Fluid Mechanics 2 Notes

7/24/2019 Fluid Mechanics 2 Notes

1/17

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- '


2/17

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.


3/17

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(


4/17

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.


5/17

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 *+%.


6/17


7/17


8/17


9/17


10/17

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.


11/17

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'(


12/17

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(


13/17

,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


14/17

%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


15/17

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


16/17

hapter +6 " urbomachiner%(


17/17

;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

Documents

Fluid Mechanics 2 Notes