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672
Start from pg 640
Tutorial 2 Done
10.11.2015:
16:30 16:45
17:30 20:00
Asf
Afdsaf
Tus te stagnation entalp! represents te entalp! of a "uid #en it is
$rougt to rest adia$ati%all!.
&ere T0is %alled te stagnation 'or total( temperature) and it represents te
temperature an ideal gas attains #en it is $rougt to rest adia$ati%all!. Te
term *2+2%p%orresponds to te temperature rise during su% a pro%ess and is
%alled te d!nami% temperature.
,oti%e tat -ineti% energ! terms do not epli%itl! appear in /s. 127 and 12)
$ut te stagnation entalp! terms a%%ount for teir %ontri$ution.
,ote tat te speed of sound in a "uid is a fun%tion of te termod!nami%properties of tat "uid.
Te speed of sound %anges #it temperature and aries #it te "uid. ,oting
tat te gas %onstant as a ed alue for a spe%ied ideal gas and te
spe%i% eat ratio - of an ideal gas is) at most) a fun%tion of temperature) #e see
tat te speed of sound in a spe%ied ideal gas is a fun%tion of temperature
alone.
a% num$er) a) is te ratio of te a%tual elo%it! of te "uid 'or an o$e%t in
still "uid( to te speed of sound in te same "uid at te same state.
,ote tat te a% num$er depends on te speed of sound) #i% depends onte state of te "uid. Terefore) te a% num$er of an air%raft %ruising at
%onstant elo%it! in still air ma! $e dierent at dierent lo%ations 'due to te
dieren%e in temperatures(.
eattempt /ample 12.3 on pg 617
,umeri%al alues of T+T0) 8+80) and p+p0are listed ersus te a% num$er in
Ta$le A13 for -91.4) #i% are er! useful for pra%ti%al %ompressi$le "o#
%al%ulations inoling air.
Te properties of a "uid at a lo%ation #ere te a% num$er is unit! 'te
troat( are %alled %riti%al properties) and te ratios in /s. '121( troug '12
20( are %alled %riti%al ratios 'ig. 121(. ;t is standard pra%ti%e in te anal!sis of
%ompressi$le "o# to let te supers%ript asteris- '
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Tese ratios are ealuated for arious alues of - and are listed in Ta$le 122.
Te %riti%al properties of %ompressi$le "o# sould not $e %onfused #it te
termod!nami% properties of su$stan%es at te %riti%al point 'su% as te %riti%al
temperature T%and %riti%al pressure 8%(.
;n tis se%tion #e %onsider te ee%ts of $a%- pressure 'i.e.) te pressure applied
at te no==le dis%arge region( on te eit elo%it!) te mass "o# rate) and te
pressure distri$ution along te no==le.
>e%ause te elo%it! of te "o# is soni% at te troat for te maimum "o# rate)
a $a%- pressure lo#er tan te %riti%al pressure %annot $e sensed in te no==le
upstream "o# and does not ae%t te "o# rate.
e%all tat 8< is te lo#est pressure tat %an $e o$tained at te troat) and te
soni% elo%it! is te igest elo%it! tat %an $e a%ieed #it a %onerging
no==le. Tus) lo#ering 8$furter as no in"uen%e on te "uid "o# in te
%onerging part of te no==le or te mass "o# rate troug te no==le. &o#eer)
it does in"uen%e te %ara%ter of te "o# in te dierging se%tion.
Te rise in te temperature of te "uid do#nstream of a so%- #ae is of maor
%on%ern to te aerospa%e engineer $e%ause it %reates eat transfer pro$lems on
te leading edges of #ings and nose %ones of spa%e reentr! ei%les and te
re%entl! proposed !personi% spa%e planes.
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edo:
12.7
12.7?
12.0
12.1
12.2
12.3
12.6 '@ou didnt get tis #rong) $ut loo- at o# te stagnation alues are
%al%ulated rst and used for te solution(
12.?0
12.?2 'tr! using angle gien in solution to aoid ina%%ura%! in%urred in reading
o from grap(
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Bapter 13 CpenBannel lo#:
Te "o# in a %annel is said to $e uniform if te "o# dept 'and tus te
aerage elo%it!( remains %onstant. Cter#ise) te "o# is said to $e nonuniform
or aried) indi%ating tat te "o# dept aries #it distan%e in te "o# dire%tion.
Ei-e pipe "o#) open%annel "o# %an $e laminar) transitional) or tur$ulent)depending on te alue of te e!nolds num$er.
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Te roude num$er is an important parameter tat goerns te %ara%ter of "o#
in open %annels.
;ndeed) te denominator of te roude num$er as te dimensions of elo%it!)
and it represents te speed %0at #i% a small distur$an%e traels in still liuid.
Terefore) in analog! to te a% num$er) the Froude number is expressedas the ratio of the ow speed to the wave speed, Fr = V/c0) ust as te
a% num$er is epressed as te ratio of te "o# speed to te sound speed) a
9 *+%.
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Tur$oma%iner!:
8ositiedispla%ement pumps '8D8s( for%e te "uid along $! olume %anges. A%ait! opens) and te "uid is admitted troug an inlet. Te %ait! ten %loses)
and te "uid is suee=ed troug an outlet. Te mammalian eart is a good
eample) and man! me%ani%al designs are in #ide use.
otord!nami% pumps
A d!nami% pump %an proide er! ig "o# rates 'up to 300)000 gal+min( $ut
usuall! #it moderate pressure rises 'a fe# atmosperes(. ;n %ontrast) a 8D8 %an
operate up to er! ig pressures '300 atm( $ut t!pi%all! produ%es lo# "o# rates
'100 gal+min(.
Tese are te Euler turbomachine equations) so#ing tat te torue) po#er)and ideal ead are fun%tions onl! of te rotortip elo%ities u1)2 and te a$solute
"uid tangential elo%ities *t1)2) independent of te aial elo%ities 'if an!(
troug te ma%ine.
,et ead & is proportional to te useful po#er a%tuall! deliered to te "uid. ;t is
traditional to %all tis po#er te water horsepower.
All pumps suer from irreersi$le losses due to fri%tion) internal lea-age) "o#
separation on $lade surfa%es) tur$ulent dissipation) et%. Terefore) te
me%ani%al energ! supplied to te pump must $e larger tan te #ater
orsepo#er. ;n pump terminolog!) te eternal po#er supplied to te pump is
%alled te brake horsepower) #i% #e a$$reiate as $p.
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Fe dene leading edge angle $1 as te $lade angle relatie to te reerse
tangential dire%tion at radius r1. ;n li-e manner #e dene trailing edge angle $2
as te $lade angle relatie to te reerse tangential dire%tion at radius r2. Fe
no# ma-e a signi%ant simplif!ing approimation. Fe assume tat te "o#
impinges on te $lade parallel to te $lades leading edge and eits te $lade
parallel to te $lades trailing edge. ;n oter #ords)
Fe assume tat te "o# is eer!#ere tangent to te $lade surfa%e #en
ie#ed from a referen%e frame rotating #it te $lade.
E/A, D;//,T T@8/S C /AB& 8G8
hapter ! " #imensional $nal%sis and &odellin'(
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Done: 7.34 7.6) DC HG/ST;C,S 7.6? C,FADSI ';8CTA,TIII(
Jot Frong:
/ample 7. on page 313 is ama=ing
7.47.52
hapter ) " Flow in *ipes(
Done: .30 .4?) DC HG/ST;C,S C T&/ A,K F&;T/ >CCK S;,B/ @CG
&A*/ AE/AD@ DC,/ HG/ST;C,S C T&/ B/,J/E >CCK
,eed to do te %on%ept uestions 130
Jot Frong:
.31
.37 ,i%e Huestion
.3?
.40
.43 @ou forgot to put E in te ro g E sin teta term
hapter + " ompressible Flow(
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,ote tat for p$less tan $a%- pressure B) tere is supersoni% "o# in te no==le
and te troat %an re%eie no signal from te eit $eaiour. Te "o# remains
%o-ed) and te troat as no idea #at te eit %onditions are.
8&is also %alled te design $a%- pressure.
Eoel! resour%e for no==le "o#:
ttp:++old###.uni$as.it+utenti+$onglioli+Jasd!n+sol
6.pdf
Eoo- at eplanation for pressures at B and & in
te de%ription $elo#III
Done: 12.1212.1?) 12.54 12.67) 12.6
Jot Frong:
12.30B
12.3?
12.45B
12.47B
12.54 ;S >CSS HG/ST;C, 'AAL;,J C BC,B/8T(
/ample 12.3 of ne# Bengel $oo-
To summari=e) for all $a%- pressures lo#er tan te %riti%al pressure 8
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%o-ed( "o# rate. >e%ause te elo%it! of te "o# is soni% at te troat for te
maimum "o# rate) a $a%- pressure lo#er tan te %riti%al pressure %annot $e
sensed in te no==le upstream "o# and does not ae%t te "o# rate.
-n uid d%namics, a &ach wave is a pressure wave travelin' with the
speed of sound caused b% a sli'ht chan'e of pressure added to a
compressible ow. hese weak waves can combine in supersonic ow to
become a shock wave if sucient &ach waves are present at an%
location. $ &ach wave is the weak limit of an oblique shock wave 1a
normal shock is the other limit2.
ran- Fite >oo-:
/ample ?.6 is ama=ing
/ample ?.? is %onfusingI
Done: 8?.10) 8?.35) 8?.40) p?.63) 8?.56) 8?.116 ?.12) ?.12? ?.135
125 not done)
Jone Frong:
?.11
?.126
?.12
hapter +3 " 4pen5hannel Flow(
Done: 13.21 13.40) 13.7? 13.M ,eed to do %on%ept uestions 13.6? 13.7)
and 13.?13.?4
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A "o# is %onsidered super%riti%al if te "o# dept ! is less tan te %riti%al "o#
dept !%. .Similarl!) te "o# is su$%riti%al if te "o# dept ! is greater tan te
%riti%al "o# dept !%.
13.3 >CSS HG/ST;C, 'ECCK AT ;TS D;SBGSS;C, AT T&/ /,D TCC F&// ;T
STAT/S T&AT &@DAGE;B NG8S A/ &;J&E@ D;SS;8AT;*/ 8CB/SS/S((
Jot Frong:
13.24B
13.25B
13.27B
13.2B
13.2?B *er! important %on%ept 'spe%i% energ! is a dierent %on%ept tan
spe%i% energ!(
13.30B A#esome reision uestion
13.31 Bool uestion
13.33 */@ ;8CTA,T HG/ST;C,
13.3
13.3? '@ou forgot to put elo%it! in te roude num$er euation(
13.40 Eoel! uestion
13.5
13.6 >CSS HG/ST;C, 'Tis uestion so#s tat te ead loss euation in terms
of initial and nal depts is in%orre%tM ,ote tat !our euation migt onl! #or-s if
te #idt is suO%ientl! largeP(
13.7 Killer HuestionI
13.?6 *er! important %on%ept uestion
13.?7 *er! ni%e %on%ept uestion
13.112
13.104 Ama=ing uestion
13.114 ; am er! %onfused a$out o# to do tese t!pes of uestionsI
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hapter +6 " urbomachiner%(
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;n te top of ig. 11.7 is plotted te net positiesu%tion ead ',8S&() #i% is
te ead reuired at te pump inlet to -eep te liuid from %aitating or $oiling.
Done: 14.20) 14.5
Jot Frong:
Huestions from ran- Fite $oo-:
Done: 11.15) 11.16) 11.17) 11.1) 11.1?) 11.22) 11.23) 11.42) 6.113) 6.114)
6.121) 6.120
Jone Frong: 11.17) 11.1) 11.23
Bengel $oo-:
Done: 6.47) 6.50) 6.53) 6.54) 6.57) 6.71) 6.72) 6.73) 14.1 14.14
Jot Frong: 6.50) 6.53) 6.73