# ME 2204 FLUID MECHANICS AND MACHINERY

Mechanics

Oct 24, 2013 (4 years and 8 months ago)

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1

T.G.PACKIA RAJ

M.E
.
, (Ph.D),

Asst. Professor
, Depar
t
ment of
Mechanical

Engi
n
eeri
n
g,

The Rajaas

E
n
gineeri
n
g College,
.

ME

2204

FLUID

MECHANICS

AND

MACHINERY

T
w
o

Marks

Questions

&

Ans
w
ers

UNIT

I

: INTRODUCTION

1.

Define

density

or

mass

density.

Density

of

a

fluid

is

d
efi
n
ed

as

the

ra
t
io

of

the

mass

of

a

fl
u
id

to

its

volume.

Densit
y
,

ρ

=

mass/volume

(Kg/m
3
)

ρ
w
a
t
e
r

=

1000

Kg/m
3

2.

Define

specific

weight

or

weight

density.

Specific

weight

or

weight

density

o
f

a

fluid

is

defined

as

t
he

ratio

be
t
ween

the
weight

of

a

fluid

to

i
t
s

volume.

Specific

w
e
ight,

γ

=

w
e
ight/volume

(N/m
3
)

γ

=

ρg

γ
w
at
er

=

9810

N/m
3

3.

Define

spec
ific

volume.

Specific

volume

of

a

fluid

is

defined

as

the

vol
u
me of

fluid

o
ccupied

by

an

unit

wt
or

unit

mass

of

a

fluid.

Specific

volume

vs

=

volume/

w
t

=

1/γ

=

1/ρg

-----

for

liquids

Specific

volume

vs

=

volume/

mass

=

1/ρ

-----

for

gases

4.

Define

dyn
amic

viscosi
ty
.

Viscosity

is

defined

as

the

property

of

fluid

which

offers

resistance

to

the
mov
e
ment

o
f

one

layer

of

fluid

over

another

layer

of

the

fluid.

du

ζ

=

μ

-------
-
-

d
y

μ

d
y
na
m
ic

v
iscosity

or

v
iscosity

or

coeffici
e
nt

o
f

v
is
cosity

(N
-
s/
m
2
)

1

N
-
s/m
2

=

1

Pa
-
s

=

10

Poise

5.

Define

Kinematic

viscosity.

It is

defined

as

the

ratio

between

the

dynamic

vi
s
c
osity

and

d
ensity

of

fluid.

ν

=

μ/ρ

(m
2
/s)

1

m
2
/s

=

10000

Stokes

(or)

1

stoke

=

10
-
4

m
2
/s

6.

Types

of

fluids.

Ideal

fluid,

R
eal

fluid,

N
e
wtonian

flui
d
,

Non
-
Newt
o
nian

fluid,

I
d
eal

Plastic

fluid.

7.

Define

Compressibility.

It is

defined

as

the

ratio

of

volumetr
i
c

strain

to

compressive

stress.

Compress
i
bilit
y
,

β =

(d

Vol/

Vol)

/ dp

(m
2
/N)

2

T.G.PACKIA RAJ

M.E
.
, (Ph.D),

Asst. Professor
, Depar
t
ment of
Mechanical

Engi
n
eeri
n
g,

The Rajaas

E
n
gineeri
n
g College,
.

8.

Define

Surface

Tension.

Surface

tension

is

defi
n
ed

as

the

tensile

force

a
c
ting

on

the

surface

of

the

liquid
in

contact

with

a

gas

or

on

the

surface

between

two

immiscible liquids

such

that

the
contact

sur
f
ace

behaves

like

a

m
e
mbrane

under

tension.

Surface

Tension,

σ

=

Force/Length

(N/m)

σ
w
a
t
e
r

=

0.0725

N/m

σ
M
e
r
c
u
r
y

=

0
.
52

N/m

9.

Surface

tension

on

li
q
uid

droplet,

σ

=

pd/4

Surface

tension

on

a

h
o
llow

bubble,

σ

=

pd/8

Surface

tension

on

a

li
q
uid

jet,

σ

=

pd/2

σ

surface

t
ension

(N/m)

d

diameter

(m)

p

pressure

inside

(N/m
2
)

p
total

=

p
i
n
si
d
e

+

p
atm

p
atm

=

101.325

x

10
3

N/m
2

10.

Define

Capillarity.

Capillarity

is

defined

as

a

phenomenon

of

rise

or

fall

of

a

l
i
quid

surface

in

a

sma
l
l
tube

relative

to

the

a
c
ent general

level

of

liq
u
id

when

the

tube

is

h
e
ld

vertically in
the

liquid.

T
he

rise

of

liquid

surface is

known

as

capillary r
i
se

while

the

fall

of

liquid
surface

is

known

as

c
a
pillary

depression.

Capillary

R
i
se

or

fall,

h

=

(4
σ

cosθ)

/ ρgd

θ

=

0

for

glass

tube

and

water

θ

=

130º

for

glass

tube

and

mercury

11.

Define

Vapour

Pressure.

When

vaporization

tak
e
s

place,

the

molecules

start

accumulating over

the

free
liquid

surface

exerting

pressure

on

the

liquid

surface. This

pres
sure

is

known

as
Vapour

pressure

of

the

liquid.

12.

Define

Control

Volume.

A

control

volume

m
a
y

be

defined

a
s

an

identi
f
ied volume

f
ixed

in

space.

The
boundaries around

the

control

volume

are

ref
e
rred

to

as

control

surfaces.

An

open
system

is

also

refer
red

t
o

as

a

cont
r
ol

volume.

13.

Write

the

c
o
ntinuity

equation.

The

equation

based

on

the

principle

of

conservation

of

mass

is

c
a
lled

continuity
equation.

δu/δx

+

δv/
δ
y

+

δ
w
/δz

= 0

-----

three

dimensional

flow

δu/δx

+

δv/
δ
y

=

0

-----

two

dimensional

flow

Q

=

a
1
v
1

=

a
2
v
2

-----

one

dimensional

flow

14.

List

the

types

of

fluid

f
l
o
w.

and

flow
Uniform

and

non
-
unifo
r
m

flow
Laminar

and

Turbulent

fl
ow

Compressible

and

incompressible

f
l
o
w

Rotational

and

ir
-
rotational

flow

One,

Two

a
nd

Three

dimensional

flow

3

T.G.PACKIA RAJ

M.E
.
, (Ph.D),

Asst. Professor
, Depar
t
ment of
Mechanical

Engi
n
eeri
n
g,

The Rajaas

E
n
gineeri
n
g College,
.

15.

Define

and

flow.

Stea
d
y

flow

Fluid

flow

is

said

to

b
e

at

any

point

in

the

fl
owing fluid

various
characteris
t
ics

such

as

velocity,

density,

pressur
e
,etc

do

not

change

with

time.

∂V/∂t

=

0

∂p/∂t

=

0

ρ
/
∂t

=

0

Unstea
d
y

f
l
ow

Fluid

flow

is

said

to

b
e

at

any

point

flowing

fluid

any

o
ne

or

all
characteris
t
ics

which

d
e
scribe

the

b
ehaviour

of

the

fluid

in

m
otion

chan
g
e

with

time.

∂V/∂t

0

∂p/∂t

0

ρ
/
∂t

0

16.

Define

Unif
orm

and

Non
-
uniform

flow.

Uniform

fl
o
w

When

the

velocity

of

flow

of

fluid

does

not

change

b
oth

in

dir
e
ction and
magnitude

from

point

to

point

in

the

flowing

fluid

for

any

given

instant

of

time,

t
h
e
flow

is

said

t
o

be

uniform.

∂V/∂s

=

0

∂p/∂s

=

0

ρ
/
∂s

=

0

Non
-
uniform

flow

If

the velocity

of

flow

of

f
luid chang
e
s

from

point

to

point

in

t
h
e flowing

fluid

at

any
instant,

the

f
low

is

said

t
o

be

non
-
uniform

flow.

∂V/∂s

0

∂p/∂s

0

ρ
/
∂s

0

17.

Compare

L
a
minar

and

Turbulent

fl
o
w.

Laminar

and

T
urbulent

fl
o
w

A

flow

is

said

to

be

laminar

if

Reynolds number

is

less

than

2000

for

pi
p
e

flow.
Laminar

flow

is

possi
bl
e

only

at

low

velocities

and

high

viscous

fluids.

In

laminar

type

of

flo
w
,

fluid

particles

move

in

lam
i
nas

or

layers

gliding

smoo
t
hly

ove
r

the

la
y
er.

Turbulent

flow

In

Turbulent

flow,

the

f
l
o
w

is

possible

at

both

velocities

and

low

viscous

f
luid. The
flow

is

said

t
o

be

turbulent if

Reyno
l
ds number

is

greater

than

4000

for

pipe

flow.

In

Turbulent

type

of

flow

fluid,

particl
e
s

move

in

a

zig

zag

m
anner.

18.

Define

Compressible

a
n
d

incompressible

flow

Compress
i
ble

fl
o
w

The

compressible flow

is

that

type

of

flow

in

which

the

density

of

the

fluid
changes

fr
o
m

point

to

point

i.e.

t
h
e

density

is not

co
n
s
t
a
nt

for

the

fluid.

It

is
e
xpressed

in

kg/sec.

ρ

consta
n
t

Incompressible

fl
o
w

The

incompressible

fl
o
w

is

that

ty
p
e

of

flow

in

which

the

density

is

c
o
nstant
for

the

fluid

f
low.

Liquids

are

generally

incompressible.

It

is

expressed

in

m
3
/s.

ρ

=

constant

4

T.G.PACKIA RAJ

M.E
.
, (Ph.D),

Asst. Professor
, Depar
t
ment of
Mechanical

Engi
n
eeri
n
g,

The Rajaas

E
n
gineeri
n
g College,
.

19.

Define

Rotational

and

Ir
-
rotational

fl
o
w.

Rotational

flow

Rotational

flow

is

that

type

of

flow

in

which

the

fluid

particles

while

flowi
n
g

along
stream

lines

and

also

ro
t
ate

t
h
eir

own

axis.

Ir
-
rotational

fl
o
w

If

the

fluid

p
articles

are

flowing

alo
n
g

stream

lines

and

do

not

rotate

the
ir
own

axis

that

type

of

flow

is

called

as

ir
-
rotational

flow

20.

Define

One,

Two

and

Three

dimensional

flow.

One

dimensional

fl
o
w

The

flow

parameter

such

as

velocity

is

a

function

of

time

and

one

space

co
-

ordinate

only.

u

=

f

(x),

v

=

0

&

w =

0.

T
w
o

d
ime
n
sional

fl
o
w

The

velocity

is

a

func
t
i
o
n

of

time

and

two

rectangular

space

co
-
ordinates.

u

=

f
1
(x
,
y
),

v

=

f
2
(x
,
y
)

&

w =
0
.

Three

dimensional

flow

The

velocity

is

a

func
t
i
o
n

of

time

and

three

mutually

perpendicular

dir
e
ctions.

u

=

f
1
(x
,
y
,z),

v

=

f
2
(x
,
y
,z)

&

w =

f
3
(x
,
y
,z
)
.

21.

Write

the

Bernoulli’s

eq
u
ation

appli
e
d

between

two

sections

p
1
/
ρg

+

v
2

/2g

+

Z

=

p

/ρg

+

v
2

/2g

+

Z

1

1

2

2

2

p/ρg

=

pressure

h
e
v
2
/2g

=

kinetic

Z

=

dat
u
m

22.

State

the

assumptions

u
s
ed

in

deriv
i
ng

Bernoulli

s

equation

Flow

is

ste
a
dy;

Flow

is

laminar;

Flow

is

irro
t
ational;

Flow

is

inc
o
mpressible;

Flui
d

is

ideal.

23.

Write

the

Bernoulli’s

eq
u
ation

appli
e
d

between

two

sections

with

losses.

p
1
/ρg

+

v
2

/2g

+

Z

=

p

/ρg

+

v
2

/2g

+

Z

+

h

1

1

2

2

2

l
o
s
s

24.

List

the

i
n
st
r
uments

works

on

the

b
a
sis

of

Bern
o
ulli’s

equati
o
n.

Venturi

meter;

Orifice

mete
r;

Pitot

tube.

25.

Define

Impulse

Momen
t
um

Equation

(or)

Mom
e
ntum

Equation.

The

total

fo
r
c
e

acting

on

fluid

is

eq
u
al

to

rate

of

change

of

momentum.
According

to

Newton’s

second

law

o
f

motion,

F

=

ma

F

dt

=

d(mv)

5

T.G.PACKIA RAJ

M.E
.
, (Ph.D),

Asst. Professor
, Depar
t
ment of
Mechanical

Engi
n
eeri
n
g,

The Rajaas

E
n
gineeri
n
g College,
.

UNIT

II :

FLOW

THROUGH

CIRCULAR

CONDU
I
TS

1.

Mention

the

range

of

Reynold’s

number

for

laminar

and

turbulent

flow

in

a

pipe.

If

the

Rey
n
old,s number

is

less

t
han

2000,

the

flow

is

laminar.

But

if

t
h
e

Reynold’s

number

is

greater

than

4
000,

the

fl
o
w

is

turbul
e
nt

flow.

2.

What

do
es

Haigen
-
Poiseulle

equation

refer

to?

The

equati
o
n

refers

to

t
he

value

of

loss

of

he
a
d

in

a

pipe

of

length

L

due

to
viscosity

in

a

laminar

flow.

3.

What

is

Ha
g
en

poiseuill
e
’s

formula?

(P
1
-
P
2
)

/ ρg

= h
f

=

32

µ
Ū
L

/ ρgD
2

The

expression

is

k
n
own

as

Hagen

poiseuille

fo
rm
ula.

Where

P
1
-
P
2

/ ρg
=
=
=
ioss
=

=
p牥ssu牥
=

Ū=
=
Ave牡ge
=
velocity,

µ

=

Coefficient

of

viscosity,

L

=

Length

of

pipe

D

=

Diame
t
er

of

pipe,

4.

Write

the

expression

for

shear

stress?

Shear

stre
s
s

ζ

=

-

(∂p/∂
x
)

(r/2)

ζmax

=

-

(∂p/∂x)

(R/
2)

5.

Give

the

formula

for

ve
l
ocity

distrib
u
tion:

-

The

formula

for

velocity

distribution

is

given

as

u

=

-

µ)

(
∂p/∂x)

(R
2
-
r
2
)

Where

R

=

of

t
h
e

pipe,

r

=

of

the

fluid

element

6.

Give

the

e
q
uation

for

average

velocity

:
-

The

equati
o
n

f
or

average

velocity

is

given

as

Ū

=

-

(1/8µ)

(∂p/∂x)

R
2

Where

R

=

of

t
h
e

pipe

7.

Write

the

relation

between

Um
a
x

and

Ū?

Umax

/ Ū

=

{

-

µ)

(∂
p
/∂x)

R
2

}

/ {

-

µ

(∂p
/
∂x)

R
2

}
Umax

/ Ū

=

2

8.

Give

the

expression

for

the

coeffici
e
nt

of

friction

i
n

viscous

flow?

Coefficient

o
f

friction

be
t
ween

pipe

and

fluid

in

viscous

flow

f

=16/

Re

Where,

f =

Re

=

Reyno
l
ds

number

9.

What

are

t
he

factors

t
o

be

dete
r
mined

when

viscous

fluid

flows

t
h
rough

the
circular

p
ip
e
?

The

factors

t
o

be

determined

are:

i.

Vel
ocity

dis
t
ribution

acr
o
ss

the

s
e
cti
o
n.

ii.

Ratio

of

maxim
u
m

velo
c
ity

to

the

average

velocity.
iii.

Shear

stress

distribu
t
i
o
n.

iv.

Drop

of

pressure

for

a

given

length.

6

T.G.PACKIA RAJ

M.E
.
, (Ph.D),

Asst. Professor
, Depar
t
ment of
Mechanical

Engi
n
eeri
n
g,

The Rajaas

E
n
gineeri
n
g College,
.

10.

Define

kinetic

energy

correction

fact
o
r?

Kinetic

ene
r
gy

factor

is

defined

as

t
he

r
atio

of

t
he

kinetic
e
nergy

of

the

flow

p
e
r
sec

based

o
n

actual

velocity

across

a

section

to

the

kinetic

e
nergy

of

the

flow

per

sec
based

on

average

ve
l
ocity

across

the

same

section.

It is

d
enoted

by

(α).

K.

E

factor

(α)

=

K.E

p
er

sec

bas
e
d

on

actual

veloc
ity

/

K
.
E

per

sec

based

on

Average

ve
l
ocity

11.

Define

momentum

correction

factor

(
β):

It

is

defin
e
d

as

the

ratio

of

momentum

of

t
h
e

flow

per

sec

based

on

actual
velocity

to

the

momen
t
um of

the

flow

per

sec

based

on

av
erage

vel
o
city

across

t
he
section.

β=

Momen
t
um

per

sec

based

on

actual

velocity/M
o
m
entum Per

sec

based

on
average

ve
l
ocity

12.

Define

Boundary

layer.

When a

real

fluid

flow

passed

a

solid

boundary,

fluid

layer

is

to

the

solid
boundary.

Due

to

fluid

undergoes retardation ther
eby

d
e
veloping a

small
region

in

t
h
e

immediate vicinity

of

the

boundary.

This

region

is

known

as

boundary
layer.

13.

What

is

mean

by

boundary

layer

gr
o
wth?

At

subsequ
e
nt

points

d
o
wnstream

of

the

edge, the

boundary

layer region
increases

b
ecause

t
he

retarded

fluid

is further

r
e
tarded.

This

is referred

as growth

of
boundary

layer.

14.

Classificati
o
n

of

bound
a
ry

layer.

(i)

Laminar

boundary

layer,

(ii)

Transition

z
o
ne,

(iii)

Turbule
n
t

boundary

layer.

15.

Define

Laminar

boundary

layer.

Near

the

ng

edge

of

the

surface of

the

plate

the

thickn
e
ss

of

boun
d
ary

lay
e
r
is

small

and

flow

is

lami
n
ar.

This

la
y
er

of

fluid

is

said

to

be

l
a
minar

boundary

layer.

The

length

of

the

plate from

the

le
a
ding

edge, upto

which

laminar

bou
n
dary

layer
exists

is

called

as

lami
n
ar

zone.

In

t
his

zone

the

velocity

profile

is

par
ab
olic.

16.

Define

transition

zone.

After

laminar

zone,

the

laminar

boundary layer

becomes unstable

and

t
he

fluid
motion

transformed

to

turbulent

b
o
undary

lay
e
r. This

sh
o
rt

length

over

which

t
h
e
cha
nges

taking

place

is

called

as

tr
a
nsition

zon
e
.

17.

Define

Turbulent

boun
d
ary.

Further

d
o
wnstream

of

transiti
o
n zone,

the

boundary

layer

is

tur
b
ulent

and
continuous

t
o

grow

in

thickness.

T
h
is

layer

of

boundary is

called

turbule
n
t

boundary
layer.

18.

Define

Laminar

sub

Layer

In the

turbulent

boundary

layer

zon
e
,

to

the

solid

s
u
rface

of the

plate

the
velocity

var
i
ation

is

in
f
l
u
enced by

v
i
scous

eff
e
c
t
s.

Due

to

very

small

thickness,
t
he
velocity

distribution

is

almost

linear.

This

region

i
s

known

as

laminar

sub

layer.

7

T.G.PACKIA RAJ

M.E
.
, (Ph.D),

Asst. Professor
, Depar
t
ment of
Mechanical

Engi
n
eeri
n
g,

The Rajaas

E
n
gineeri
n
g College,
.

19.

Define

Boundary

layer

T
hickness.

It

is

defined

as

the

distance

from

t
he

solid

b
o
undary

measured

in

y
-
direction

to
the

point,

w
here

the

velocity

of

fl
u
id

is

approximately equal

to

0.99

times

the

free
stream

vel
o
city

(U)

of

the

fluid.

It is

denoted

by

δ.

20.

List

the

various

types

of

boundary

layer

thickness.

Displace
m
ent

thickn
e
s
s
(
δ*),

M
o
m
entum

thickn
e
ss(θ),

Ener
g
y

thickness
(
δ**)

21.

Define

displacement

thickness.

The

displ
a
cement

thickness

(δ)

is

d
efined

as

t
h
e

distanc
e

b
y

which the

boundary
should

be

displaced

to

compensate for

the

reduction

in

flow

rate

on

account

of
boundary

layer

formati
o
n.

δ*

=

[

1

(u/U)

]

d
y

22.

Define

momentum

thickness.

The

m
o
me
n
tum thickness

(θ)

is

defined

as

the

distance

by

which

the

boun
dary
should

be

d
isplaced

to

compensate

for

the

re
d
uction

in

momentum

of

the

flowing
fluid

on

account

of

bou
n
dary

layer

f
o
rmation.

θ

=

[

(u/U)

(u/U)
2

]

d
y

23.

Define

energy

thickness

The

energy

thickness
(
δ**)

is

defined

as

the

distance

by

which

the

bo
undary
should

be

displac
e
d

to

compe
n
sate

for

the

reduction

in

kinetic

ene
r
gy

of

the

fl
o
wing

fluid
on

account

of

boundary

layer

format
i
on.

δ**

=

[

(u
/
U)

(u/U)
3

]
dy

24.

What

is

meant

by

energy

loss

in

a

pi
p
e?

When

the

fluid

flows

t
h
rough a

pipe,

it

loo
ses

some

energy

or

due

to
frictional

r
e
sistance a
n
d

other

reasons.

It

is

called

ene
r
gy

loss.

The

losses

a
r
e
classified

as;

Major

losses

and

Minor

losses

25.

Explain

the

major

loss
e
s

in

a

pipe.

The

major

energy

losses

in

a

pi
p
e

is

mainly

due

to

the

fr
ictional

resistance
caused

by

t
he

shear

fo
r
c
e

between

the

fluid

par
t
icles

and

b
o
undary

walls

of

the

p
ipe
and

also

d
u
e

to

viscosi
t
y

of

the

fluid.

26.

Explain

mi
n
or

losses

in

a

pipe.

The loss

o
f

energy

or

due

to

change

of

velocity

of

the

flowing

flui
d

in
magnitude

or

direction

is

called

minor

losses.

It

includes: sudden

expansion

of

the
pipe,

sudd
e
n

contracti
o
n of

the

pipe,

bend

in

a

pipe,

pipe

fittings

and

o
bstruction in
the

pipe,

etc.

27.

State

Darcy
-
Weisbach

equation

OR

What

is

t
he

expression

for

loss

due

to
friction?

h
f

=

4flv
2

/
2
gd

where,

h
f

=

loss

d
ue

to

friction

(m),

L

=

Length

of

the

pipe

(m
),

d

=

Diamet
e
r

of

the

pipe

(m),

V

=

Velocity

of

flow

(m/sec)

f =

Coeffici
e
nt

of

friction

8

T.G.PACKIA RAJ

M.E
.
, (Ph.D),

Asst. Professor
, Depar
t
ment of
Mechanical

Engi
n
eeri
n
g,

The Rajaas

E
n
gineeri
n
g College,
.

28.

What

are

the

factors

in
fl
uencing

the

frictiona
l

loss

in

pipe

f
l
o
w?

Frictional

r
e
sistance

for

the

turbulent

flow

is,

i.

Proportional

to

v
n

where

v

varies

from

1.5

to

2.0.
ii.

Proportional

to

the

density

of

fluid.

iii.

Proportional

to

the

area

of

surface

in

contact.
iv.

Independent

of

pressure.

v.

D
epend

on

the

nature

of

the

surface

in

contact.

29.

Write

the

expression

for

loss

of

due

to

sud
d
en

enlargement

of

the

pipe.

h
exp

=

(V
1
-
V
2
)
2

/2g

Where,

h
e
x
p

=

Loss

of

due

to

sudden

e
nlargement

of

pipe.

V
1

=

Veloci
t
y

of

flow

at

pipe

1;

V
2

=

Veloci
ty

of

flow

at

pipe

2.

30.

Write

the

expression

for

loss

of

due

to

sud
d
en

contraction.

h
con

=0.5

V
2
/2g

h
con

=

Loss

of

due

to

sudden

contraction.

V

=

Velocity

at

outlet

of

pipe.

31.

Write

the

expression

for

loss

of

at

the

entr
a
nce

of

the

pip
e.

hi

=0.5
V
2
/2g

hi

=

Loss

of

at

ent
r
ance

of

pip
e
.

V

=

Velocity

of

liquid

a
t

inlet

of

the

pipe.

32.

Write

the

expression

for

loss

of

at

exit

of

the

pipe.

ho

=

V
2
/2g

where,

ho

=

Loss

of

he
a
d

at

exit

of

the

pipe.

V

=

Velocity

of

liquid

at

inlet

and

outlet

of

the

pi
p
e.

33.

Give

an

ex
p
ression

for

loss

of

due

to

an

o
b
struction

in

pipe

Loss

of

he
a
d

due

to

an

obstruction

=
V
2

/ 2g

(

A/

Cc

(A
-
a

)

-
1

)
2

Where,

A

=

area

of

pipe,

a

=

Max

ar
e
a

of

obstruc
t
ion,

V

=

Velocity

of

liquid

in

pipe

A
-
a

=

Area

o
f

flow

of

li
q
uid

at

sec
t
i
o
n

1
-
1

34.

What

is

co
m
pound

pipe

or

pipes

in

series?

When

the

pipes

of

diffe
r
ent

length

and

different

diameters are

connect
e
d end

to
end,

then

t
h
e

pipes

are

called

as

c
o
mpound

pipes

or

pipes

in

series.

35.

What

is

mean

by

paralle
l

pipe

and

write

the

governing

equati
o
ns.

When

the

pipe

divides

into

two

or

more

branches and

again

join

together
downstream

to

form a

single

pipe

t
h
en it

is

call
e
d

as

p
ipes

in

parallel.
T
he governing
equations

a
r
e:

Q
1

=

Q
2

+

Q
3

h
f1

=

h
f2

36.

Define

equi
valent

pipe

a
nd

write

the

equation

to

obtain

equivalent

pipe

diameter.

The

single

pipe

replaci
n
g

the comp
o
und

pipe

with

same

di
a
m
eter

with
o
ut

change
in

discharge

and

l
o
ss

is

known

as

equival
e
nt

pipe.

L

=

L
1

+

L
2

+

L
3

5

5

5

(L/d
5
)

=

(L
1
/d
1

)

+

(L
2
/d
2

)

+

(L
3
/d
3

)

9

T.G.PACKIA RAJ

M.E
.
, (Ph.D),

Asst. Professor
, Depar
t
ment of
Mechanical

Engi
n
eeri
n
g,

The Rajaas

E
n
gineeri
n
g College,
.

37.

What

is

meant

by

Moo
d
y’s

chart

and

what

are

the

uses

of

Moody’s

chart?

The

basic

chart

plotted

against

Darcy
-
Weisbach

friction

factor

against

Reynold’s
Number

(Re)

for

the

variety

of

relative

roughness

and

flow

regimes. The

relative
r
oughness

is

the

ratio

of

the

mean

height

of

roughness

of

the

pipe

a
nd

its
diameter

(
ε
/D).

Moody’s

diagram

is

accurate

to

ab
o
ut 15%

for

d
esign

calculations

and
u
s
ed for

a
large

number

of

applications. It

c
a
n

be

used

for

non
-
circ
u
lar

conduits

and

also

f
o
r
open

chan
n
els.

38.

Define

the

terms

a)

Hy
d
raulic

e
nt

line

[HGL]

b)

Total

Energy

line

[TEL]
Hydraulic

line:

I
t

is

defined

as

the

line

which

gives

the

sum

of

pressure

and

datum

of

a

flowing

fluid

in

a

p
i
p
e

with

resp
e
c
t

the

refer
e
nce

line.

HGL

=

Sum

of

Pressure

and

Datum

Total

ener
g
y

line:

Total

energy

lin
e

is

defined as

the

line

which

gives

the

sum

of
pressure

dat
u
m

and

kinetic

h

of

a

flowing

fluid

in

a

pipe

with
respect

to

some

reference

li
n
e.

TEL

=

Sum

of

Pressure

Datum

and

Velocity

h
e

10

T.G.PACKIA RAJ

M.E
.
, (Ph.D),

Asst. Professor
, Depar
t
ment of
Mechanical

Engi
n
eeri
n
g,

The Rajaas

E
n
gineeri
n
g College,
.

UNIT

III :

DIMENSIONAL

ANALYSIS

1.

Define

dimensional

analysis.

Dimensional

analysis

is

a

mathemat
ic
al

tech
n
iq
u
e

which

makes

use

of

t
he

study
of

dimensions

as

an

aid

to

soluti
o
n

of

several

engineeri
n
g

problems. It

plays

a
n
important

role

in

research

work.

2.

Writ
e

the

uses

of

di
m
ension

analysis?

It helps

in

t
e
sting

the

dimensional

homogeneity

of

any

equation

of

fluid

motion.

It helps

in

d
eriving

equations

expressed

in

terms

of

non
-
dimensional

par
a
meters.

It

helps

in

planning

model

tests

and

presenting

experimental

results

in

a
systematic

manner.

3.

List

the

p
r
imary

and

d
erived

quantities.

Primary

or

Fundamental quantities:

The

var
i
ous

physic
a
l

quantities

used

to
describe

a

given

phenomenon can

be

described

by

a

set

of

quantities

which

are
indepe
ndent

of

each

ot
h
er. These

q
uantities

are

known

as

f
undamental

quantities

o
r
primary

qu
a
ntities.

Mass

(M),

Length

(L),

Time

(T)

and

T
emperature
(
θ)

are

the
fundamental

quantities.

Secondary or

Derived

quantities:
All

other

quantities

s
u
ch

as

area,

volum
e
,
velocity,

acceleration, energy,

p
o
wer,

etc

are

termed

a
s

derived

quantities

o
r
secondary

quantities

b
e
cause

they

can

be

expressed

by

primary

qua
nti
t
ies.

4.

Write

the

dimensions

for

the

foll
o
wings.

D
y
namic

v
i
scosity

(μ)

ML
-
1
T
-
2
,

Force

(F)

-

MLT
-
2
,
Mass

density

(
ρ)

ML
-
3
,

Po
w
er

(P)

-
M
L
2
T
-
3

5.

Define

dimensional

homogeneity.

An

equation

is

said

to

be

dimensionally

homog
e
neous if

the

dimensions

of

the
terms

on

its

LHS

are

same

as

the

dimensions

of

the

terms

on

its

RHS.

6.

Mention

the

methods

available

for

dimensional

analysis.

Rayleigh

m
e
thod,

Bucki
n
ghum

π

me
t
hod

7.

State

Buckingham’s

π

theorem.

It

states

that

“if

there

are

‘n’

variabl
e
s

(both

ind
e
pendent

&

d
ependent

variables)
in

a

physical

phenomenon and

if

these

variables

contain

‘m’

functional

dimensions
and

are

related

by

a

dimensionally

homogeneous equati
o
n,

then

the

variables

are
arranged

in
t
o

n
-
m

dime
ns
ionless

te
r
ms.

Each

term

is

called

π

term”.

8.

List

the

r
e
peating

variables

used

in

Buckingh
a
m

π

theor
e
m.

Geometric
a
l

Properties

l, d, H,

h, etc,
Fl
o
w

Properties

v,

a,

g,
ω
,

Q,

etc,
Fluid

Properties

ρ,

μ,

γ,

etc.

9.

Define

model

and

pr
o
totype.

The

small

scale

replica

of

an

actual

st
ructure or

the

ma
c
hine

is

kn
o
wn

as

its
Model,

while

the

actual

structure

or

machine

is

called

a
s

its

Prototype. Mostly
models

are

much

smaller

than

the

correspondi
n
g

prototype.

10.

Write

t
h
e

of

model

analysis.

11

T.G.PACKIA RAJ

M.E
.
, (Ph.D),

Asst. Professor
, Depar
t
ment of
Mechanical

Engi
n
eeri
n
g,

The Rajaas

E
n
gineeri
n
g College,
.

Model

test

are

quite

ec
o
nomica
l

and

convenient.

Alterations

can

be

conti
n
ued

until

most

suita
b
le

d
esign

is

ob
t
ained.

Modification

of

prototype

based

on

t
h
e

model

results.

The

information

t
he

performance

of

pr
o
totype

can

be

obtained

well

in

11.

List

the

ty
pes

of

si
milarities

or

s
i
militude

us
e
d

in

model

anlaysis.

Geometric

similarities,

K
inematic

similariti
e
s
,

Dynamic

similar
i
ties

12.

Define

geometric

similarities

It

exists

be
t
ween

the

model

and

p
r
ototype

if

the

ratio

of

c
o
rresponding lengths,
dimensions

in

the

mod
e
l

and

the

p
r
ototype

are

equal. S
u
ch

a

ra
t
io

is

known

a
s
“Scale

Ratio”.

13.

Define

kinematic

similarities

It

exists

be
t
ween

the

model

and

prototype if

the

pat
h
s

of

the

homogeneous
moving

par
t
icles

are

g
e
ometrically similar

and

if

the

ra
t
io

of

the

flow

pr
operties

i
s
equal.

14.

Define

dynamic

similarities

It

exits

b
e
tween

mo
d
el

and

the

prototype

which

are

geometr
i
cally and
kinematically

similar

a
n
d

if

the

ratio

of

all

forces

acting

on

the

model

a
nd

prototy
p
e
are

equal.

15.

Mention

the

various

forces

co
n
s
i
dered

in

fluid

flow.

Inertia

force,

Viscous

fo
rc
e,

Gravi
t
y

force,

Pressure

fo
r
ce,

Surface

Tension

force,

Elasticity

fo
r
ce

16.

Define

model

law

or

similarity

l
a
w.

The

condition

for

existence

of

completely

dy
namic

similarity

betwe
e
n

a

model
and

its

pro
t
ot
ype

are

denoted

by

e
quation

ob
t
ained

from

dimensionl
e
ss

numbers.
The

laws

on

which

the

models

are

designed for

dyn
a
mic

similarity are

called

Model
laws

or

Laws

of

Similari
ty
.

17.

List

the

various

mo
d
el

laws

applied

in

model

analysis.

Reynold’s
=
Model
=
iaw,

Froude’s
=
Model
=
iaw,

Euler’s
=
Model
=
iaw,

Weber

Mo
d
el

Law,

Mach

Model

Law

18.

State

Reynold’s

model

law

For

the

flow,

where

in

a
ddition to

i
n
ertia

force

the

viscous force

is

the

only

other
predominant force,

the

similarity

of

flow

in

t
h
e

model

and

its

pro
to
t
ype

can

be
establish
e
d,

if

the

Renold’s

number

is

same

for

both

the

systems.

This

is

known

a
s
Reynold’s

model

law.

Re
(p)

=

Re
(m)

19.

State

Froude’s

model

law

When

the

f
orces

of

gravity

can

be

considered

t
o

be

the

on
l
y

pred
o
minant force
which

c
ontrols

the

motion

to the

for
c
e

of inertia,

the

dyn
a
mic

similarities

o
f
the

flow

in

a
ny

two

such

systems

c
a
n

be

es
t
ablished, if

the

Froude

number

for

both
the

system

is

the

same.

This

is

kn
o
wn

as

Froude

Model

Law.

Fr
(p)

=

Fr

(m)

20.

State

Euler’s

model

law

In

a

fluid

system

where

supplied

p
r
essures

are

the

controlling

forces

in

to

inertia

fo
r
c
es

and

ot
h
er

forces

a
r
e

either

enti
r
ely

absent

or

in
-
signi
f
ic
a
nt

the

Euler’s
12

T.G.PACKIA RAJ

M.E
.
, (Ph.D),

Asst. Professor
, Depar
t
ment of
Mechanical

Engi
n
eeri
n
g,

The Rajaas

E
n
gineeri
n
g College,
.

number

for

both

the

model

and

pro
t
otype

which

known

as

Euler

Model

Law.

21.

State

Weber’s

model

law

When

surf
a
c
e

tension

effect

pred
o
minates in

to

inertia

force

then

the
dynamic

similarity

is

obt
a
ined

by

equating

the

W
eber’s

number

for

both

model

and

its
prototype,

which

is

call
e
d

as

Weber

Model

Law
.

22.

State

Mach’s

model

law

If

in

any

p
h
enomenon

only

the

forces

resulti
n
g

from

ela
s
tic

compression a
r
e
significant

in

to inertia

forces

and

all other

forces

may

be neglected,

then

t
h
e
dynamic

similarity

between

model

and

its protot
y
pe

may

be
ac
hieved

by equating

the
Mach’s

number

for

both

the

systems.

This

is

k
n
own

Mach

Model

Law.

23.

Classify

the

hydraulic

models.

The

hydraulic

models

are

classified

as:

Undisto
r
ted

model

&

Distorted

model

24.

Define

undistorted

model

An

undistorted

model

is t
hat

which

is

geometr
i
cally

similar

to

i
ts

prototype,

i.e.

the
scale

ratio

f
or

corresp
o
nding linear

dimensions

of

the

mo
d
el

and

its

p
rototype

are
sa
m
e.

25.

Define

distorted

model

Distorted

models

are

those

in

which

one

or

more

terms

of

the

mo
d
el

are

not
id
entical

wi
t
h

their

coun
t
erparts

in

t
h
e

prototype.

26.

Define

Scale

effect

An

effect

in

fluid flow t
h
at results

fr
o
m

changing

the

scale,

b
ut

not

the

s
h
ape,

of

a
body

around

which

the

flow

passes.

27.

List

the

of

distorted

model.

The

results

i
n

steeper

water

surface

slopes

and

magnificati
o
n

of

wave

h
eights

in
model

can

be

obtained

b
y

providing

true

vertical

structure

wi
t
h

accuracy.

The

model

size

can

be

r
educed

to

l
o
wer

down

the

cast.

Sufficient

tr
a
c
tate

force

can be

developed

to

produce

be
d movement

with a

small
model.

28.

Write

the

dimensions

f
o
r

the

followings.

Quantities

Symbol

Unit

Dimension

Area

A

m
2

L
2

Volume

V

m
3

L
3

Angle

Α

Deg.

Or

R
a
d

M
0
L
0
T
0

Velocity

v

m/s

L
T
-
1

Angular

Ve
l
ocity

ω

T
-
1

Speed

N

rpm

T
-
1

Acceleration

a

m/s
2

LT
-
2

Gravitatio
n
al

Acceleration

g

m/s
2

LT
-
2

Discharge

Q

m
3
/s

L
3
T
-
1

Discharge

per

meter

run

q

m
2
/s

L
2
T
-
1

Mass

Dens
i
ty

ρ

Kg/m
3

M
L
3

Sp.

Weight

o
r

Unit

Weight

N/m
3

M
L
-
2
T
-
2

D
y
namic

V
i
scosity

μ

N
-
s/m
2

M
L
-
1
T
-
1

13

T.G.PACKIA RAJ

M.E
.
, (Ph.D),

Asst. Professor
, Depar
t
ment of
Mechanical

Engi
n
eeri
n
g,

The Rajaas

E
n
gineeri
n
g College,
.

Kinematic

viscosity

m
2
/s

L
2
T
-
1

Force

or

Weight

F

or

W

N

MLT
-
2

Pressure

or

Pressure

i
ntensity

p

N/
m
2

or

Pa

ML
-
1
T
-
2

Modulus

of

Elasticity

E

N/m
2

or

Pa

ML
-
1
T
-
2

Bulk

Modu
l
us

K

N/m
2

or

Pa

ML
-
1
T
-
2

Workdone

or

Ener
g
y

W

or

E

N
-
m

ML
2
T
-
2

Torque

T

N
-
m

ML
2
T
-
2

Po
w
er

P

N
-
m/s

or

J/s

or

Watt

M
L
2
T
-
3

14

T.G.PACKIA RAJ

M.E
.
, (Ph.D),

Asst. Professor
, Depar
t
ment of
Mechanical

Engi
n
eeri
n
g,

The Rajaas

E
n
gineeri
n
g College,
.

UNIT

I
V : ROTO

DYNAMIC

MACHINES

1.

What

are

fl
u
id

machines

or

Hydraulic

machines?

The

machines which

use

the

liquid

or

gas

for

the

transfer

of

energy

fr
o
m

fluid

to
rotor

or

from

rotor

to

fluid

are

known

as

fluid

machines.

2.

How

are

fluid

machines

classified?

Fluid

machines

are

classified

into

two

categories depending upon

transfer

of
energy:

1.

Turbines

hydraulic

energy

is

converted to

mechanical
energy

and

then
electric
a
l

e
n
ergy.

2.

Pumps

electrical

e
nergy

is

converted

to

mechanical

energy
and

then

hydraulic

ene
r
gy.

3.

What

are

c
a
lled

turbines?

Hydraulic

turbines

are

t
he

machines

which

use

the

energy

of

water

and convert

it
into

mechanical en
ergy.

The

mech
a
nical energy

developed

by

a

turbine

is

used

in
running

the

electric
a
l

g
e
nerator

which

is

direc
t
ly

coupled

to

t
he

shaft.

4.

What

is

kn
o
wn

as

Euler’s

equation

f
or

turbo
-
m
a
chines?

The

general

expression

for

the

work

done

per

s
e
cond

on

impell
er

is

ρQ[V
w
1
u
1

+

V
w
2
u
2
]

5.

Define

Gross

of

a

turbine.

The

differe
n
ce

between

race

l
e
vel

and

tail

r
ace

level

is

known

as

Gross

6.

Define

Net

of

a

tu
r
bine.

It

is

also

called

effective

and

is

defined

as

t
he

available

at

t
h
e

i
nlet

of
the

turbine.

H

=

H
g

h
f

7.

What

are

the

efficie
n
ci
e
s

of

a

turbi
n
e?

Hydraulic

efficiency

Mechanical

efficiency

Volumetric

efficiency

Overall

efficiency

8.

Define

Hydraulic

efficie
n
cy.

It

is

defined

as

the

ratio

of

the

power

given

by

water

to

th
e

runner

of

a

turbine

to
the

power

supplied

by

the

water

at

the

inlet

of

t
h
e

turbine.

Po
w
er

deli
v
ered

to

runner

(runner

p
o
w
er)

η
h

=

--------
-
---------------
-
---------------
-
---------------
-
---

Po
w
er

su
p
plied

at

inl
e
t

(
w
ater

p
o
w
er)

Water

power

=

γQH

=

(1/2)

m

v
2

9.

Define

Mechanical

ef
f
iciency.

The

ratio

of

the

power

available at

the

shaft

of

the

turbine

to

the

power

delivered
t
o

the

runn
e
r

is

defined

as

mechanical

efficiency.

Po
w
er

avai
l
able

at

the

shaft

(shaft

p
o
w
er)

η
m

=

--------
-
---------------
-
---------------
-
---------------
-
---

Po
w
er

deli
v
ered

to

runner

(runner

p
o
w
er)

15

T.G.PACKIA RAJ

M.E
.
, (Ph.D),

Asst. Professor
, Depar
t
ment of
Mechanical

Engi
n
eeri
n
g,

The Rajaas

E
n
gineeri
n
g College,
.

10.

Define

volumetric

efficiency.

The

ratio

of

the

vo
lume

of

the

water

actually striking the

runner

to

the

volume of
water

supplied

to

the

tu
r
bine

is

de
f
i
n
ed

as

volumetric

efficie
n
cy.

11.

Define

Overall

efficiency.

It

is

defined as

the

ratio

of

the

power

available at

the

shaft

of

the

turbine

to

the
power

su
pplied

by

the

water

at

the

i
n
let

of

the

tu
r
bine.

Po
w
er

avai
l
able

at

the

shaft

(shaft

p
o
w
er)

η
o

=

-----------------------
-
---------------
-
---------------
-
--

Po
w
er

su
p
plied

at

inl
e
t

(
w
ater

p
o
w
er)

η
o

=

η
h

η
m

η
v

(or)

η
o

=

η
h

η
m

12.

What

are

an

impulse

turbine

and

a

r
eaction

turbine?

Impulse

Turbine:

If

at the

inlet

of the

turbi
n
e,

the

energy

avai
lable

is only

kinetic

energy,

the

turbine
is

k
n
own

as

impulse

tu
r
bine.

T
h
e

p
ressure at

t
he

inlet

of

t
he

turbine

is

atmosphere.
This

turbine

is

used

for
h
igh

T
he

water

strikes

the bucket

along

t
h
e tangent

of
the

runner.

Ex:

Pelton

Wheel

Turbine.

Re
action

Turbine:

If

at

the

inlet

of

the

t
u
rbine,

the

water

possesses kinetic

energy

as

well

as
pressure

energy,

the

t
u
rbine

is

k
n
own

as

re
ac
tion

turbi
n
e.

As

the

water

flows
through

the

runner,

the

water

is

under

pressu
r
e

and

the

pressure en
e
rgy

goes

on
ch
anging

i
n
to

kine
t
ic

e
nergy.

The

runner

is

completely

enclosed

in

an

air
-
t
ight

casing and

t
he

runner and

casing is

completely

full

of

water.

This

turbi
n
e is

used

for

medium

he
a
ds.

Ex:

Francis

Turbin
e
.

13.

Define

Jet

Ratio.

It

is

defined as

the

ratio

of

the

pitch

diameter (D)

of

the

Pelton

wheel

to

t
h
e
diameter

of

the

jet

(d).

It

is

denoted

by

‘m’

and

is

given

as

m

=

D/d

14.

Classificati
o
n

of

hydraulic

turbines:

(a)

Based

on

t
y
pe

of

ener
g
y

available

at

inlet

Impulse

turbine

(Pelton

wheel)

Reaction

tu
r
bi
ne

(Francis

turbine,

K
aplan

turbi
n
e,

Propeller

turbine)

(b)

Based

on

available

at

inlet

High

turbine

[ >

250

m

]

-

(Pelton

wheel)

Medium

he
a
d

turbine

[

60

to

250

m

]
-

(Francis

t
urbine)

Low

turbine

[ <

6
0

m

]

(Ka
p
lan

turbine,

Prope
ller

turbine)

(c)

Based

on

specific

speed

High

specific

speed

tur
b
ine

(Kapl
a
n

turbine,

Propeller

turbine)
Medium

sp
ec
ific

speed

t
urbine

-

(Francis

turbi
n
e)

Low

specific

speed

turbine

-

(Pelton

wheel)

(d)

Based

on

direction

of

flow

through

runner
Tangenti
al

flow

turbine

flow

turbine
Axial

flow

turbine

Mixed

flow

t
urbine

16

T.G.PACKIA RAJ

M.E
.
, (Ph.D),

Asst. Professor
, Depar
t
ment of
Mechanical

Engi
n
eeri
n
g,

The Rajaas

E
n
gineeri
n
g College,
.

15.

Define

flow

reaction

turbine

a
nd

their

types.

If

water

flows

in

the

direction in

the

turbi
n
e

then

it

is

r
eferred

as

flow
turbine.

Types:

Inward

flo
w

re
a
ction

turb
i
ne:
If

the

water

flows

from

outwar
d
s to

inwards
through the

runner,

the

turbine

is

k
n
own

as

inward

flow

reaction turbine. Here
the

outer

di
ameter of

t
h
e

runner

is

inlet

diamet
e
r whereas
t
he

inner

d
i
a
meter of

t
h
e
runner

is

ou
t
let

diam
eter.

Out
w
ard r
a
dial

fl
o
w

r
e
action turbine:

If

the

w
ater

flows

f
r
om

inwards

to

outwards
through

the runner,

the

t
urbine

is called

as outw
a
rd

flow

reaction

turbine.

Here
the

outer

di
ameter of

t
h
e

runner

is

outlet

diam
e
ter whereas

the

inner

d
i
a
meter
of

t
h
e
runner

is

inlet

diameter.

16.

What

is

mean

by

Draft

T
ube?

The

draft

t
u
be

is

a

pipe

of

a
rea

which

connects

the

outlet

of
the

runner

t
o

the

tail

race.

One

end of

the

draft

tube

is

con
n
ected

to

the outlet of

the
runner

while

the

other

e
nd

is

sub
-
merged

below

the

level

of

water

in

the

tail

race.

17.

Why

do

draft

tubes

have

enlarging

p
assage

area

in

the

direc
t
ion

of

flow?

The pressu
r
e

at

the

exit of

the

reaction

turbine

is

generally

l
e
ss than at
m
ospheric
and

this

m
akes the

w
ate
r

NOT

to

discharge

directly to

the

tail

r
a
ce.

By

the
introduction

of

draft

tube,

which has

enlarged

area

in

the

di
r
ection

of

fl
o
w,

the

kinetic

reduces

and

pressure

increases.

There

by

discharge of

water

to

the

tail
race

safel
y
.

18.

U
ses

of

dra
f
t

tube:

Discharges

water

to

tail

race

safely

Converts

a

large

proportion

of

rejec
t
ed

kine
t
ic

e
nergy

into

useful

press
u
re

energy

Net

of

the

turbine

is

increas
e
d.

19.

Types

of

draft

tube:

Conical

draft

tube,

Simple

elbow

tube,

Moody

g

tube

and

Elbow

draft
tube

with

ci
r
c
ular

inlet

a
nd

rectangular

outlet.

20.

Define

specific

speed

of

a

turbine.

It

is

d
e
fined

as

the

sp
e
ed

of

the

tu
r
bine

which

is

geometrically similar

and

it

will
develop

unit

power

when

working

u
nder

unit

h
e

N
s

=

N

√P/

(
H)
5/4

21.

Define

Runaway

speed

of

Turbine.

The

max

speed

reached by

the

turbine

after

the

removal
o
f

the

exter
n

is
called

ru
na
way

speed

of

turbine. The

various

rotating

c
o
mponents

of

the

turbi
n
e
should

be

d
esigned

to

r
emain

safe

at

the

runaw
ay

speed.

22.

List

the

cha
r
acteristic

c
u
rves

of

Hydraulic

turbin
e
.

Main

Char
ac
teristic

Curves

(or)

Co
ns
tant

Curves
Operating

Characteristic

Curves

(or)

Constant

Speed

Curves
Muschel

Curves

(or)

C
o
nstant

Efficiency

Curves

17

T.G.PACKIA RAJ

M.E
.
, (Ph.D),

Asst. Professor
, Depar
t
ment of
Mechanical

Engi
n
eeri
n
g,

The Rajaas

E
n
gineeri
n
g College,
.

2

23.

What

is

roto

dynamic

p
ump?

When

the

i
n
crease

in

p
r
essure

is

d
eveloped by

rotating

i
m
peller

or

by

action

of
centrifugal

f
orce

then

t
h
e

pump

is

called

as

roto

dynamic

pump.

24.

Define

Centrifugal

pump.

Hydraulic

pump

means

it

converts

me
c
hanical

energy

into

hydraulic

e
n
ergy.

If

the

mechanical energy

is

converted

into

pressu
r
e

energy

means

of

cen
t
rifugal

force
acting

on

t
h
e

fluid,

the

hy
draulic

machine

is

called

Centrifugal

Pump.

25.

Define

Specific

spe
e
d

of

a

centrifug
a
l

pump.

The

specific

speed

of

a

centrif
u
gal pump

is

defined

as

the

sp
e
ed

of

a
geometrically

similar

pump

which

would

deliver

1

m
3
/s

against

a

of

1

m.

N
s

=

N

Q/

(
H)
3/4

(OR)

N
s

=

N

√P/

(
H)
5/4

26.

Efficienci
e
s

of

a

Centrifugal

Pump:

Manometr
i
c

Efficien
c
y
:

The

ratio

o
f

the

man
o
metric

to

the

he
a
d

imparted

by

the

impeller

to

the
water

is

kn
o
wn

as

manometric

efficiency.

Manometr
i
c

g

H
m

η
ma
n
o

=

----------
---------
-
---------------
-
---------------
-
---

=

-----------

imparted

b
y

i
mpeller

to

w
ater

V
w
2
u
2

impar
t
ed

by

impeller

to

water

=

V
w
2
u
2
/g

Mechanical

Efficien
c
y
:

The

ratio

of

the

power

available

at

the

impeller

to

the

power

at

the

s
h
aft

of

t
h
e
c
entrifugal

pump

is

kn
o
wn

as

mechanical

ef
f
ici
e
ncy.

P
o
w
er

at

the

impeller

η
mech

=

----------------------------
-
----

Shaft

Po
w
e
r

Power

at

the

impeller

=

workdone

by

impeller

per

sec

=
ρQ

V
w
2
u
2

Overall

Eff
i
cien
c
y
:

The ratio of

power

output

of

the

pump

to

the

power

input

to

the

pump

is

called

as
overall

efficiency.

Weight

of

w
ate
r

lifted

x

Hm

η
o

=

--------
-
---------------
-
---------------
-
-

Shaft

Po
w
e
r

27.

Define

Manometric

The

manometric

is

defined

a
s

the

against

which

a

centri
f
ugal

pump
has

to

work.

H
m

=

imparted

b
y

the

impeller

to

the

w
a
t
er

loss

of

H
m

=

V
w
2
u
2
/g

-

loss

of

H
m

=

h
s

+

h
d

+

h
fs

+

h
fd

+

v
d

/2g

18

T.G.PACKIA RAJ

M.E
.
, (Ph.D),

Asst. Professor
, Depar
t
ment of
Mechanical

Engi
n
eeri
n
g,

The Rajaas

E
n
gineeri
n
g College,
.

28.

Differentiate

static

&

man
o
metric

Sl. No.

Static

Manometr
i
c

1

The vertical

dist
a
nce

to

liquid
surface

in

sump

to

tank.

Total

that

must

be

prod
uced
by

pump

t
o

satisfy

the

external

requirements.

2

Loss

of

h
e

in

the

pump

is

not
considered.

The

friction

loss

&

kinetic

he
a
d
are

conside
r
ed.

3

H

=

H
s

+

H
d

H
m

=

H
s

+

H
d

+

h
fd

+

v

2
/2g

d

2

2

29.

Minim
u
m

speed

for

starting

a

Centrif
ugal

Pump,

H
m

=

u
2

/2g

-

u
1

/2g

30.

What

is

mean

by

multi

stage

pump?

If

more

than

one

impell
e
r

is

used

in

pump

then

s
uch

type

is

known

as

multistage
pump.

Impellers

in

series

Number

of

impellers

are

mounted

on

a

common

shaft.

This
increases

t
h
e

total

Total

=

n

H
m

Impellers

in

parallel

Impellers

a
re

mounted

in

separate shaft.

T
h
is

increases

t
h
e

discharge.

Total

disch
a
rge

=

n

Q

31.

Compare

Centrifugal

P
ump

&

Rec
i
procating

P
ump.

Sl. No.

Centrifugal

Pump

Reciprocating

Pump

1

Its

dischargi
ng

capacity

is

more.

Its

discharging

capacity

is

low.

2

It

can

be

us
ed

for

lif
t
ing

highly

visc
o
us
liquids.

It

can

handle

only

pure

water

or

less
viscous

liq
ui
ds.

3

Its

maintenance

cost

is

low.

Its

maintenance

cost

is

h
igh.

4

It can

be

o
p
erated

at

ver
y

high

speed.

High

speed

may

cause

cavitatio
n
s
and

separation.

32.

Define

Priming

of

a

cent
r
ifugal

pump.

Priming

of

a

centrifug
a
l

pump

is

d
efined

as

t
h
e

operation

in

which

t
h
e

suction
pipe,

casing

of

the

pump and

a

por
t
ion

of

the

d
elivery

pipe

up

to

the

d
e
livery

va
l
v
e

is
completely filled

up

fr
o
m

outside

source

with

the

liquid

to

be

raised

by

the

pump
before

starting

the

pump.

33.

Define

cavitation.

Cavitation

is

defined

a
s

the

phe
n
omenon of

formation

of

vapour

bubbles

of

a
flowing

liquid

in

a

region

where

the

pressure of

the

fluid

falls

bel
o
w

its

vapour
pressure

a
n
d

the

sudd
e
n

collapsing of

these

vapour

bubbl
e
s

in

a

regi
o
n

of

higher
pressure.

34.

What

are

pump

characteristics?

Pump

char
ac
teristic means

the

ch
a
racter
i
stic curves

of

a

pump.

Characteri
stic
curves

of

c
e
ntrifugal p
u
mps

are

defined

as

those

curves

which

are

plot
t
ed

from

the
results

of

a

number

of

tests

on

the

centrifugal
p
ump.

These

curves

are

necessary
t
o
predict

the

b
ehaviour

and performa
n
ce

of

the

pump

when

t
h
e

pump

is

working

under
dif
ferent

fl
o
w

rate,

and

speed.

19

T.G.PACKIA RAJ

M.E
.
, (Ph.D),

Asst. Professor
, Depar
t
ment of
Mechanical

Engi
n
eeri
n
g,

The Rajaas

E
n
gineeri
n
g College,
.

UNIT

V :

P
O
SIT
I
VE

DISPLACEMENT

MACH
I
NES

1)

What

is

a

r
e
ciprocating

pump?

Reciprocati
n
g

pump

is

a

positive

displ
a
cement

pump.

This

means

the

l
iquid

is
first

sucked

into

the

cyli
n
der

and

then

displac
e
d

or

pushed

b
y

the

thrust

of

a

piston.

2)

What

is

sin
g
le

acting

p
u
mp

and

double

acting

p
ump?

If

the

water

is

in

contact with

one

si
d
e

of

the

pis
t
on

the

pump

then

it

is

known

as
single

ac
t
ing

reciprocati
n
g

pump.

For

one

complete

revolution

one

suction

stroke

and
one

deliver
y

stroke

occ
u
rs.

If

the

water

is

in

cont
a
c
t with

both

sides

of

the

p
iston

the

p
u
mp

then

it

is

called
double

acti
n
g

reciprocating pump.

F
or

one

complete

revolution

two

suction

strokes
and

two

delivery

strokes

occurs.

3)

What

is

Discharge

through

a

Recip
r
o
cating

Pump?

For

Single

acting

Reciprocating

Pump:

Discharge

(
Q
T
)=ALN/60

For

Double

acting

Reciprocating

Pump:

Q
T

=
2
ALN/60

A=Area

of

the

Cyclinder

(
m
2
),

L=Length

of

Stroke

(m),

N=S
p
eed

of

Crank

(rpm)

4)

What

is

the

Workdone

b
y

Reciprocating

Pump

per

sec?

For

Single

acting

Reciprocating

Pump:

Workdone

=

ρgALN(hs+hd)/60

For

Double

acting

Reciprocating

Pump:

Work

done=

2ρgALN(hs+h
d
)/60

Where,

ρ=Density

of

Water

(kg/m
3
),

A=Area

of

the

Cylinder

(
m
2
),

L=

Stroke

Length

(m),

N=Speed

(rpm),

hs,

hd=Suction

and

Deli
very

he
a
d

(m).

5)

Define

slip

a
nd

%

slip.

The difference

between

the

theoretical

discharge

(Q
T
)

and a
c
tual

discha
r
ge

(Q
ac
t
)

is

known

as

slip

of

the

p
ump.

Slip =

Q
T

-

Q
act

%

Slip

= [ (
Q
T

-

Q
act
)
/
Q
T

]

x

100

If
Q
act

is

more

than

the

Q
T

then

slip

w
ill

be

iv
e.

If
Q
act

lesser

than

Q
T

then

the

slip

will

be

+ive.

6)

Define

coefficient

of

dis
c
harge

of

reciprocating

p
u
mp?

It

is

defin
e
d

as

the

ratio

of

actual

discha
r
ge

to

theoretical discharge of
reciprocati
n
g pump.

C
d
=Qa/Qth.

If

C
d

>

1

then

ive

slip

occurs

and

if

C
d

<

1
then

+ive

slip

occurs.

7)

Write

the

ex
pression
f
or

pressure

due

to

acc
e
le
r
ation in

s
u
ction

and
delivery

pipes.

Pressure

h

due

to

acceleration

in suction

pipe,

h
as

=

(l
s
/g)

(
A/a
s
)

ω
2
r

C
os
ω
t

Where,

l
s

-

length

of

suction

pipe;

A

area

of

piston

cylinder,

a
s

area

of

suction

p
i
p
e;

ω

angular

velocity;

r

of

crank.

Pressure

h

due

to

acceleration

in delivery

pipe,

h

=

(l
d
/g)

(A/a
d
)

ω
2
r

C
os
ω
t

Where,

l
d

-

length

of

delivery

pipe;

A

area

of

piston

cyli
nd
e
r,

a
d

area

of

delivery

pipe;

ω

angular

velocity;

r

of

crank.

Max

press
u
re

due

to

acceleration,

h
a

=

(l/g)

(A/a)

ω
2
r

20

T.G.PACKIA RAJ

M.E
.
, (Ph.D),

Asst. Professor
, Depar
t
ment of
Mechanical

Engi
n
eeri
n
g,

The Rajaas

E
n
gineeri
n
g College,
.

8)

Write

the

expression

for

due

to

friction

in

s
u
ction

and

d
e
livery

pipes.

loss

due

to

friction

in suc
tion

pipe

is,
h
fs

=

(4fl
s
/
2
gd
s
)

[

(A/a
s
)

ω
2
r

Sin
ω
t

]
2

Where,

f

coefficient

of

friction;

l
s
-

length

of

suction

pip
e
;

A

area

of

piston
cylinder,

a
s

area

of

suction

pip
e
; d
s

diameter

of

suction

pipe;

ω

Angular
velocity;

r

of

cr
a
nk.

loss

due

to

friction

in deliv
e
r
y

pipe

is,
h
fs

=

(4fl
s
/
2
gd
s
)

[

(A/a
s
)

ω
2
r

Sin
ω
t

]
2

Where,

f

coeffici
e
nt

of

friction;

l
s

-

length

of

delivery

pipe;

a
s

area of

delivery
pipe;

d
s

diameter

of

delivery

pipe;

9)

Define

indicator

diagr
a
m?

Th
e

indica
t
or

diagram

for

a

recip
r
ocating p
u
mp

is

defi
n
ed

as

the

g
raph

drawn
between

the

pressure

h

in

the

cylinder

and the

distance

traveled

by

the

piston

for
one

complete

revolution

of

the

crank.

10)

Define

ideal

indicator

di
a
gram?

It

is

defined

as

the

graph

between

pressure

in

the

cylinder

and

stroke
length

of

the

crank

under

ideal

con
d
ition

is

known

as

ideal

i
n
dicator

diagr
am
.

During

the

suction

str
o
ke,

the

pr
e
ssure in

t
h
e

cylinder

is

below

a
t
mospheric
pressure.

During

the

delivery

stroke,

the

pressure in

the

cylinder

is

above

a
t
mospheric
pressure.

P
r
e
s
s
u
r
e

h

H
atm

e

a
d

Delivery

s
t
r
ok
e

h
d

L = Stroke L
e
ngth

h
s

Su
c
tion
s
t
roke

Stro
k
e Leng
th

11)

What

is

t
h
e

relation

b
etween

Work

done

of

a

Pump

and

Area

of

I
ndicator

Diagra
m

?

Work

done

by

the

pump

is

proporti
o
nal

to

the

a
r
ea

of

the

In
d
icator

diagr
am
.

12)

What

is

the

Work

done

by

the

Pump

per

sec

d
ue

to

accel
e
ration

and

f
r
iction

in
the

suction

and

delivery

Pipes?

For

single

acting

:

Workdone/sec

=

ρgALN(h
s
+h
d
+0.67h
fs
+0.67h
f
d
)/60

For

Double

acting

:

Workdone/sec

=

2
ρgALN(h
s
+h
d
+0.67h
fs
+0.67h
f
d
)/60

Where,

h
f
s
,

h
f
d

=loss

of

due

to

friction

in

s
u
ction

and

d
e
livery

pipes.

21

T.G.PACKIA RAJ

M.E
.
, (Ph.D),

Asst. Professor
, Depar
t
ment of
Mechanical

Engi
n
eeri
n
g,

The Rajaas

E
n
gineeri
n
g College,
.

13)

What

is

an

air

vessel?

An

air

vessel

is

a

cl
o
s
e
d

chamber

containing

compressed air

in

the

t
o
p

po
rtion
and

liquid

a
t

the

bott
o
m

of

the

c
h
amber. At

the

base

of

the

chamber

there

is

a
n
opening

thr
o
ugh

which

the

liquid

may

flow

into

the

vessel

or

o
ut

from

the

vessel.
When

the

liquid

enters

the

air

vessel,

the

air

g
ets

compressed further

and

when

the
li
quid

flows

out

of

the

vessel,

the

a
ir

will

expand

into

the

chamber.

14)

What

is

the

purpose

of

a
n

air

vessel

fitted

in

the

pump?

o

To

obtain

a

continuous

supply

of

li
q
uid

at

a

uni
f
orm

rate.

o

To

save

a

considerable

amount

of

work

in

overcoming

the

frictio
n
a
l

resistance

in

the

sucti
o
n

and

delivery

pipes,

and

o

To

run

the

pump

at

a

high

speed

wi
t
h

out

separ
a
tion.

15)

What

is

the

work

saved

by

fitting

a
n

air

vessel

in

a

single

acting,

dou
b
le

acting
pump?

Work

saved

by

fitting

ai
r

vessels in

a

single

ac
ti
ng

p
ump

is

84.87%, In

a
double

acti
n
g

pump

the

work

saved

is

39.2%.

16)

Define

Cavi
t
ation.

If

the

pressure

in

the

cylinder

is

b
e
low

the

vapour

pressu
r
e,

the

dissolved gases
will

be

libe
r
ated

from

the

liquid

and

air

bubbles

are

formed.

This

proc
e
ss

is

t
ermed
as

cavitaion.

17)

Define

sep
a
ration

pressure

and

se
p
aration

pressure

Due

to

caviation

process

the

conti
n
uous flow

of

fluid

will

g
e
t

affected

a
nd
separation takes

place.

The

pressure

at

which

separation takes

place

is

known

as
separation

pressure

a
n
d

the

correspon
d
ing to

sep
a
ration

pressure

is

call
e
d
separation

p
ressure

he
a
d.

For

water

the

limiting

value

of

separ
a
tion

pressu
r
e

is,

h
sep

=

-

7.8

m

(Gauge

pressure)

h
sep

=

10.3

7.8

=

2.5

m

(Absolute

pressure)

18)

How

will

you

obtain

the

max
i
mum

s
peed

during

suction

str
o
ke?

The

absolu
t
e

will

be

minim
u
m

a
t

the

begin
n
ing of

sucti
o
n

stroke.
Thus,

in

the

cylinder

the

separati
o
n taking

pl
a
ce

at

the

beginning of

suction

stroke
only.

In

this

case,

the

absolu
t
e

pressure

will

be

equal

to

the

s
e
paration
pressure.

h
sep

=

H
atm

(h
s

+

h
as
)

[or]

h
as

=

H
atm

h
s

h
sep

But

max
i
m
u
m

pressure

due

to

acceleration

in

suction

pipe

is

,

h
as

=

(l
s
/g)

(
A/a
s
)

ω
2
r

Equating

both

the

angular

velocity
(
ω)

and

Sp
e
ed

(N)

are

o
btained.

This

N

is

the

maximum

speed

of

the

pump

during

the

suction

str
o
ke

without

s
e
paration.

19)

How

will

you

obtain

the

max
i
mum

s
peed

during

delivery

stroke?

The

absolu
t
e

pressure

h

will

be

minim
u
m

at the

end

of

d
elivery

stroke.
Thus,

in

t
h
e

cylinder

the

separat
ion

t
aking

pl
a
c
e at

the

end

o
f

delivery

stroke

only.

In
this

case,

t
h
e

absolute

p
ressure

he
a
d

will

be

eq
u
al

to

the

se
p
aration

pressure.

22

T.G.PACKIA RAJ

M.E
.
, (Ph.D),

Asst. Professor
, Depar
t
ment of
Mechanical

Engi
n
eeri
n
g,

The Rajaas

E
n
gineeri
n
g College,
.

h
sep

=

H
atm

+

h
s

-

h

[or]

h

=

H
atm

+

h
d

h
sep

But

max
i
m
u
m

pressure

due

to

acceleration

in

delivery

pipe

i
s

,

h

=

(l
d
/g)

(A/a
d
)

ω
2
r

Equating

both

the angular

velocity

(
ω) and

Sp
e
ed

(N) are
o
btained.

This

N

is

the
max
i
mum

s
pped

of

the

pump

during

the

delivery

stroke

wit
h
out

separation.

20)

What

is

mean

by

M
a
ximum

speed

of

a

Reciprocating

Pump?

The m
a
xim
u
m

s
peed

at

which

no

separation

fl
o
w is

taking

place

in

the

cylinder

is
called

maximum

speed

of

a

recip
r
ocating

p
u
mp.

It

will

be

the

least

value

of
speeds

ob
ta
ined

from

maxim
u
m

speed

during

suction

stroke

and

maximum

speed

during

delivery

stroke.

21)

Write

th
e

workdone

saved

by

fitting

t
he

air

vess
e
l

in

recipr
oc
ating

pump.

By fitting

the

air

vessel

t
he

l
o
ss

due

to fric
t
ion

in

sucti
o
n

and

delivery

pipe

is
reduced.

This

reduction in

the

loss

saves

a

certain

amo
u
nt

of

energy.
Therefore,

the

workdone

s
aved

is

given

by,

Workdone

saved

by

workdone

against

fric
t
ion

workdone

against
friction

Fitting

airvessel

without

a
irvessel

with

airvessel

22)

Write

the

formula

for

workdone

a
g
ainst

fric
t
ion

with

air

vessel

in

r
e
ciprocating
pump.

Workdone

agains
t

friction

w
ith

a
i
rvessel

=

[K/π]

ρ
g
Q

[
4
fl/2gd]

[(A/a)

ω
r]
2

Where,

K

=

1

for

si
n
gle

acting

r
e
ciprocating

pump
K

=

2

for

double

acting

r
eciprocating

pump
Q

=

theoretical

dischar
g
e

(m
3
/s)

Q

=

ALN/60

for

single

ac
ting

reciprocating

pump

Q

=

2ALN/
6
0

for

doubl
e

acting

reciprocating

pump
f =

coeffici
e
nt

of

friction

l =

length

of

pipe

(m)

d

=

diameter

of

pipe

(m)
A

=

area

of

piston

(m2)

a

=

area

of

pipe

(m2)

ω

=

angular

velocity

ω

=

2πN/60

r

=

of

crank

23)

What

will

be

the

total

%

work

saved

by

fi
tting

the

air

vessel?

For

single

a
cting

recipr
o
cating

pump

=

84.8

%
For

double

acting

reciprocating

pump

=

39.2

%