FM Objective Pdf

FLUID MECHANICS
4 FLUID DYNAMICS

CLASS WORK QUESTIONS :

TWO MARKS QUESTIONS
1. Figure shows the schematic for the measurement of velocity of air (density = 1.2 kg/m3) through

a constant - area duct using a pitot tube and a water-tube manometer. The differential head of
water (density = 1000 kg/m3) in the two columns of the manometer is 10 mm. Take acceleration
due to gravity as 9.8 m/s2. The velocity of air in m/s is

[GATE-ME-11]
a) 6.4

b) 9.0

c) 12.8

d) 25.6

2. A water container is kept on a weighing 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 [GATE-ME-03]

a) mg + ρ QU b) mg + 2 ρ QU c) mg + ρ QU2/2 d) ρ QU2/2

3. A mercury manometer is attached to a section of the pipe shown in the figure. Mercury levels

are indicated when there is no water flowing through the pipe. When water starts flowing through

the pipe continuously at contant rate in the direction of the arrow, the level of mercury at B :

[GATE-ME-87]

4. 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 imcompressible
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 ?
[GATE-ME-05]

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FLUID MECHANICS

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

5. A smooth pipe of diameter 200 mm carries water. The pressure in the pipe at section S1

(elevation : 10 m) is 50 kPa. At section S2 (elevation : 12 m) the pressure is 20 kPa and velocity

is 2 ms-1. Density of water is 1000 kgm-3 and acceleration due to gravity is 9.8 ms-2. Which of

the following is TRUE ? [GATE-ME-10]

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

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

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

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

6. A jet of water issues from a Nozzle with a velocity 20 m/s and it impinges normally on a flat

plate moving away from it at 10 m/s. The cross-sectional area of the jet is 0.01 m2, and the

density of water = 1000 kg/m3. The force developed on the plate is : [GATE-ME-90]

a) 1000 N
b) 100 N
c) 10 N
d) 2000 N

7. 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 instantaneoous discharge velocity
is [GATE-ME-12]
a)

b)

c)

d)

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FLUID MECHANICS

8. Water flows through a pipe of diameter 0.30 m. What would be the velocity V for the conditions

shown in the figure below ? [GATE-ME-88]

9. Consider steady incompressible and irrotational flow through a reducer in a horizontal pipe

where the diameter is reduced from 10 cm. The pressure in the 20 cm pipe just upstream of the

reducer is 150 kPa. The fluid has a vapour pressure of 50 kPa and a specific weight of 5 kN/m3.

Neglecting frictional effect, the maximum discharge (in m3/s) that can pass through the reducer

without causing cavitation is [GATE-ME-09]

a) 0.05 b) 0.16 c) 0.27 d) 0.38

10. Air flows through a venture 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, then ‘x’ is

[GATE-ME-03]

a) (ρU2/2K) - Ds2

b) (ρU2/8K) D4 π Ds2
-1

Dt4

c) (ρU2/2K) D2 π Ds2
-1

Dt2

d) (ρU2/2K) D4 π Ds2
-1
t
D4

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FLUID MECHANICS

11. A fan in the duct shown below sucks air from the ambient and expels it as a jet at 1 m/s to the
ambient. Determine the gauge pressure at the point marked as A. Take the density of air as
1 kg/m3.

12. In a syringe as shown in the figure, a piston of 1 cm2 cross section is pushed at a constant speed

of 10 cm/s to eject water through an outlet of 1mm2. Determine the force requied to move the

piston. Neglecting osses. [GATE-ME-89]

13. Water is coming out from a tap and falls vertically downwards.At the tap opening, the stream diameter
is 20 mm with uniform velocity of 2 m/s. Accele2ragti(oZnQd−ueZtRo)gravity is 9.81 m/s2. Assuming steady,

inviscid flow, constant atmospheric pressure everywhere and neglecting curvature and surface tension

effects, the diameter in mm of the stream 0.5 m below the tap is approximately. (GATE-ME-13)

a) 10 b) 15 c) 20 d) 25

14. An ideal water jet with volume flow rate of 0.05 m3/s strikes a flat plate placed normal to its path and

exerts a force of 1000N. Considering the density of water as 1000 kg/m3, the diameter 9in mm) of the

water jet is _______________. (GATE-ME-14) (S-1)

15. Asiphon is used to drain water from a large tank as shown in the figure below.Assume that the level

of water is maintained constant. Ignore frictional effect due to viscosity and losses at entry and exit.At

the exit ofthe siphon, the velocity of water is (GATE-ME-14)(S-3)

a) b) 2g(ZP − ZR ) c) 2g(ZO − ZR ) d) 2gZQ

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FLUID MECHANICS

16. Water ( = 1000 kg/m3) flows through a venturimeter with inlet diameter 80 mm and throat diameter

40 mm. The inlet and throat gauge pressures are measured to be 400 kPa and 130 kPa respectively.

Assuming the venturimeter to be horizontal and neglecting friction, the inlet velocity (in m/s) in ____.

(GATE-15-Set-1)

17. APrandtl tube (Pilot-static tube with C = 1) is used to measure the velocity of water. The differential

manometer reading is 10 mm of liquid column with a relative density of 10.Assuming g = 9.8 m/s2, the

velocity of water (in m/s) is _________. (GATE-15-Set-3)

18. In a vertical piston-cylinder arrangement the force applied to the piston, pushed water through a

nozzle as shown in the fiture. The water flows out from the nozzle, and reaches the top of its trajectory.

The kinetic and pressure energies at points (1), (2) and (3), respectively, are (GATE-PI-15)

a) (small and large), (large and zero) and (zero and zero)

b) (small and zero), (large and large) and (small and zero)

c) (large and zero), (zero and large) and (large and zero)

d) (large and small), (small and zero) and (small and large)

ρ
19. The water jet exiting from a stationary tank through a circular opening of diameter 300 mm impinges

on a rigid was as shown in the figure. Neglect all minor losses and assume the water level in the tank to
remain constant. The net horizontal force experiened by the wall is ___________ kN.
Density of water is 1000 kg/m3.
Acceleration due to gravity g = 10 m/s2.

FLUID DYNAMICS : CLASS ROOM OBJECTIVE (ANS)
1-c, 2-a, 3-sol, 4-a, 5-c, 6-a, 7-a, 8-sol, 9-b, 10-d, 11- 0.5 N/m2, 12- F = 9.999N, 13-b, 14-56.4,
15-b, 16-6, 17-1.328, 18-a, 19-8.765

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FLUID MECHANICS

1. A jet of water (area Aj, velocity Vj, density ) impinges horizontally on a curved vane which
deflects the jet through 600 upwards. If the vane travels horizontally at a speed ‘u’ find

(GATE-ME-87)

(a) the force experienced by the vane, and (b) the power developed by the vane.

2. AJet of water with a velocity V1 (Figure shown below) and area of cross-sectionA1enters a stream

of slow moving water in a pipe of area A2 and velocity V2. The two stream enter with the same

pressure P1.After thoroughly mixing in the pipe the stream emerges as a single stream with velocity

V3 and pressure p2. If there are no losses in the flow, determine (p2 – p1) for V1 = 20 m/s, V2 =

10 m/s, A = 0.01 m2, A = 0.02 m2, density of water = 1000 kg/m3. (GATE-ME-90)
12

3. A Venturimeter (throat diameter = 10.5 cm) is fitted to a water pipe line (internal diameter =
21.0 cm) in order to monitor flow rate. To improve accuracy of measurement, pressure difference
across the venturimeter is measured with the help of an inclined tube manometer, the angle of inclination
being 300 (see figure below). For manometer reading of 9.5 cm of mercury, find the flow rate.

ρDischarge coefficient of venture is 0.984. ρ (GATE-ME-92)

22. Water ( = 1000 kg/m3) flows horizontally through a nozzle into the atmosphere under the

conditions given below. (Assuming steady state flow) (GATE-ME-01)

At inlet : At outlet :
A2 = 10-4 m2;
A1 = 10-3 m2; P2 = Patm
V1 = 2 m/sec;
P1 = 3 x 105 Pa (gauge)

Determine the external horizontal force needed to keep the nozzle

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FLUID MECHANICS
5A LAMINAR FLOW

1. The Velocity profile of a fully developed laminar flow in a straight circular pipe, as shown in

the figure, is given by the expression. [GATE-ME-09]

-R2 dp r2
u(r) = 4µ dx 1-
R2

dp

Where dx is a constant.

The average velocity of fluid in the pipe is

a) - R2 dp b) - R2 dp c) - R2 dp R2 dp
4µ dx 2µ dx
8µ dx d) - µ dx

2. For a fully developed flow through a pipe, the ratio of the maximum velocity to the average

velocity is __________. (fill in the blank) [GATE-ME-94]

3. Maximum velocity of a one-dimensional incompressible fully developed viscous flow, between

two fixed parallel plates, is 6 ms-1. The mean velocity (in ms-1) of the flow is [GATE-ME-10]

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

proportional to ............ (Mean velocity / squre of the mean velocity) [GATE-ME-09]

5. The pressure drop for laminar flow of a liquid in a smooth pipe at normal temperature and

pressure is [GATE-PI-09]

a) Directly proportional to density b) inversely proportional to density

c) independent of density d) proportional to (density)0.75

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

u = u0(1- 4r2/D2), where r is the radial distance from the centre. If the viscosity of the fluid is
µ , the pressure drop across a length L of the pipe is
[GATE-ME-06]

a) µ u0L b) 4µ u0L c) 8µ u0L d) 16µ u0L

D2 D2 D2 D2

7. The discharge in m3/s for laminar flow through a pipe of diameter 0.04 m having a centre lline

velocity of 1.5 m/s is [GATE-ME-88]
d) 3π/10000
a) 3π/50 b) 3π/2500 c) 3π/5000

8. Water is flowing through a horizontal pipe of constant diameter and the flow is laminar. If the

diameter of the pipe is increased by 50% keeping the volume flow rate constant, them the

pressure drop in the pipe due to friction will decrease by [GATE-PI-11]

a) 33% b) 50% c) 70% d) 80%

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FLUID MECHANICS

9. For laminar flow through a long pipe, the pressure drop per unit length increase. [GATE-ME-96]

a) in linear proportion of the cross-sectional area

b) in proportion of 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

10. Two pipes of uniform section but different diameters carry water at the sasme volumetric flow

rate. Water properties are the same in the two pipes. The Reynolds number, based on the pipe

diameter, [GATE-PI-09]

a) is the same in the both pipes b) is large in the narrow pipe

c) is smaller in the narrower pipe d) depends on the pipe material

11 A 0.20 m diameter pipe 20 Km long transport oil at a flow rate of 0.01 m3/s. Calculate the power

required to maintain the flow if the dynamic viscosity and density of oil are 0.08 Pa-sec and

900 Kg/m3. [GATE-ME-88]

12. Water flows through a pipe having an inner radius of 10 mm at the rate of 36 kg/hr at 250 C is 0.001

kg/m.s. The Reynolds number of the flow is__________ [GATE-ME-14]

13. For a fully developed flow of water in a pipe having diameter 10cm, velocity 0.1 m/s and kinematic

viscosity 10-5 m2/s, the value of Darcy friction is_________ [GATE-ME-14]

14. Water flows through a 10mm diameter and 250 m long smooth pipe at an average velocity of

0.1m/s. The density and the viscosity of water are 997kg/m3 and 855C10-6n.s/m2, respectively.

Assuming fully- developed flow, the pressure drop (in pa) in the pipe is______ [GATE-ME-14]

15. A fluid of dynamic viscosity 2x10-5 kg/m.s and density 1kg/m3 flows with an average velocity of

1m/s through a long duct of rectangular (25 mm x 15mm) cross-section.Assuming laminar flow, the

pressure drop (in Pa) in the fully developed region per meter length of the duct is ____________.

(GATE-ME-14)(S-3)

16. For a fully developed laminar flow of water (dynamic viscosity 0.001 Pa-s) through a pipe of radius

5 cm, the axial pressure gradient is -10 Pa/m The magnitude of axial velocity (in m/s) at a radial

location of 0.2 cm is ___________. (GATE-15-Set2)

17. The head loss for a laminar incompressible flow though a horizontal circular pipe is h1 Pipe length and
fluid remaining the same, if the average flow velocity doubles and the pipe diameter reduces to half its

previous value, the head loss is h . The ratio h .h is (GATE-15-set-2)
2 21
a) 1 b) 4 c) 8 d) 16

18. Consider a fully developed steady laminar flow of an incompressible fluid with viscosity µ

through a circular pipe of radius R. Given that the velocity at a radial location or R/2 from the
centerline of the pipe is U , the shear stress at the wall is KµU R, where K is _______________

11

(GATE-16-Set-3)

“Don’t wait for someone else to make your life terrific.
That’s your job”

5A : LAMINAR FLOW
1-a, 2- twice, 3-c, 4-mean velocity, 5-c, 6-d, 7-d, 8-d, 9-c, 10-b., 11- 4.074 Kw, 12-636.62, 13-
0.064, 14-6840, 15-138.86, 16-6.24, 17-c, 18-2.667

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FLUID MECHANICS

5B TURBULENT FLOW

1. Consider stady 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 fluid particle is [GATE-ME-07]

1 c) 0 d) ∞

a) 5 b)

5

2. The parameters which determines the friction factor for trubulent flow in a rough pipe are :

[GATE-ME-88]

a) Froude number are relative roughness b) Froude number and Mach number

c) Reynolds number and relative roughness d) Mach number and relative roughness

3. Oil flows through a 200 mm diameter horizontal cast iron pipe (friction factor, f = 0.0225) of

length 500m. The volumetric flow rate is 0.2m3/s. The head loss (in m) due to friction is

(assume g = 9.81 m/s2)

a) 116.18 b) .0116 c) 18.22 d) 232.36

4. 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

[GATE-ME-06]

a) √ 2gh1
b) √ 2gh2
c) √ 2g h2 - h1
d) √ 2g h2 + h1

5. In the case of turbulent flow of a fluid through a circular tube (as compared to the case of

laminar flow at the same flow rate) the maximum velocity is ..................... , shear stress at the

wall is .................... , and the pressure drop across a given length is ................... The correct

words for the blanks are, respectivly ; [GATE-ME-87]

a) Higher, higher, higher b) higher, lower, lower

c) Lower, higher, higher d) lower, higher, lower

Linked question for 6 & 7 :

A syringe with frictionless planger contains water and has its end 100 mm long needle of 1 mm

diameter.

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FLUID MECHANICS

6. Assuming ideal flow, the force F in Newton required on the plunger to push out the water is

a) 0 b) 0.04 c) 0.13 d) 1.15

7. Neglect losses in the cylinder and assume fully developed laminar viscous flow throughout the

needle ; the Darcy friction factor is 64/Re, Where Re is the Reynolds number. Given that the
viscosity of water is 1.0 x 10-3 kg/m s, the force F in Newton required on the plunger is

a) 0.13 b) 0.16

c) 0.3 d) 4.4

8. Fluid is flowing with an average velocity of V through a pipe of diameter d. Over a length of L,

the “head” loss is given by fLV2 . The firction factor, f, for laminar flow in terms of Reyonds

2D

number (Re) is _________ (fill the blank) [GATE-ME-94]

9. Water at 250C is following through a 1.0 km long G.I. pipe of 200 mm diameter at the rate of

0.07 m2/s. If value of Darcy friction factor for this pipe is 0.02 and density of water is

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

[GATE-ME-09]

a) 1.8 b) 17.4 c) 20.5 d) 41.0

10. Shown below are three tanks, tank 1 without an orifice tube and tanks 2 and 3 with orifice tubes

as shown. Neglecting losses and assuming the diameter of orifice to be much less than that of

the tank, write expressions for the exit velocity in each of the three tanks. [GATE-ME-93]

11. The discharge velocity at the pipe exit in figure is [GATE-ME-98]
a) √ 2gH © Copyright : Ascent Gate Academy 60
b) √ 2gh
c) √ gH - h
d) 0

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FLUID MECHANICS

12. Oil is being pumped through a straight pipe, the length, diameter and volumetric flow rate are

all doubled in a new arrangement. The pipe friction factor, however, remains constant. The

ratio of pipe frictional losses in the new arrangment to that in the original configuration would

be 1 [GATE-PI-08]
c) 2 d) 4
1 b) 2

a)

4

13. A 400 m long horizontal pipe is to deliver 900 kg of oil (S = 0.9, v = 0.0002 m2/s) per minute.If

the head loss is not to exceed 8 m of oil. find the pipe diameter. [GATE-ME-89]

[Friction factor in laminar flow ; f = 64/R )
e

14. Consider the saline bottle shown. If ρ is the density of saline, find

a) Pressure at A,

b) The velocity of flow of saline through the tube.

(Neglect viscous losses in tube). Atomospheric pressure = Patm.
[GATE-ME-87]

15. For steady, fully developed flow inside a straight pipe of diameter D, neglecting gravity effects, the
wallττ∆uh2hsww12phe=ca)r∆4τsptLwrDe=ss∆2pLDare
pressure drop over a length L and the related by (GATE-ME-13)
a) ∆pD2 d) 4∆pD
b) τ = 4L3 τ = D
w w

16. Consider the turbulent flow of a fluid through a circular pipe of diameter, D. Identify the correct pair of

statements. (GATE-Me14)(S-3)

I. The fluid is well-mixed II. The fluid is unmixed III. ReD < 2300 IV. ReD > 2300

a) I, III b) II, IV c) II, III d) I, IV

17. The instantaneous steam-wise velocity of a turbulent flow is given as follows :

u(x, y, z, t) = u(x, y, z) + µ`(x, y, z, t)

The time-average of the fluctuating velocity u‘ (x,y,z,t) (GATE-16-Set-1)

a) u‘/2 b) − u c) zero d)
18. In a fully developed t2urbulent flow though a circular pipe, a head loss of h is observed. The
1

diameter of the pipe is increased by 10% for the same flow rate and a head loss of h is
2

noted. Assume friction factor for both the case of pipe flow is the same. The ratio of is

closest to (GATE-PI-16)

a) 0.34 b) 0.62 c) 0.87 d) 1.00

5B : TURBULENT FLOW

1-a, 2-c, 3-a ,4-c, 5-c, 6-b, 7-c, 8- 64/Re, 9-b, 11-b, 12-a, 13-162 mm, 14- (a) Patm / Pgh2, (b) VD = √2g (h1 - h2), 15-a, 16-d,

17-c, 18-b

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FLUID MECHANICS
6 BOUNDARY LAYER

ONE MARK QUESTIONS

1. A streamlined body is defined as a body about which (GATE-ME-87)

a) The flow is laminar b) The flow is along the streamlines

c) The flow separation is suppressed d) The drag is zero

2. The predominant forces acting on an element of fluid in the boundary layer over a flat plate in

a uniform parallel stream are : (GATE-ME-90)

a) Viscous and pressure forces

b) Viscous and inertia force

c) Viscous and body forces

d) intertia and pressure forces

3. The necessary and sufficient condition which brings about separation of boundary layer is

d P > 0 (True / False) (GATE-ME-94)
dx

4. As the transition from laminar to turbulent flow is induced in a cross flow past a circular

cylinder the value of the drag coefficient drops : (GATE-ME-94)

State True / False

5. Flow separation in flow past a solid object is caused by (GATE-ME-02)

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

6. If ‘x’ is the distance measured from the leading edge of a flat plate, then laminar boundary layer

thickness varies as (GATE-ME-02)

a) 1 / x b) x4/5 c) x2 d) x1/2

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

with the directon of an incoming uniform free stream. 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 (GATE-ME-07)

a) F < ½

b) F = ½

c) F =1

d) F > 1

8. Within a boundary layour for a steady incompressible flow, the Bernoulli equation.

a) holds because the flow is steady

b) holds because the flow is incompressible

c) holds because the flow is transitional

d) does not hold because the flow is frictional

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FLUID MECHANICS

TWO MARKS QUESTIONS
1. For air flow over a plate, velocity (U) and boundary layer thickness (δ) can be expressed

respectively, as

U 3y - 1 y 3 δ = 4.64 x
Uα =2δ 2 δ
; √ Rex

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

of 1.23 kg/m3, then wall shear stress at x = 1 m , is (GATE-ME-04)

a) 2.36 x 102 N/m2 b) 43.6 x 10-3 N/m2

c) 4.36 x 10-3 N/m2 d) 2.18 x 10-3 N/m2

Statement for Linked Answer Questoin : 02 & 03.

A smooth flat plate with a sharp leading edge is

place amont a gas stream flowing at U = 10 m/s.

The thickness of the boundary layer at section r - s

is 10 mm, the breadth of the plate is 1 m (into the
paper) and the density of the gas ρ = 1.0 kg/m3.

Assume that the boundary layer is thin, two -

dimensional, and follows a linear velocity distribution,
µ = U (y/δ), at the section r - s, where y is the height

from plate.

2. The mass flow rate (in kg/s) across the section q - r is

a) zero b) 0.05 c) 0.10 d) 0.15

3. The integrated drag force (in N) on the plate, between p - s, is

a) 0.67 b) 0.33 c) 0.17 d) zero

4. An incompressible fluid flows over a 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 sat the same location, in

mm will be (GATE-ME-12)

a) 4 b) 2 c) 0.5 d) 0.25

5. Consider laminar flow of water over a flat plate of length im. If the boundary layer thickness at A

distance of 0.25 m from the leading edge of the plate is 8mm, the boundary layer thickness (in mm),At

a distance of 0.75m, is________ [GATE-ME-14]

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FLUID MECHANICS

Statement of Linked Ans Q 06 & 07
Consider a steady incompressible flow through a channel is shown below

The velocity profile is uniform with a value of u0 at the inlet setionA. The velocity profile at setion B

down steam is (GATE-ME-07)

Vm y , 0<y<δ
δ

u = Vm, δ<y<H-δ
H - δ< y - H

Vm H-y ,
δ

6. The ratio Vm is
u0

1 1 1
1-2(δ/H) 1-(δ/H) 1+(δ/H)
{a) b) 1 c) d)

7. The ratio PA-PB (where PA and PB are the pressure at section A and B respectively and p is the
1 2
2 pu0

density of the fluid ) is

a) 1 -1 1 c) 1 -1 d) 1
1-2(δ/H) b) (1-(δ/H)2 (1-(2δ/H))2 (1+(2δ/H))2

8. Air (p = 1.2 kg/m3 and kinemtic viscosity, v= 2x10-5 m2s) with a velocity of 2m/s flows over the top

surface of a flat plate of length 2.5 m. If the average value of friction coefficient is Cr = 1.328
Rex

the total drag force (in N) per unit width of the plate is ________.

(GATE-15-Set-1)

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FLUID MECHANICS

9. A seady laminar boundary layer is formed over a flat plate as shown in the figure. The free stream
velocity of the fluid is U0. The velocity profile at the inlet a-b is uniform while that at a downstream

y y2
location c-d is given by u = U0 2 δ - δ

The ratio of the mass flow rate, m leaving through the horizonatla section b-d to that entering through
bd

the vetical section a-b is (GATE-16-Set-1)

FIVE MARKS QUESTIONS

1. The velocity profile across a boundary layer on a flat plate may be approximated as linear

Vx(x,y) = V0y /δ(x)
Where V0 is the Velocity far away and δ(x) is the boundary layer thickness at a distance x from

the leading edge, as shown below , (GATE-ME-93)

a) Use an appropriate control volume to determine the rate of mass influx into the boundary

layer up to x.

b) Obtain the x - momentum influx into the boundary layer up to x.

c) In which direction (up or down) does the shear stress act on the face AB of the fluid element

shown near the plate ?

“As a rule, men worry more about what they can’t see
than about what they can”

BOUNDARY LAYER : (ANS)
One marks Ques : 1-c, 2-b, 3-sol, 4-sol, 5-b, 6-d, 7-d, 8-d Two marks Ques : 1-c, 2-b, 3-c, 4-c.5-
13.86, 6-c, 7-b, 8-0.0159, 9-0.33

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FLUID MECHANICS

7 TURBO MACHINERY

ONE MARK QUESTIONS

1. In terms of speed of rotation of the impeller N, discharge Q and a change in total head H,

through the machine, the SP. Speedd for pump is _______________ (fill the blank)

(GATE-ME-94)

2. Kaplan turbine is (GATE-ME-97)

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

3. If there are ‘m’ physical quantitites and ‘n’ fundamental dimensions in a particular process, the

number on non-dimensional parameter is (GATE-ME-02)

a) m + n b) m x n c) m - n d) m / n

4. In a Pelton wheel, the bucket peripheral speed is 10 m/s, the water jet velocity is 25m/s and

volumetric flow rate of the jet is 0.1 m3/s. If the jet deflection angle is 1200C and the flow is

ideal, the power developed is (GATE-ME-06)

a) 7.5 kW b) 15.0 kW c) 22.5 kW d) 37.5 kW

5. A phenomenon is medeled using n dimensional variable with k primary dimensions. The

number of non-dimensional variables is (GATE-ME-10)

a) k b) n c) n - k d) n + k

6. A hydraulic turbine develops 1000 kW power for a head of 40 m. If the head is reduced to 20 m,

the power developed (in kW) is (GATE-ME-10)

a) 177 b) 354 c) 500 d) 707

7. The velocity triangles at the inlet and exit of the rotor of a turbo machine are shown. V denostes

the absolute velocity of the fluid, W denotes the relative of the fluid and U denotes the blade

velocity. Subjscripts, 1 and 2 refer to inlet and outlet respectively. If V2 = W1 and V1 = W2, then

the degree of reaction is (GATE-ME-12)

a) 0

b) 1

c) 0.5

d) 0.25

8. In order to have maximum power from a Pelton turbine, the bucket speed must be (GATE-ME-13)

a) equal to the jet speed b) equal to half of the jet speed

c) equal to twice the jet speed d) independent of the jet speed

9. Kaplan water turbine is commonly used when the flow through its runner is (GATE-ME-14)(S-4)

a) axial and the head available is more than 100 m

b) axial and the head vailable is less than 10 m

c) radial and the head availble is more than 100 m

d) mixed and the head avaible is about 50 m

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FLUID MECHANICS

10. Consider two hydraulic turbines identical specific speed and effective head at the inlet. If the speed

ratio of the two turbines is 2, then the respective power ratio is ___________.

(GATE-16-Set-1)
11. The blade and fluid velocities for an axial turbine are as shown in the figure.

The magnitude of absolute velocity at entry is 300 m/s at an angle of 650 to the axial direction, while the

magnitude of the absolute velocity at exit is 150 m/s. The exit velocity vector has a component in the

downward direction. Given that the axial (horizontal) velocity is the same at entry and exit, the specific

work (in kJ/kg) is ________________. (GATE-16-Set-3)

TWO MARKS QUESTIONS

1. Cavitation in a hydraulic reaction turbine is mostPNl1i1kely to occur at t he turbine (GATE-ME-93)
a) Entry b) Exit  PN22c)Stator exit d) Rotor exit

2. Specific speed of a Kaplan turbine ranges between (GATE-ME-93)

a) 30 to 60 b) 60 to 300 c) 300 to 600 d) 600 to 1000

3. At a hydro electric power plant site, available head had flow rate are 24.5 m and 10.1 m3/s

respectively. If the turbine to be installed is required to run at 4.0 revolution per second (rps)

with an overall efficiency of 90%, then suitable type of turbine for this site is (GATE-ME-04)

a) Francis b) Kaplan c) Pelton d) Propeller

4. A centrifugal pump is required to pump water to an open water tank situated 4 km away from

the location of the pump through a pipe of diameter 0.2 m having Darey’s friction factor for

0.01. The average speed of water in pipe is 2 m/s. If it is to maintain a constant head of 5 m in

the tank, neglecting other minor losses, the absolute discharge present at the pump exist is

(GATE-ME-04)

a) 0.449 bar b) 5.503 bar c) 44.911 bar d) 55.203 bar

5. A large hydraulic trubine is to generate 300 kW at 100 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 generatged

by the model (in kW) will be (GATE-ME-06)

a) 2.34 b) 4.68 c) 9.38 d) 18.75

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FLUID MECHANICS

6. A horizontal - shaft centrifugal pump lifts water at 650C. The suction nozzle is one meter below
pump centerline. The pressure at this point equals 200 kPa gauge and velocity is 3 m/s. Steam
tables show saturation pressure at 650C to 25 kPa, and specific volume of the saturated liquid is
0.00102 m3/kg. The pump Net Positive Suction Head (NPSH) in meter is (GATE-ME-06)

a) 24
b) 26
c) 28
d) 30

7. The inlet angle of runner blades of a Francis turbine of 900. 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 (GATE-ME-07)

a) 25% b) 50% c) 80% d) 89%

8. 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 (GATE-ME-07)

a) N/4 b) N/2 c) N d) 2N

9. Match the items in columns I and II (GATE-ME-07)

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-1, S-4

c) P-3, Q-4, R-1, S-2 d) P-1, Q-2, R-3, S-4

10. Water having a density of 1000 kg/m3, issues from a Nozzle with a velocity of 10 m/s and the jet

strikes a bucket mounted on a Pelton wheel. The wheel rotates at 10 rad/s. The mean diameter

or the wheel is 1 m. The jet is split into two equal streams by the bucket, such each stream is

deflected by 1200, as shown in the figure. 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

(GATE-ME-08)

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)

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FLUID MECHANICS

FIVE MARKS QUESTIONS

1. Find the gain in power output in KW when an elbow type draft tube is fitted to a vertically

mounted Francis turbine. The exit of the turbine is in the same sevel as the tail race level. The

flow discharged into the draft tube is 70 m3/sec. With a velocity of 8 m/sec., which is in the

axial direction. Assume 75% efficiency for the draft tube and 85D% for the overall efficiency of

the turbine. The area ratio of the draft tube is 2.0. (GATE-ME-87)

2. A Pelton turbine with an effective head of 450 m operates at a speed wuch that the hydraulic

efficiency is 0.9. The relative velocity is reduced by 9% due to bucket friction. The whirl velcity

at the exit is zero for the above condition. Find the bucket speed and the flow deflection. Find

the hydraulic efficiency if an effecitive head falls to 420 m, the speed of the turbine remaining

the same and velocity coefficient of nozzle is 0.98. (GATE-ME-88)

3. Identify the type of trubo machinery for the following two cases. Specify the reasons.

(GATE-ME-90)

a) Wheel velocity is the same at the inlet outlet, (U1 = U2 = U) ; whirl velocity at the inlet is

more than the whirl velocity at the outlet; optimum ratio of blade-to-working substance speed,

(U/C0 = 0.707)
b) Power developed = 430 KW; operating head = 300 m; speed = 600 rpm

4. A 7 MW hydro turbine working under a head of 10 m at a rotational speed of 125 rpm is to be

designed and developed by conducting model tests in a laboratory. Maximum possible

discharge to the model is 600 liters per second at a constant head of 5 m. Determine the

minimum scale of the model and its speed if the expected efficiency of the model is 85%.

(GATE-ME-91)

5. A hydro turbine is required to give 25 MW at 50 m head and 90 rpm runner speed. The

laboratory facilities avaialbe, permit testing of 20 kW models at 5 m head. What should be the

model runner speed and model to prototype scale ratio ? (GATE-ME-92)

6. In a hydroelectric station, water is available at the rate of 175 m3/s under a head of 18 m. The

turbines run at a speed of 150 rpm with overall efficiency of 82% . Find the number of turbines

required if they have the maximum specific speed of 460. (GATE-ME-96)

7. A water turbine delivering 10 MW power is to be tested with the help of a geometrically similar

1:8 model, which runs at the same speed as the proto-type. (GATE-ME-97)

a) Find the power developed by the model assuming the efficiencies of the model and the

proto-type are queal

b) Find the ratio of the heads and the ratio of mass rates between the proto-type and the model.

****************************

“Good is not good where better is expected”

TURBO MACHINERY (ANS.)
One Marks Ques
1-sol, 2-b, 3-c, 4-c, 5-c, 6-b, 7-c, 8-b, 9-b, 10-0.25, 11-52.807
Two Marks Ques
1-d, 2-c, 3-a, 4-b, 5-a, 6-a, 7-c, 8-c, 9-a, 10-d

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