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FLUID MECHANICS AND HYDRAULIC MACHINES
1. Defne density or mass density.Density of a uid is dened as
the ratio of the mass of a uid to its volume.Density, ρ =
mass/volume (Kg/m3 )
ρwater = !!! Kg/m3
2. Defne speif !ei"#t or !ei"#t density."#e$i$ weight or weight
density of a uid is dened as the ratio %etween the weight
of a uid to its volume."#e$ifi$ weight, & = weight/volume
('/m3 )w = ρgwwater = ! '/m3
$. Defne speif %o&'me."#e$i$ volume of a uid is dened as the
volume of uid o$$u#ied %y an unit wt or
unit mass of a uid."#e$ifi$ volume vs = volume/ wt = /w = /ρg
***** for li+uids
"#e$ifi$ volume vs = volume/ mass = /ρ ***** for gases (.
Defne dynami %isosity.is$osity is dened as the #ro#erty of uid
whi$h o-ers resistan$e to the movement of
one layer of uid over another ada$ent layer of the uid.
τ = 0 dynami$ vis$osity or vis$osity or
$oeffi$ient of vis$osity ('*s/m1 )
'*s/m1 = 2a*s = ! 2oise). Defne *inemati %isosity .t is
dened as the ratio %etween the dynami$ vis$osity and density of
uid.
4 = /ρ (m
1
/s) m1 /s = !!!! "to5es (or) sto5e = !*6 m1 /s+.
,ypes o- 'ids.deal uid, 7eal uid, 'ewtonian uid, 'on*'ewtonian uid,
deal 2lasti$ uid.8. Dene 9om#ressi%ility.t is dened as the ratio of
volumetri$ strain to $om#ressive stress.9om#ressi%ility, : = (d ol/
ol) / d# (m1 /')/. List t#e press're meas'rin" de%ies0
) ;anometers.1) ;e$hani$al gauges.
. Defne manometers0
;anometers are dened as the devi$es used for measuring the
#ressure at a #oint in a uid %y %alan$ing the $olumn of uid %y
the same or another $olumn of theuid.. 3#at is me#ania&
"a'"es0
;e$hani$al gauges are dened as the devi$es used for measuring
the #ressure%y %alan$ing the uid $olumn %y the s#ring or dead
weight.14. List t#e me#ania& press're "a'"es.
) Dia#hragm #ressure gauge.1)
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"teady owCluid ow is said to %e steady if at any #oint in the
owing uid various$hara$teristi$s su$h as velo$ity, density,
#ressure,et$ do not $hange with time.F/Ft = !, F#/Ft = ! ,Fρ/Ft =
!>nsteady owCluid ow is said to %e unsteady if at any #oint
owing uid any one or all$hara$teristi$s whi$h des$ri%e the
%ehaviour of the uid in motion $hange with
time.F/Ft G ! F#/Ft G ! Fρ/Ft G !2(. Defne Uni-orm and
Non:'ni-orm o!.
Uni-orm o!Hhen the velo$ity of ow of uid does not $hange %oth in
dire$tion and magnitudefrom #oint to #oint in the owing uid for any
given instant of time, the ow is saidto %e uniform.F/Fs = ! F#/Fs =
! Fρ/Fs = !Non:'ni-orm o!f the velo$ity of ow of uid $hanges from
#oint to #oint in the owing uid at any instant, the ow is said
to %e non*uniform ow.
F/Fs G ! F#/Fs G ! Fρ/Fs G !2). Compare Laminar and ,'r
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@he ow #arameter su$h as velo$ity is a fun$tion of time and one
s#a$e $o*ordinateonly. u = f (I), v = ! w = !.@wo dimensional ow@he
velo$ity is a fun$tion of time and two re$tangular s#a$e
$o*ordinates. u =f (I,y), v = f 1(I,y) w =!.@hree
dimensional ow@he velo$ity is a fun$tion of time and three mutually
#er#endi$ular dire$tions.
u = f (I,y,), v = f 1(I,y,) w = f 3(I,y,).2.
3rite t#e 6erno'&&i7s e8'ation app&ied
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$. 3#at is t#e ma=im'm t#eoretia& s'tion #ead possi
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(. SEED REULA,I>N @>ERNIN >F ,HE EL,>N
3HEEL >sually, hydrauli$ tur%ines are $ou#led to ele$troni$
generators. @hese generators arere+uired to run at $onstant s#eed
irres#e$tive of variations in the head and #ower out#ut. Hhenthe
load on the tur%ine $hanges, the s#eed may also $hange, (i.e.,
without load the s#eedin$reases and with over load, the s#eed
de$reases). Qen$e, the s#eed of the runner must %emaintained
$onstant to have a $onstant s#eed of generator. @his is done %y
$ontrolling the +uantity
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of water owing on the runner a$$ording to the load variations.
@his s#eed regulation is5nown as governing and it is usually done
automati$ally %y a governor.)4.o%ernin" Me#anism -or t#e e&ton
!#ee& E servomotor governor (also 5nown as oil
#ressure governor) is shown in Ciguret $onsists of (l) a
servomotor, (1) relay valve or $ontrol valve, (3) a$tuator
($entrifugal governor),(6)oil sum#, (S) oil #um# and (T) oil su##ly
#i#es.3orin"
@he $entrifugal governor (a$tuator) is driven %y the tur%ine
shaft through a %elt or gear. Hhen theload on the generator
redu$es, the tur%ine s#eed in$reases. t $auses the following
a$tions to ta5e #la$e one after another..Cly %all of the
governor moves u#ward, 1."leeve moves u#ward,3.eft hand end of main
lever rises,6.
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6.@he #iston in the $ontrol valve moves u#ward in the $y
%inder,S.Jil under #ressure is for$ed from the $ontrol valve to the
right side of the #iston in theservomotor,T."ervomotor #iston moves
to the left #ushing the oil in the less side to the oil
sum#."imultaneously, the s#ear moves %a$5ward. @he %a$5ward
movement of the s#ear in$reases theo#ening of the nole outlet.
@hus, a large +uantity of water stri5es the runner and the
normals#eed of the tur%ine is restored.
o%ernin" o- Franis ,'r
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that the eIa$t %ehaviour of the unit under varying wor5ing
$onditions are #re*determined.@hese are o%tained %y manufa$turers
%y $ondu$ting eI#eriments on models in a la%oratory and%y doing eld
tests on the site. @he #hysi$al #arameters $ontrolling the
#erforman$e of a tur%ineare s#eed ',#ower out#ut 2, head Q,
dis$harge B, the #osition of gate o#ening (nole o#eningor guide
%lade o#ening)V, and the eA$ien$y of the tur%ine. @he %ehaviour of
the units arere#resented %y $urves $alled tur%ine
$hara$teristi$s.@he $hara$teristi$s of tur%ines are o%tained under
three di-erent $ategories*U
(a) ;ain $hara$teristi$s (Qead $onstant)(%) J#erating
$hara$teristi$s ("#eed $onstant)($) ;us$hel $urves (WA$ien$y
$onstant)
A. Main #arateristis9n this $ase, the head is 5e#t
$onstant and the s#eed is varied %y varying the load on the
tur%ine.@he governing me$hanism is dis$onne$ted from the system so
that the eI#eriments are #erformed at $onstant gate o#enings.
@hree set of $urvesP s#eed*dis$harge, s#eed*#ower
ands#eed*eA$ien$y,ea$h for 2elton, Cran$is and Ka#lan tur%ines,
have %een shown in Cigure (a), (%) and ($).Speed %s dis#ar"e
'r%e9
Cor a given area of ow, the dis$harge de#ends u#on Q /1 for
a 2elton tur%ine. "in$e Qis $onstant, the #eri#heral s#eed of the
tur%ine is $onstant and therefore, thedis$harge is inde#endent of
s#eed. n rea$tion tur%ines, dis$harge de#ends u#on thevelo$ity of
ow. @he #eri#heral s#eed of the tur%ine varies with the s#eed and
the %lade angles(that is $onstant for a Cran$is tur%ine), the
velo$ity of ow will de$rease with in$reasings#eed. @hus, dis$harge
de$reases with the in$rease in s#eed. n Ka#lan tur%ines, thereverse
is true and therefore, dis$harge in$reases with the in$rease in
s#eed.Speed %s po!er 'r%e9
2ower is #ro#ortional to angular s#eed. Hhen ' is ero, the
angular s#eed is ero and when 'e+uals runaway s#eed, the out#ut
#ower is again ero. @hus, the s#eed*#ower $urves for tur%inesare
#ara%oli$ in nature.Speed %s e;ieny 'r%e9@he s#eed*eA$ien$y $urves
for tur%ines are similar to s#eed*#ower $urves.6. >peratin"
C#arateristis9n a hydroele$tri$ #ower station, tur%ines are $ou#led
with ele$tri$al alternators for #rodu$ingele$tri$ity at a $onstant
fre+uen$y and therefore, they must run at $onstant s#eed. @hehead
and dis$harge de#ends u#on their availa%ility in the storage
reservoir. @he #ower out#ut de#ends u#on the demand from the
lo$ality, and the #ower out#ut*eA$ien$y, dis$harge*#owerand
eA$ien$y $urves are im#ortant and have %een shown in Cigure (a)and
(%).C. Constant e;ieny 'r%e9t is evident from s#eed*eA$ien$y and
s#eed*#ower $urves that there are two values of s#eedfor the same
#ower*out#ut and eA$ien$y, eI$e#t for the #oint of maIimum eA$ien$y
o$$urring at the designed s#eed. @hus, we should lo$ate the
region of $onstant eA$ien$y so that thetur%ines are o#erated with
maIimum eA$ien$y. @he eA$ien$y $urves are #lotted inCigure
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G1.Ho! to mae t#e manometer more sensiti%e0 .%y using
narrow tu%e as manometer.1. %y using non*sti$5 uid li5e mer$ury.3.
ma5ing the manometer in$lined
2. Defne S'r-ae ,ension."urfa$e tension is dened as the tensile
for$e a$ting on the surfa$e of the li+uid in
$onta$t with a gas or on the surfa$e %etween two immis$i%le
li+uids su$h that the$onta$t surfa$e %ehaves li5e a mem%rane under
tension.
"urfa$e @ension, X = Cor$e/ength ('/m)X water = !.!81S '/m
X ;er$ury = !.S1 '/m$. S'r-ae tension on &i8'id
drop&et? X = #d/6"urfa$e tension on a hollow %u%%le, X =
#d/"urfa$e tension on a li+uid et, X = #d/1X 0 surfa$e tension
('/m)d 0 diameter (m) # 0 #ressure inside
('/m1 ) #total = #inside L #atm #atm = !.31S I !3
'/m1
(. Defne Capi&&arity.9a#illarity is dened as a
#henomenon of rise or fall of a li+uid surfa$e in a small tu%e
relative to the ada$ent general level of li+uid when the tu%e is
held verti$ally in theli+uid. @he rise of li+uid surfa$e is 5nown
as $a#illary rise while the fall of li+uidsurfa$e is 5nown as
$a#illary de#ression.
9a#illary 7ise or fall, h = (6X $osY) / ρgdY = ! for glass tu%e
and water Y = 3!Z for glass tu%e and mer$ury). Defne apo'r
ress're.Hhen va#oriation ta5es #la$e, the mole$ules start
a$$umulating over the free li+uid
surfa$e eIerting #ressure on the li+uid surfa$e. @his #ressure
is 5nown as a#our #ressure of the li+uid.
+. Defne Contro& o&'me. E $ontrol volume may %e
dened as an identied volume Ied in s#a$e. @he
%oundaries around the $ontrol volume are referred to as $ontrol
surfa$es. En o#ensystem is also referred to as a $ontrol
volume.
/. 3rite t#e ontin'ity e8'ation.
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@he e+uation %ased on the #rin$i#le of $onservation of mass is
$alled $ontinuitye+uation.
[u/[I L [v/[y L [w/[ = ! ***** three dimensional ow[u/[I L [v/[y
= ! ***** two dimensional owB = av = a1v 1 ***** one
dimensional ow
. List t#e types o- 'id o!."teady and unsteady ow
>niform and non*uniform owaminar and @ur%ulent ow9om#ressi%le
and in$om#ressi%le ow7otational and ir*rotational owJne, @wo and
@hree dimensional ow. 3#at are t#e -ators in'enin" t#e
-ritiona& &oss in pipe o!0
Cri$tional resistan$e for the tur%ulent ow is,i. 2ro#ortional to
v n where v varies from .S to 1.!.ii. 2ro#ortional to the
density of uid.iii. 2ro#ortional to the area of surfa$e in
$onta$t.iv. nde#endent of #ressure.
v. De#end on the nature of the surfa$e in $onta$t.
14. 3rite t#e e=pression -or &oss o- #ead d'e to s'dden
en&ar"ement o- t#e pipe.
heI# = ( * 1 )1 /1gHhere, heI# = oss of head
due to sudden enlargement of #i#e. = elo$ity of ow at #i#e N
1 = elo$ity of ow at #i#e 1.11. 3rite t#e e=pression -or
&oss o- #ead d'e to s'dden ontration.h$on =!.S
1 /1gh$on = oss of head due to sudden $ontra$tion. =
elo$ity at outlet of #i#e.12. 3rite t#e e=pression -or &oss o-
#ead at t#e entrane o- t#e pipe.
hi =!.S 1 /1ghi = oss of head at entran$e of #i#e. =
elo$ity of li+uid at inlet of the #i#e.1$. 3rite t#e e=pression -or
&oss o- #ead at e=it o- t#e pipe.ho = 1 /1gwhere, ho
= oss of head at eIit of the #i#e. = elo$ity of li+uid at inlet and
outlet of the #i#e.1(. i%e an e=pression -or &oss o- #ead d'e
to an o
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@he single #i#e re#la$ing the $om#ound #i#e with same diameter
without$hange in dis$harge and head loss is 5nown as e+uivalent
#i#e.
= L 1 L 3(/dS ) = ( /dS ) L (1 /d1S ) L
(3 /d3S )
1/. Defne t#e terms a Hydra'&i "radient &ine HL
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^m=
2. Defne %o&'metri e;ieny.@he ratio of the volume of the
water a$tually stri5ing the runner to the volume of water
su##lied to the tur%ine is dened as volumetri$ eA$ien$y.
2. Defne >%era&& e;ieny.
t is dened as the ratio of the #ower availa%le at the shaft of
the tur%ine to the #ower su##lied %y the water at the inlet of
the tur%ine.
2ower availa%le at the shaft (shaft #ower)^o =
**********************************************************2ower
su##lied at inlet (water #ower)^o = ^h ^m ^v (or) ^o = ^h ^m$4.
3#at are an imp'&se t'r
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$2. Defne Radia& o! reation t'r
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's = ' bB/ (Q)3/6 (J7) 's = ' b2/ (Q)S/6
(1. E;ienies o- a Centri-'"a& 'mp9;anometri$
WA$ien$yP@he ratio of the manometri$ head to the head im#arted %y
the im#eller to the water is 5nown as manometri
e;ieny .
;anometri$ Qead g Qm^mano =
******************************************************* =
***********
Qead im#arted %y im#eller to water w1u1Qead im#arted %y
im#eller to water = w1u1 /gMe#ania& E;ieny9@he ratio
of the #ower availa%le at the im#eller to the #ower at the shaft of
the$entrifugal #um# is 5nown as me$hani$al eA$ien$y.
2ower at the im#eller^me$h =
*********************************
"haft 2ower2ower at the im#eller = wor5done %y im#eller #er se$
= ρB w1u1
>%era&& E;ieny9
@he ratio of #ower out#ut of the #um# to the #ower in#ut to the
#um# is $alled asoverall eA$ien$y.
Height of water lifted I Qm^o =
******************************************
"haft 2ower (2. Defne Manometri Head.@he manometri$ head is
dened as the head against whi$h a $entrifugal #um# hasto wor5.
Qm = head im#arted %y the im#eller to the water 0 loss of headQm
= w1u1 /g * loss of headQm = hs L hd L hfs L hfd L
v d1 /1g
($. Di5erentiate stati #ead K manometri #ead."l. 'o.
"tati$ Qead ;anometri$ Qead @he verti$al head distan$e to li+uid
surfa$e in
sum# to overhead tan5.@otal head that must %e #rodu$ed %y
#um#to satisfy the eIternalre+uirements.
1 oss of head in the #um# is not $onsidered. @he fri$tion head
loss 5ineti$ head are$onsidered.
3 Q = Qs L Qd Qm = Qs L Qd L hfd L
v d1
/1g45. Distinguish between impulse turbines and reaction
turbines. Impulse turbine Reaction turbine
1. All the available fuid energy isconverted in inetic energy.
2.!lades are in action only "henthey are in the #ront o#
theno$$le.3. %ater &ay be allo"ed to enter
'nly a (ortion o# fuid energy isconverted into inetic
energy.!lades are in action all the ti&e. %ater is
ad&itted over thecircuerence o# the "heel.
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a (art or "hole o# the "heelcircuerence.4. )he "heel does not
run #ulland air has #ree access to thebucets.5. *nit is installed
above the tailrace.
6. )here is no loss "hen the fo"is regulated.
%ater co&(letely +lls the vane(assages throughout the
o(eration o# the turbine.*nit is e(t entirely sub&erged
in"ater belo" the tail race. )here is al"ays a loss "hen the
fo" is
regulated.
44. Show that the maximum hydraulic efciency o a pelton bucket
is !!".
#ns. , - Absolute velocity - , / v
ydraulic eciency-
.$ath lineath line is the line traced by a given (article. )his
is generated by inecting a dyeintothe fuid and #ollo"ing its (ath
by (hotogra(hy or other &eans%.Streak line
trea line concentrates on fuid (articles that have gone through
a +ed station o
r(oint. At so&e instant o# ti&e the (osition o# all
these (articles are &ared and a line
is dra"n through the&. uch a line is called a strea line
&.Stream linestrea& lines are a series o# curvesdra"n
tangent to the &ean velocity vectors o# a
nu&ber o# (articles in the fo".ince strea& lines are
tangent to the velocity vector at
every (oint in the fo" +eldthere can be no fo" across a
strea& line
4.'irculation
circulation is de+ned as the line integral o# velocity about
this closed (ath. )he sy&bolused is 5.(orticity(orticity is
de)ned as circulation per unit area. i.e.* ,orticity - circulation
(erunit area here area
UNI, 9 >SI,IE DISLACEMEN, MACHINES1 3#at is a reiproatin"
p'mp07e$i#ro$ating #um# is a #ositive dis#la$ement #um#. @his means
the li+uid is rst su$5ed into the $ylinder and then dis#la$ed
or #ushed %y the thrust of a #iston.2 3#at is sin"&e atin" p'mp
and do'
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t is dened as the gra#h %etween #ressure head in the $ylinder
and stro5e lengthof the $ran5 under ideal $ondition is 5nown as
ideal indi$ator diagram.During the su$tion stro5e, the #ressure in
the $ylinder is %elow atmos#heri$ #ressure.During the delivery
stro5e, the #ressure in the $ylinder is a%ove
atmos#heri$ #ressure.11 3#at is t#e re&ation
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hse# = Qatm 0 (hs L has ) \or] has = Qatm 0 hs 0 hse#
