4. FLUID MECHANICS AND MACHINERY

GATE 1995 1. A fluid is said to be Newtonian when the shear stress is

(A) directly proportional to the velocity gradient

(B) inversely proportional to the velocity gradient

(C) independent of the velocity gradient

(D) none of the above

2. In fully developed laminar flow in a circular pipe, the head loss due to friction is directly

proportional to …………… (mean velocity/square of the mean velocity)

3. State TRUE or FALSE

The specific speed of an impulse hydraulic turbine will be greater than the specific

speed of a reaction type hydraulic turbine.

4. The force F needed to support the liquid of density d and the vessel on top in the

figure below is:

(A) gd [ha - ( H-h) A] (B) gdHA

(C) gdHa (D) gd (H-h) A

5. The velocity components in the x and y directions are given by

u = λxy3 - x2y

v = xy2 - 3/4y4

The value of λ for a possible flow field involving an incompressible fluid is:

(A) - 3/4 (B) - 4/3 (C) 4/3 (D) 3

GATE 1996 6. In flow through a pipe, the transition from laminar to turbulent flow does not

depend on

(A) velocity of the fluid (B) density of the fluid

(C) diameter of the pipe (D) length of the pipe

7. The dimension of surface tension is

(A) ML-1 (B) L2T-1 (C) ML-1T-1 (D) MT-2

8. A mercury manometer is used to measure the static pressure at a point in a water pipe

as shown in Fig. The level difference of mercury in the two limbs is 10 mm. The gauge

pressure at that point is

(A) 1236 Pa (B) 1333 Pa (C) zero (D) 98 Pa

9. For laminar flow through a long pipe, the pressure drop per unit length increases

(A) in linear proportion to the cross-sectional area

(B) in proportion to the diameter of the pipe

(C) in inverse proportion to the cross-sectional area

(D) in inverse proportion to the square of cross-sectional area

GATE 1997

10. The specific speed of a centrifugal compressor is generally

(A) higher than that of an axial compressor

(B) less than that of a reciprocating compressor

(C) independent of the type of compressor, but depends only on the size of the

compressor

(D) more than the specific speed of the reciprocating compressor but less that of the

axial compressor

11. Kaplan turbine is

(A) a high head mixed flow turbine (B) a low head axial flow turbine

(C) an outward flow reaction turbine (D) an impulse inward flow turbine

12. Refer to figure, the absolute pressure of gas A in the bulb is

(A) 771.2 mm Hg

(B) 752.65 mm Hg

(C) 767.35 mm Hg

(D) 748.8 mm Hg

13. The Reynolds number for flow of a certain fluid in a circular tube is specified as 2500.

What will be the Reynolds number when the tube diameter is increased by 20% and

the fluid velocity is decreased by 40% keeping fluid the same?

(A) 1200 (B) 1800 (C) 3600 (D) 200

14. The following data pertain to a single stage impulse steam turbine:

Nozzle angle = 20°

Blade velocity = 200 m/s

Relative steam velocity at entry = 350 m/s

Blade inlet = 30°

Blade exit angle = 25°

If blade friction is neglected, the work done per kg steam is

(A) 124 kJ (B) 164 kJ (C) 169 kJ (D) 174 kJ

GATE 1998

15. If VN and α are the nozzle exit velocity and nozzle angle in an impulse turbine, the

optimum blade velocity is given by

(A) VN cos 2α (B) VN sin 2α (C) �� ���α

� (D) ��

16. Curtis stage, Rateau stage and a 50% reaction stage in a steam turbine are examples

of

(A) different types of impulse stages

(B) different types of reaction stages

(C) a simple impulse stage, a velocity compounded impulse stage and reaction stage

(D) a velocity compounded impulse stage, a simple impulse stage and a reaction

stage

17. For the data listed below for two journal bearings A and B, predict the flow conditions

in the bearings

(A) laminar in both A and B (B) turbulent in both A and B

(C) laminar in A and turbulent in B (D) turbulent in A and laminar B

18. The isentropic heat drop in the nozzle of an impulse steam turbine with a nozzle

efficiency 0.9, blade velocity ratio 0.5, and mean blade velocity 150 m/s in kJ/kg is

(A) 50 (B) 40 (C) 60 (D) 75

19. The discharge velocity at the pipe exit in

figure is

(A) 2�

(B) 2��

(C) �� � ��

(D) 0

20. Match the correct pairs between List I and List II

List I List II

(A) High head, low flow rate (1) Streamlined body

(B) Low head, high flow rate (2) Boundary layer

(C) Heat transfer (3) Orifice meter

(D) Low drag (4) Centrifugal pump

(5) Axial flow pump

(6) Nusselt number

GATE 1999

21. If ‘p’ is the gauge pressure within a spherical droplet, the gauge pressure within bubble

of the same fluid and of same size will be

(A) p/4 (B) p/2 (C) p (D) 2p

22. If velocity of water inside a smooth tube is doubled, the turbulent flow heat transfer

coefficient between the water and the tube will

(A) remain unchanged

(B) increase to double its value

(C) increase but will not reach double its value

(D) increase to more than double its value

23. Kinematic viscosity of air at 20˚C is given to be 1.6×10-5m2/s. Its kinematic viscosity at

70˚C will be very approximately:

(A) 2.2×10-5 m2/s (B) 1.6×10-5 m2/s

(C) 1.2×10-5 m2/s (D) 10-5 m2/s

24. Which of the following statements does NOT apply to the volumetric efficiency of a

reciprocating air compressor

(A) It decreases with increase in inlet temperature

(B) It increases with decrease in pressure ratio

(C) It increases with decrease in clearance ratio

(D) It decreases with increase in clearance to stroke ratio

25. Water flows through a vertical contraction from a pipe of diameter d to another of

diameter d/2. The flow velocity at the inlet to the contraction is 2 m/s and pressure

200kN/m2. If the height of the contraction measures 2m, the pressure at the exit of the

contraction will be very nearly

(A) 168 kN/m2 (B) 192 kN/m2 (C) 150 kN/m2 (D) 174 kN/m2

GATE 2000

26. Which of the following is a pressure compounded turbine?

(A) Parsons (B) Curtis (C) Rateau (D) all the three

27. When the speed of a centrifugal pump is doubled, the power required to drive the

pump will

(A) increase 8 times (B) increase 4 times

(C) double (D) remain the same

28. In Figure, if the pressure of gas in bulb A is 50 cm Hg vacuum and , patm = 76 cm Hg,

the height of column H is equal to

(A) 26 cm

(B) 50 cm

(C) 76 cm

(D) 126 cm

29. Navier Strokes equation represents the conservation of

(A) Energy (B) mass

(C) Pressure (D) momentum

30. For a compressible fluid, sonic velocity is

(A) a property of the fluid

(B) always given by (γRT)1/2 , where γ, R and T are respectively the ratio of specific

heats, gas constant and temperature in K

(C) always given by (∂p/∂ρ)s1/2 where p, ρ and s are respectively pressure, density and

entropy.

(D) always greater than the velocity of fluid at any location.

GATE 2001

31. The SI unit of kinematic viscosity (ν) is

(A) m2 / sec (B) kg / (m-sec)

(C) m / sec2 (D) m3 / sec2

32. A static fluid can have

(A) non-zero normal and shear stress

(B) negative normal stress and zero shear stress

(C) positive normal stress and zero shear stress

(D) zero normal stress and non-zero shear stress

33. The Rateau turbine belongs to the category of

(A) pressure compounded turbine

(B) reaction turbine

(C) velocity compounded turbine

(D) radial flow turbine

34. A single-acting two-stage compressor with complete intercooling delivers air at 16 bar.

Assuming an intake state of 1 bar at 15°C, the pres sure ratio per stage is

(A) 16 (B) 8 (C) 4 (D) 2

35. The 2-D flow with velocity �� = (x+2y+2)�� + (4-y)�� is

(A) compressible and irrotational

(B) compressible and not irrotational

(C) incompressible and irrotational

(D) incompressible and not irrotational

GATE 2002

36. A positive value of Joule-Thomson coefficient of a fluid means

(A) temperature drops during throttling

(B) temperature remains constant during throttling

(C) temperature rises during throttling

(D) none of these

37. If there are m physical quantities and n fundamental dimensions in a particular

process, the number of non-dimensional parameters is

(A) m + n

(B) m × n

(C) m - n

(D) m / n

38. If x is the distance measured from the leading edge of a flat plate, the laminar

boundary layer thickness varies as

(A) l/x (B) x4/5 (C) x2 (D) x1/2

39. Flow separation in flow past a solid object is caused by

(A) a reduction of pressure to vapour pressure

(B) a negative pressure gradient

(C) a positive pressure gradient

(D) the boundary layer thickness reducing to zero

40. The value of Biot number is very small (less than 0.01) when

(A) the convective resistance of the fluid is negligible

(B) the conductive resistance of the fluid is negligible

(C) the conductive resistance of the solid is negligible

(D) none of these

GATE 2003

41. Considering the variation of static pressure and absolute velocity in an impulse stream

turbine, across one row of moving blades

(A) both pressure and velocity decrease

(B) pressure decreases but velocity increases

(C) pressure remains constant, while velocity increases

(D) pressure remains constant, while velocity decreases

42. A water container is kept on a weighting balance. Water from a tap is falling vertically

into the container with a volume flow rate of Q; the velocity of the water when it hits the

water surface is U. At a particular instant of time the total mass of the container and

water is m. The force registered by the weighing balance at this instant of time is

(A) mg + ρQU (B) mg + 2ρQU

(C) mg + ρQU2/2 (D) ρQU2/2

43. Air flows through a venturi and into atmosphere. Air density is ρ; atmospheric pressure

is Pa ; throat diameter is Dt ; exit diameter is D and exit velocity is U. the throat is

connected to a cylinder containing a frictionless piston attached to a spring. The spring

constant is k. the bottom surface of the piston is exposed to atmosphere. Due to the

flow, the piston moves by distance x. assuming incompressible frictionless flow, x is

(A) (ρQU2/2) ᴨD2s

(B) (ρU2/8k) ���

�� � 1� ᴨD2s

(C) (ρU2/2k) ���

�� � 1� ᴨD2s

(D) (ρU2/8k) ���

�� � 1� ᴨD2s

44. A centrifugal pump running at 500 rpm and at its maximum efficiency is delivering a

head of 30m at a flow rate of 60 liters per minute. If the rpm is changed to 1000, then

the head H in meters and flow rate Q in liters per minute at maximum efficiency are

estimated to be

(A) H = 60, Q = 120

(B) H = 120, Q = 120

(C) H = 60, Q = 480

(D) H = 120, Q = 30

45. Match the following

P. Curtis 1. Reaction steam turbine

Q. Rateau 2. Gas turbine

R. Kaplan 3. Velocity compounding

S. Francis 4. Pressure compounding

5. Impulse water turbine

6. Axial turbine

7. Mixed flow turbine

8. Centrifugal pump

(A) P – 2 Q – 1 R – 7 S - 6 (B) P – 3 Q – 1 R – 5 S - 7

(C) P – 1 Q – 3 R – 1 S – 5 (D) P – 3 Q – 4 R – 7 S - 6

GATE 2004

46. An incompressible fluid (kinematic viscosity, 7.4 ×10-7 m2/s, specific gravity, 0.88) is

held between two parallel plates. If the top late is moved with a velocity of 0.5 m/s

while the bottom one is held stationary, the fluid attains a linear velocity profile in the

gap of 0.5 mm between these plates; the shear stress in Pascals on the surface of top

plate is

(A) 0.651×10-3 (B) 0.651

(C) 6.51 (D) 0.651×103

47. A fluid flow is represented by the velocity field ���= ax�� + ay��, where a is a constant. The

equation of streamline passing through a point (1, 2) is

(A) x – 2y = 0

(B) 2x + y = 0

(C) 2x – y = 0

(D) x + 2y = 0

48. For a fluid flow through a divergent pipe of length L having inlet and outlet radii and R1

and R2 respectively and a constant flow rate of Q, assuming the velocity to be axial

and uniform at any cross section, the acceleration at the exit is

(A) 2Q (R1 - R2) / π LR23

(B) 2Q2 (R1 - R2) / π2 LR2

3

(C) 2Q2 (R1 - R2) / π2 LR2

5

(D) 2Q2 (R2 – R1) / π2 LR2

5

49. The following data about the flow of liquid was observed in a continuous chemical

process plant

Flow rate

(litres/sec) 7.5 to 7.7 7.7 to 7.9 7.9 to 8.1 8.1 to 8.3 8.3 to 8.5 8.5 to 8.7

Frequency 1 5 35 17 12 10

Mean flow rate of the liquid is

(A) 8.00 litres/sec (B) 8.096 litres/sec

(C) 8.16 litres/sec (D) 8.26 litres/sec

50. For air flow over a flat plate, velocity (U) and boundary layer thickness (δ) can be

expressed respectively, as

! =

"�

#$ − %� �#

$�"; δ =

&.(&)*+,

If the free stream velocity is 2m/s, and air has kinematic viscosity of 1.5×10-5 m2/s and

density of 1.23 kg/m3, the wall shear stress at x = 1m, is

(A) 2.36 × 102 N/m2 (B) 43.6 × 10-3 N/m2

(C) 4.36 × 10-3N/m2 (D) 2.18 × 10-3 N/m2

51. A Centrifugal pump is required to pump water to an open water tank situated 4km

away from the location of the pump through a pipe of diameter 0.2m having Darcy’s

friction factor of 0.01. The average speed of water in the pipe is 2 m/s. If it is maintain

a constant head of 5 m in the tank, neglecting other minor losses, the absolute

discharge pressure at the pump exit is

(A) 0.449 bar (B) 5.503 bar (C) 44.911 bar (D) 55.203 bar

52. The pressure gauges G1 and G2 installed on the system show pressures of PG1 = 5.00

bar and PG2 = 1.00 bar. The value of unknown pressure P is

(A) 1.01 bar (B) 2.01 bar (C) 5.00 bar (D) 7.01 bar

53. Match the following

P. Reciprocating pump 1. Plant with power output below 100 kW

Q. Axial flow pump 2. Plant with power output b/w 100 kW to MW

R. Microhydel plant 3. Positive displacement

S. Backward curved vanes 4. Draft tube

5. High flow rate, low pressure ratio

6. Centrifugal pump impeller

(A) P-3 Q-5 R-6 S-2 (B) P-3 Q-5 R-2 S-6

(C) P-3 Q-5 R-1 S-6 (D) P-4 Q-5 R-1 S-6

GATE 2005

54. The velocity components in the x and y directions of a two dimensional potential flow

are u and v respectively. Then ∂u/∂x is equal to

(A) ∂v/∂x (B) - ∂v/∂x (C) ∂v/∂y (D) - ∂v/∂y

55. A venturimeter of 20 mm throat diameter is used to measure the velocity of water in a

horizontal pipe of 40 mm diameter. If the pressure difference between the pipe and

throat sections is found to be 30 kPa, then neglecting frictional losses, the flow velocity

is

(A) 0.2 m/s (B) 1.0 m/s (C) 1.4 m/s (D) 2.0 m/s

56. A U-tube manometer with a small quantity of mercury is used to measure the static

pressure difference between two locations A and B in a conical section through which

an incompressible fluid flows. At a particular flow rate, the mercury column appears as

shown in the figure. The density of mercury is 13600 kg/m3 and g = 9.81 m/s2. Which of

the following is correct?

(A) Flow direction is A to B and PA – PB = 20 kPa

(B) Flow direction is B to A and PA – PB = 1.4 kPa

(C) Flow direction is A to B and PB – PA = 20 kPa

(D) Flow direction is B to A and PB – PA = 1.4 kPa

57. In the velocity diagram shown below, u = blade velocity, C = absolute fluid velocity and

w = relative velocity of fluid and the subscripts 1 and 2 refer to inlet and outlet. This

diagram is for

(A) an impulse turbine (B) a reaction turbine

(C) a centrifugal compressor (D) an axial flow compressor

GATE 2006

58. For a Newtonian fluid

(A) shear stress is proportional to shear strain

(B) rate of shear stress is proportional to shear strain

(C) shear stress is proportional to rate of shear strain

(D) rate of shear stress is proportional to rate of shear strain

59. In a two-dimensional velocity field with velocities u & ν along the x & y directions

respectively, the convective acceleration along the x-direction is given by

(A) u ∂u/∂x + ν ∂u/∂y (B) u ∂u/∂x + ν∂ν/∂y

(C) u ∂v/∂x + ν ∂u/∂y (D) v ∂u/∂x + u ∂u/∂y

60. In a Pelton wheel, the bucket peripheral speed is 10 m/s, the water jet velocity is

25 m/s and volumetric flow rate of the jet is 0.1m3/s .If the jet deflection angle is 120°

and the flow is ideal, the power developed is

(A) 7.5 kW (B) 15.0 kW (C) 22.5 kW (D) 37.5 kW

61. A two-dimensional flow field has velocities along the x and y directions given by

u = x2 t and ν = - 2xyt respectively, where t is time. The equation of streamlines is:

(A) x2y = constant (B) xy2 = constant

(C) xy = constant (D) not possible to determine

62. The velocity profile in fully developed laminar flow in a pipe of diameter D is given by

u = uo (1- 4r2/D2) where r is the radial distance from the center. If the viscosity of the

fluid is µ, the pressure drop across a length L of the pipe is

(A) µuoL / D2 (B) 4µuoL / D2 (C) 8µuoL / D2 (D) 16µuoL / D2

63. A siphon draws water from a reservoir and discharges it out at atmospheric pressure.

Assuming ideal fluid and the reservoir is large, the velocity at point P in the siphon

tube is

(A) 2gh%

(B) 2gh�

(C) 2g�h� � h%�

(D) 2g�h� � h%�

64. A large hydraulic turbine is to generate 300 kW at 1000 rpm under a head of 40 m.

For initial testing, a 1:4 scale model of the turbine operates under a head of 10 m. the

power generated by the model (in kW) will be

(A) 2.34 (B) 4.68

(C) 9.38 (D) 18.75

65. A horizontal shaft centrifugal pump lifts ware at 65°C. The suction nozzle is one meter

below pump centerline. The pressure at this point equal 200 kPa gauge and velocity is

3 m/s. Steam tables show saturation pressure at 65°C is 25 kPa, and specific volume

of the saturated liquid is 0.001020 m3/kg. The pump Net Positive suction Head (NPSH)

in meters is

(A) 24 (B) 26 (C) 28 (D) 30

GATE 2007

66. Water has a critical volume of 0.003155 m3/kg. A closed and rigid steel tank of volume

0.025m3 contains a mixture of water and steam at 0.1MPa. The mass of the mixture is

10kg. The tank is now slowly heated. The liquid level inside the tank

(A) will rise

(B) will fall

(C) will remain constant

(D) may rise or fall depending on the amount of heat transferred

67. Consider an incompressible laminar boundary layer flow over a flat plate of length L,

aligned with the direction of an oncoming uniform free steam. If F is the ratio of the

drag force on the front half of the plate to the drag force on the rear half, then

(A) F < 1/2 (B) F = 1/2 (C) F = 1 (D) F > 1

68. In a steady flow through a nozzle, the flow velocity on the nozzle axis is given by

v = uo (1+3x/L) i, where x is the distance along the axis of the nozzle from its inlet

plane and L is the length of the nozzle. The time required for a fluid particle on the axis

to travel from the inlet to the exit plane of the nozzle is

(A) /

01 (B)

/"01

ln 4

(C) /

&01 (D)

/�.201

69. Consider steady laminar incompressible axi-symmetric fully developed viscous flow

through a straight circular pipe of constant cross sectional area at a Reynolds number

of 5. The ratio of inertia force to viscous force on a fluid particle is

(A) 5 (B) 1/5 (C) 0 (D) ∞

70. The inlet angle of runner blades of a Francis turbine is 90˚. The blades are so shaped

that the tangential component of velocity at blade outlet is zero. The flow velocity

remains constant throughout the blade passage and is equal to half of the blade

velocity at runner inlet. The blade efficiency of the runner is

(A) 25% (B) 50% (C) 80% (D) 89%

71. A model of a hydraulic turbine is tested at a head of 1/4th of that under which the full

scale turbine works. The diameter of the model is half of that of the full scale turbine. If

N is the RPM of the full scale turbine, then the RPM of the model will be

(A) N/4 (B) N/2 (C) N (D) 2N

72. Which combination of the following statements about steady incompressible forced

vortex flow is correct?

P: Shear stress is zero at all points in the flow.

Q: Vorticity is zero at all points in the flow.

R: Velocity is directly proportional to the radius from the centre of the vortex.

S: Total mechanical energy per unit mass is constant in the entire flow field

(A) P and Q (B) R and S (C) P and R (D) P and S

73. Match the following

Column I Column II

P Centrifugal compressor 1. Axial flow

Q Centrifugal pump 2. Surging

R Pelton wheel 3. Priming

S Kaplan turbine 4. Pure impulse

(A) P – 2 Q – 3 R – 4 S - 1 (B) P – 2 Q – 3 R – 15 S - 4

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

GATE 2008

74. For flow of fluid over a heated plate, the following fluid properties are known:

Viscosity = 0.001 Pa.s; specific heat at constant pressure = 1kJ/kg.K; thermal

conductivity = 1W/mK. The hydrodynamic boundary layer thickness at a specified

location on the plate is1 mm. The thermal boundary layer thickness at the same

location is

(A) 0.001 mm (B) 0.01mm (C) 1mm (D) 1000mm

75. For the continuity given by ∇���.∇��� = 0 to be valid, where ∇��� is the velocity vector, which

one of the following is a necessary condition?

(A) Steady flow (B) Irrotational flow

(C) Inviscid flow (D) Incompressible flow

76. In a steady state steady flow process taking place in a device with a single inlet and a

single outlet, the work done per unit mass flow rate is given by w = -4 �567089+8:;9+8 , where

v is the specific volume and p is the pressure. The expression for w given above

(A) is valid only if the process is both reversible and adiabatic

(B) is valid only if the process is both reversible and isothermal

(C) is valid for any reversible process (D) is incorrect; it must be w = -4 65�7089+8:;9+8

77. Water having a density of 1000kg/m3, issues from a nozzle with a velocity 0f 10 m/s

and the jet strikes a bucket mounted on a pelton wheel. The wheel rotates at 10 rad/s.

The mean diameter of the wheel is 1m. The jet is split into two equal streams by the

bucket, such that each stream is deflected by 120˚, as shown in the fig. Friction in the

bucket may be neglected. Magnitude of the torque exerted by the water on the wheel,

per unit mass flow rate of the incoming, jet is

(A) 0 (N.m) / (kg/s) (B) 1.25 (N.m) / (kg/s)

(C) 2.5 (N.m) / (kg/s) (D) 3.75 (N.m) / (kg/s)

GATE 2009

78. A frictionless piston-cylinder device contains a gas initially at 0.8MPa and 0.015 m3.

It expands quasi-statically at constant temperature to a final volume of 0.030 m3.The

work output (in kJ) during this process will be

(A) 8.32 (B) 12.00 (C) 554.67 (D) 8320.00

79. A compressor undergoes a reversible, steady flow process. The gas at inlet and outlet

of the compressor is designated as state 1 and state 2 respectively. Potential and

kinetic energy changes are to be ignored. The following notations are used:

ν = specific volume and P = pressure of the gas.

The specific work required to be supplied to the compressor for this gas compression

process is

(A) 4 <5��% (B) 4 �5<�

% (C) �%�<� � <%� (D) − <���% � ���

80. Water at 25°C is flowing through a 1.0km long G .I pipe of 200mm diameter at the rate

of 0.07m3/s. If value of Darcy friction factor for this pipe is 0.02 and density of water is

1000kg/m3 , the pumping power (in kW) required to maintain the flow is

(A) 1.8 (B) 17.4 (C) 20.5 (D) 41.0

81. Consider steady, incompressible and irrotational flow through a reducer in a horizontal

pipe where the diameter is reduced from 20cm to 10cm. The pressure in the 20cm

pipe just upstream of the reducer is 150kPa. The fluid has a vapour pressure of 50kPa

and a specific weight of 5 kN /m3. Neglecting frictional effects, the maximum discharge

(in m3/s) that can pass through the reducer without causing cavitation is

(A) 0.05 (B) 0.16

(C) 0.27 (D) 0.38

82. You are asked to evaluate assorted fluid flows for their suitability in a given laboratory

application. The following three flow choices, expressed in terms of the two-

dimensional velocity fields in the xy-plane, are made available.

P. u = 2y, v = - 3x

Q. u = 3xy, v = 0

R. u = 2x, v = 2y

Which flow(s) should be recommended when the application requires the flow to be

incompressible and irrotational?

(A) P and R (B) Q

(C) Q and R (D) R

83. The velocity profile of a fully developed laminar flow in a straight circular pipe, as

shown in the figure, is given by the expression

u (r) = - *�&= >?@

?AB >1 � C�*�B Where >?@

?AB is a constant.

The average velocity of fluid in the pipe is

(A)- *�D= >?@

?AB (B) - *�&= >?@

?AB

(C) - *��= >?@

?AB (D) - *�= >?@

?AB

GATE 2010

84. The maximum velocity of a one-dimensional incompressible fully developed viscous

flow, between two fixed parallel plates, is 6ms-1. The mean velocity (ms-1) of the flow is

(A) 2 (B) 3 (C) 4 (D) 5

85. A phenomenon is modeled using n dimensional variables with k primary dimensions.

The number of non-dimensional variables is

(A) k (B) n

(C) n-k (D) n+k

86. A hydraulic turbine develops 1000kW power for a head of 40m. If the head is reduced

to 20m, the power developed (in kW) is

(A) 177 (B) 354

(C) 500 (D) 707

87. A smooth pipe of diameter 200mm carries water. The pressure in the pipe at section

S1 (elevation: 10m) is 50kPa. At Section S2 (elevation: 12m) the pressure is 20kPa

and velocity is 2ms-1Density of water is 1000kgm-3 and acceleration due to gravity is

9.8ms-2.Which of the following is TRUE?

(A) flow from S1 to S2 and head loss is 0.53 m

(B) flow from S2 to S1 and head loss is 0.53 m

(C) flow from S1 to S2 and head loss is 1.06 m

(D) flow from S2 to S1 and head loss is 1.06 m

88. Match the following

P:Compressible flow U:Reynolds number

Q:Free surface flow V:Nusselt number

R:Boundary layer flow W:Weber number

S:Pipe flow X:Froude number

T:Heat convection Y:Mach number

Z:Skin friction coefficient

(A) P-U; Q-X; R-V; S-Z; T-W

(B) P-W; Q-X; R-Z; S-U; T-V

(C) P-Y; Q-W; R-Z; S-U; T-X

(D) P-Y; Q-W; R-Z; S-U; T-V

GATE 2011

89. A streamline and an equipotential line in a flow field

(A) Are parallel to each other

(B) Are perpendicular to each other

(C) Intersect at an acute angle

(D) Are identical

90. A pump handling a liquid raises its pressure from 1 bar to 30 bar. Take the density of

the liquid as 990kg / m3 . The isentropic specific work done by the pump in kJ/kg is

(A) 0.10 (B) 0.30

(C) 2.50 (D) 2.93

91. The ratios of the laminar hydrodynamic boundary layer thickness to thermal boundary

layer thickness of flows of two fluids P and Q on a flat plate are 1/2and 2 respectively.

The Reynolds number based on the plate length for both the flows is 104 . The Prandtl

and Nusselt numbers for P are 1/8and 35 respectively. The Prandtl and Nusselt

numbers for Q are respectively

(A) 8 and 140

(B) 8 and 70

(C) 4 and 70

(D) 4 and 35

92. Figure shows the schematic for the measurement of velocity of air (density = 1.2kg/m3)

through a constant–area duct using a pitot tube and a water-tube manometer. The

differential head of water (density = 1000kg /m3 ) in the two columns of the manometer

is 10mm. Take acceleration due to gravity as 9.8m/ s2. The velocity of air in m/s is

(A) 6.4 (B) 9.0 (C) 12.8 (D) 25.6

GATE 2012

93. Oil flows through a 200 mm diameter horizontal cast iron pipe

(friction factor, f = 0.0225) of length 500 m. The volumetric flow rate is 0.2 m3/s. The

head loss (in m) due to friction is (assume g = 9.81m/s2)

(A) 116.18 (B) 0.116 (C) 18.22 (D) 232.36

94. The velocity triangle at the inlet and exit of the rotor of a turbomachine are shown.

V denotes the absolute velocity of the fluid, W denotes the relative velocity of the fluid

and U denotes the blade velocity. Subscripts 1 and 2 refer to inlet and outlet

respectively. If V2 = W1 and V1 = W2 , then the degree of reaction is

(A) 0 (B) 1 (C) 0.5 (D) 0.25

95. An incompressible fluid flows over a flat plate with zero pressure gradient. The

boundary layer thickness is 1 mm at a location where the Reynolds number is 1000. If

the velocity of the fluid alone is increased by a factor of 4, then the boundary layer

thickness at the same location, in mm will be

(A) 4 (B) 2 (C) 0.5 (D) 0.25

96. A large tank with a nozzle attached contains three immiscible, inviscid fluids as shown.

Assuming that the changes in h1,h2 and h3 are negligible, the instantaneous discharge

velocity is

(A) E2��" �1 � FGFH

IGIH � F�

FHI�IH�

(B) 2���% � �� � �"�

(C) E2� �FGIGJF�I�JFHIHFGJF�JFH

�

(D) E2� �FGI�IHJF�IHIGJFHIGI�FGIGJF�I�JFHIH

�

ANSWERS

1. A 2. Meanvelocity 3. False 4. 5. D

6. A 7. D 8. B 9. C 10. D

11.B 12.A 13.B 14. 15.D

16.C 17. 18.A 19.B 20.A-4, B-5, C-6, D-1

21.D 22.C 23.A 24.A 25.C

26.C 27.B 28.A 29.D 30.B

31.A 32.B 33.A 34.C 35.D

36.A 37.C 38.D 39.D 40.A

41.D 42.A 43.D 44.D 45.D

46.B 47.C 48.B 49.C 50.A

51.B 52.C 53.C 54.D 55.D

56.A 57.B 58.C 59.A 60.C

61.A 62.D 63.C 64.A 65.C

66.B 67.C 68.D 69.A 70.D

71.C 72.C 73.A 74.C 75.D

76.C 77.D 78.A 79.B 80.B

81.B 82.D 83.A 84.C 85.B

86.B 87.C 88.D 89.B 90.D

91.A 92.C 93.A 94.C 95.C

96.A