr r r D= - +^ h
Note : The value 3.43 /m sV3 = is not a solution of the original equations,
equation (i), (ii) and (iii). With this value the right hand side of equation (vi) is
negative (i.e . . . . ( . ) .V103 6 11 14 103 6 11 14 3 43 24 532 2- = - =- ). As seen from the
left hand side of equation (vi), this cannot be. This extra root was introduced
by squaring equation (vi).
Thus v3o (0.08) 2.80 0.0141 /m sA V 43 32 3
# #p= = =
Also, from equation (iii)
60 1.529 5.10 (2.80)V12 2
#= + or 3.62 /m sV1 =
or v1o (0.10) 3.62 0.0284 /m sA V 41 12 3
# #p= = =
and from equation (i), we get
3.62 0.64 0.64 2.80V2 #= + or 2.86 /m sV2 =
or v2o (0.08) 2.86 0.014 /m sA V 4 42 22 3p
# #= = =
FM 6.55 Option (A) is correct.We take point (1) at the free surface of tank and point (2) at the exit of the pipe. Then, the energy equation between these two points.
gp
gV z2
11
12
1r a+ + gp
gV z h2 L
22
22
2r a= + + +
Since ,p p patm1 2= = ,V 01 , 0,z2 = and V 02 = (Velocity head negligible)
Above equation becomes
z1 hL= and h hL=where h is the liquid height in the tank at any time t .
Now hL f dL
gV2
2
#=
For fully developed laminar flow
f /Re Vd
64 64n= =
Thus hL Vd d
Lg
V642
2
n# #=
dL
gV6422
n#=
The average velocity
V Av
dv
dv
4
4c
2 2
p p= = =o o o
hL d
Lg d
v6421 4
2 2n
p# #= o
dL
d gv
g dLv64
24 128
2 2 4#
np p
n#= =o o
h hL = g d
Lv1284p
n= o ...(i)
From mass conservation, above equation must be equal to change of liquid height in the tank.
The flow is laminar and flow rate is given by ( 90cq = )
vo ( )
lp l D128
4
mp gD= -
or p p pD
lv l1281 2 4p
m gD = - = +o
...(i)
Thus g . . 0.87 9.81 8.53 /kN mS G H O 32# #= = =g
and m ( . . ) 2.2 10 0.87 999 0.191 /N s mS G H O4 2
2nr n r # # # -= = = =-
Equation (i) gives
pD ( . )
. 8.53 10 40 020
128 0 191 4 4 104
43
#
# # # ##p #= +
-
. 10 / . /N m kN m1 119 111 95 2 2#= = ...(ii)
From manometer equation,
p2 p h h hm1 1 2g g g= - + -
Where mg g. . 1.3 9.81 12.74 /kN mS G H Om3
2 #= = =and h2 h l h1= + - or h h h l2 1+ = +Thus p p1 2- g( ) ( )p h h h h lm m2 1 g g g gD= = + - =- - +
...(iii)Combine equation (ii) and (iii), we get
.111 9 (12.74 8.53) 8.53 4h #=- - +or h 18.5 m=-Note: Since h 0< , the manometer is displaced in the direction opposite that shown in the original figure.
FM 6.58 Option (B) is correct.The divided cross section of the pipe into 1 cm thick annual regions is shown in table.The flow rate is to be determined by using midpoint velocity values for each section. Therefore
vo [ ]V dA V r ravg cA
avg out in2 2
c
pS= = -#
. . (0.01) 0 . . 0.02 0.0126 4 6 1
26 1 5 22 2 2p p# # #= + - + + -b b ] ]l l g g6 6@ @
. . . . . . 0.04 0.0325 2 4 4 0 03 0 02 2
4 4 2 0 2 22 2p p# # #+ + - + + -b ] ] b ] ]l g g l g g6 6@ @
Thus the minimum h is h 0= (no flow) and the maximum h is for Re 2100= .
2100 .. .V
0 19 818900 0 023# #
=b l
gr g=
or V 10.06 /m s=For the flowing fluid, Bernoulli’s equation gives
pg
V z21 1
2
1g + + pg
V z fDl
gV
2 22 2
2
2
2
g= + + + z z1 2=
and V V V1 2= =
Thus p p1 2- f Dl
gV2
2
# # g=
(i)
And for laminar flow
f Re64= or .f 2100
64 0 0305= =
From equation (i),
pD 0.0305 ..
.( . )
8900p p 0 0230 5
2 9 8110 06
1 2
2
## # #= - =
304 /N m39 2=From manometer equation, we get
( ) . .p H h S G h HH Ooil oil1 2g g+ + - -g p2= p p p1 2D = - ( . . )S G hH O2 g= -g
or h ( )
0.5 m7 9800 8900
30439 10#
= - =
Hence 0.5 mh0 10# #
FM 6.60 Option (C) is correct.
We take point (1) at free surface of the tank and point (2) at the reference level at exit. By applying energy equation for a control volume between these two points
gp
gV z h2 pump
11
12
1r a+ + + gp
gV z h h2 turbine L
22
22
2r a= + + + +
Since p p patm1 2= = , 0,z2 = h 0turbine = , and 0V1 ,