Барлит В.В. Гидравлические турбины

tl

B

BepruKanbHofi

oceBoft

ruAporyp6HHe

c

paAsaJIbHbIM

Hanpa-

tsJrflrouIHM

an[apaToM

Ha BxoAe

B

pa6oqee

KoJIeco

I{MeeT

MeCTo

onpe-

AeJreH

Haf

Hep

aBHoMep

HocTb

p

ac[peAeJleH

H fl oceBo

fi H

oKp

yx(Hofi

cocraB'

JrsrO111HX

a6COlnrHofi

CKOpOCTH,

BbI3bIBaeMaf'

B OCHOBHOM'

IIOBOpO'

a

Fuc. I

I

l. Bsr6op

pacqerHblX

ceqeHlil"t ronacrH.

a0a

Puc.

ll0.

floror

Ha

BxoAe

H

BbIxoAe

H3

oceBoro

pa6oqelo

KoJIeca:

d-pac[pgAeJrerrHe

oCeaofi

cKopocTH

BAoJIb

paAHyca;

6--PaCnpeAereHEe

MoMeIITa

cKgpocTtr;

€

-

rr3ueue"rr"

"u*pfri'it"nj*C

sl

pa6ouuu"lr.+Tf1

npH

pa3nuqublx

o{kpbrrnsx

HanpaBrltlou{ero

-roM

noToKa

nepeA

pa6orIHM

KoJIecoM.

flpuueu,

xapaKTep

H3MeHeIIHff

COCTaBJIflTTqHX

Um

u

i

,uo

a6co.nOrHofl

gKOpOCTH

nOTOKa

nOCJIe

HaIIpaB-

(aur)r:

f

t(r)

-

constl;

vzt

f

,t)

:

COflStz.

OAuaxo

onbITHbIe

AaH

HbIe

I'l ccJIeAoB

aHHfl

rrcToKa

B

ilpoTorlHoft

qacrll

MOAeJIefi

rulpo-

Typ6HH

noKa3blBalor'

tITo

oceBafl

cocraB-

IflIOilIaq

uzt

noToKa

He[ocTofHHa

BAOJIb

paAHyca

H

yBeIHrIHBaeTCs

oT

BTyJIKH

K

i<artaepe

pa6oqero

KoJIeca.

llpt

pacqere

perrreroK

ilpoQHrefi

o6uqso

npHHHMarO{

nunefiHuri

'saKoil

lI3MeHeHHg

ur,

:

f

(r),

ilpH

KOTOpOI\I

BerHqHHzOqY

KaMepbI

Ha

10-20

%

^

6onawe,

r{eM

y BTyJIKH

pa6o-

qeio

KoJreca

(psc. 110,

a).

Cor,nacHg sKcnepur\reHTaJrbHblM AaHHbIM

Ha

OTITHI\{aJIbHOM

pex{HMe

pa2;4ailb1an

COcTaBJIg

1o1\afl.

Ur

a6CO.irnrHoft

CKOpOCTH

HeBeJIHKa'

nO-

sTOMy

MOX(HO npeA[OJIO)KHTb,

IITO

noToK

ABH)KeTCg

BAOJIb

[OBepxHo-

cTefi

ToKa, 6nusxux

K

IIHJIHHApHqecKHM.

npn

sToM

AoIIyqeHHH

KoJIb'

222

JIflIOIqeTO

annapaTa,

npHMepHo'

OAHHaKOB'

Pacnpege;renne

ocesofi

cOCTaBJIflIoIqefi

cKopocTn

rlo

paAHyrY

.o-:7_

:f

(r).

Kax

noxa3aHo

BbIIIIe,

ABI{x(eHHe

x(HAKocTH

no

UHJIHHApIIqeCI(HM

z

roBepxHocrqM

roKa

u9_ty_?T"o

rIpH

BbITIoJI'

'

HeHHH

cJIeAyIoulHx

ycnoBvtit

s

noroKe:

ueBble

nJIoIqaAH,tIoToKa He H3l'rcHqroTcs,

H

cofJracHo ypaBHeHHro

Hepa3-

pbrBHocrH

3HarreHHq

oceBbrx cKopocrefi

H Hx pac[peAeJreHHe

BAoJrb

pa-

Al{yca

Ha

BbIxoAe

raKl{e

x(e,

KaK H Ha

BXoAe

B

pa6oqee

KoJreco.

Be.nrr-

qHHa

oceBofi cKopocTH

Ha cpeAHeM IIHJIHHApHTTeCKoM

ceqeHHH

onpeAe-

.rrflercs

no

Qopruyae

%.,r

(312)"

Ha

rrepHQepHrl

(313),

ql

uzt

i

o?

-

a?",)

3HarIeHHg

oceBofi

H

y

BTy,lKr.r:

cocTaBJrfrorqer?

cKopocTH

Eas

ocraJrbHbrx

ceqeHnfi npuulluaror

JruHefiuufi saKoH

uz

-

I

@.

PacnpeleJleHne

MoMeHTa

cKopocTH

out

:.f(r).

LlgueseHHe

MoMeHra

cKopocrn

noroKa

Ha

BXoAe e

pa6ovee

KoJreco

(a"r)r:

f

(r)

raKxe saBH-

cHT OT

QOprrlU

rroJiocrH,

rrapaMerpoB

HanpaBJrsroqero

annap

ara v

pe-

xLIMa

pa6omt

ruAporyp6yuat

Kax

noxasbrBaror

orrbrrHbre

HccJreAoBa-

nwn

pa6orlHx

KoJIec, npu

onrHMaJIbHoM

pex(HMe

Ha

BbrxoAe H3

pa6or{ero,

KOJIeCa

saKpyrKa

noroKa

y

BTyJTKH npHMepHo paBHa

HyJrro,

a Ha

repH-

Qepuu

(a"r)r:

+

0,2q,gHlc'1.

PasHocrr

A,

(a"r):

(aur)r-(aur),

rrpu-

HHMaror oAuHaKosofi

Anq

Bcex

noBepxHocrefi

roKa.

flp,

pacqere

pa6ouero

KoJIeca

Ha

pex(HM

HoMHHa.nluofi

MorrlHocrr4

saAarcrcs

3HaKorreperuresuofi

saxpyrxofi

noroKa

Ha

BbrxoAe H3

pa6o-

qero

KoJIeca

(pnc.

110,

a). Coraacso

gKcnepHA{eHTaJrbHbrM

AaHHbrM

Ha

pex(aMe

HoMlIHaJIruotl

I\{ouIHocTH

rroToK y

BTy/rKH r.rMeer

orpHuareJrb-

HyIo 3aKpyrKy,

a Ha

nepuQepuu

rIoJIo)KHreJIbHyrc

(10

+-20o/o

o't BeJrH-

quHbr

rlrgHla).

3aAaeuiucb

pacrpeAeJreHnav

(aur)r:

f

(r)

BAo/rb

pa-

Ar4yca,

npH noruorrlH ypaBHeHHs

n.

3finepa

oilpeAeJrfror

3Har{eHHs

(a"r),

Ha

BXoAe

e

pa6ouee

KoJreco Ha

pacqerHbrx

cerreHr,rsx.

Taxinnr

o6pasou,

npa rrpuHflrbrx

BerurruHax

Qi;

ni H 3aBucrMocrflx

or:

f

(r),

(aur)r:

f

(r),

(aur)r:

f

(r) 3HaqeHHq

cxopocrefi a,,:

u,,i

ttt: tlzi Uuri uu"

H3BecTHbI

IIa Ka)I{Aoft

nonepxHocTH

ToKa.

3ro

nosso,'IfeT

nocrpoaTb

BXoAHbte

H BbIxoAHbIe

TpeyroJrbHHKH

cKopocrefi

,

Heo6xoAHMF,re

Arr

nocr'reAyioulHx

pacqeroB

perueroK

npoQn"nefi.

$

fZ.

[ocrpoeune

BxoAnbrx

n Bbrxo4rrrrx

rpeyroJrruurcoB

cffopocreft na

pacrrerHbrx

rroBepxHocrsx

rorca

trtts

pacriera

Qopuu

npoQn,rn perrerKH

Ha

pacqernoft

noBepxHocrr.i

ToKa

ueo6xoAHMo

onpeAgilHTb

BXoAHbre

H

BbrxoAHbre

yr/rbt,

a

raK1(e He-

Koropbre

napaMerpbi

HeBosMyrqeHHoro

noroKa.

C erofi

qeJrbro

crpoflT

rpeyfo"tlbHuKx

cKopocru

rloroKa

Ha

BXoAe H

BbrxoAe us

pa6overo

KoJreca

(pu9.

106).

flocrpoeHHe

BxoAHbrx

H

BbrxoAHbrx rpeyroJrbHuKoB

cKopo-

crefi

BbrrroJrHsror

B

greAyroqerl

nocJreAoBareJrbHocru.

uznep:

Irlo."o;

I

or"r:0,9ttr"r.

I

o6/nun,

(ra6"u.

23).

Cpe4nar

BeflHrrHHa

oceeoft

cocraBJlsroqefi

cKopocrn

noroKa

uz orlpe-

AeJlsercs

no

Qopt'ry.ne

4Qi

t)rrcp:

I)r2cp:

*

eft;,

nlc'

Oxpyx<Hbre cKopocrn

noroKa

Ha

BxoAe

H BbIxoAe

H3

neca

Ha

pacqerHoM

rlHJIHHApHqecKoM

ceqeHHH:

nni

llL:

l)Z: f

i,i

:

f,

3O

,

ltt/C.

flo.nlsyrcb rrpnHsrbrM

3aKoHoM

pacnpeAeJleHHs MoMeHTa

cKopocrH

BAoJIb

paAgyca

Ha BbIxoAe

I{s

pa6ouero

Koneca

(puc.

110,

a), onpeAe-

.ngrcfgHa.IeHr.rs

ou,v

BeJIHTIHHbI

yrJIoB

B,

pacuerHblx

cetleHafi:

(314)

pa6ouero

xo-

(315)

(316)

Auanoruqnbre

BbrrrncreHur

BbrnoJIHflrcT

Anfl

Tex xe

ceqeHrfi

Ha BxoAe

a

pa6ovee

KoJIeco:

\rgH

. ,

au,

':

T

+

t'ur' 'uc;

tgPr:#'

'

-

uL- au,

Onp

e4e.n n

lor

BeJI

HqH

HbI I{

Ha

n

p

aBJI eHHe

cpeAHeBexrop

uofi

orHochreJrbHoro

noroKa lg^

\ng,

pacqerHblx

ceqegufi:

'^@*raz

TEP*:

,^u:

-p;r'

"---z

+1"

-+(ou,*

o,,)f

V,Z

t

(317)

(318)

cKopocrl{

'vlo;

(319)

(320)

Pesy,llraTbl

pacqeToB

noMeu1arcr

s

ra6nxUy

(ctvt.

npuMep

pacqeTa'

'ra6t.

25), ro

AaHHbrM

Koropofi

cyAnr o

roM,

HacKoJIbKo

yAarrHo

IIpH-

+Iflrbl

HcxoAHbIe napaluerpbl

peueroK H

pacnpeAeJleHue

cKopocTefi

a"

LI

uu

Ha

BXoAe

H

BbrxoAe

H3

pa6ouero KoJIeca.

oAUUrnr H3 KpHTepHeB

OUeHKH

QOpTUU

JrOnacTH

flB.rlfleTcfl

pa3HOCTb

yf,roB

Ap

ycrauonxu

npoQu.rreft

y

BrynKIl

Py"'.

"'

H

Ha

nepu$epuu

py...

r"p

(prrc.

ll2,

a,

6), KoTopafl

cyulecrBeHuo

B.IIHffeT Ha

gH_epreTn-

d{ecKHe

H KaBr.rrarlHoHHbre

xapaKTepr{cTHKtl

pa6ouero

Koneca.

B

coor-

BeTcTBHH c HMercIqHMHcfi

AaHHbIMH

HOMCHKJIATYPHbIX

PA6OUUX

KOJICC

224

f

I

i

I

L

l,

I

AP

:

Fr"'.

".

-

Pv"T.nep

:_

!!

+ 18",

rAe

Py",

:

P*-e.

Ecnu [epe-

KpyrKa

JrorracrH (puc.

112,

a)

6o.nture

pi:xortren4yeuofi,

Heo6xoAarrlo

Id3MeHHTb

rrapaMeTpbr

perxeToK

HJrH

npHHflTb

ApyrHe

yrJrbr

aTaKH

H

pac_

qeT

noBTopHTb.

3saqesufl

yrJroB

aranr

H

xapaKTep

Hx

HsMeHeHHr

BAoJrb

parlyca

npHHHMaIor

rla

ocHoBaHHH

onbrra

paspa6orKn

nyquHx

pa6ovHx

KoJrec:

y

prynKn

o6H,rHo

He

6o.ueecr

<

6

+

l0o,

a Ha nepnQepun

&

-

O

-+

2".

flo npuHflT-brl{.

3HarreHH

flM

d

y

BryJrKH

H

Ha

nepraq'epraH

crporr

rrapa-

6o.rrya-f(r).

Pttc.

ll2.

K

onpeAereHuro yrnoB

ycraHoBKH

Jrorracru y

BTynKH

H Ha nepu@pua:

c

-

nepuQepnft

Hoe'

"?T?;#T5fl"'fl:T:t'"3";#?"lT?x1tlo."*o*'un

ua

nep'sep'u

Bee4enlle

yrJIoB

aranr

o6ocnossrBaercr

cneAyrorqHl{H

coo6paxe-

HHTMH.

lllgnecrFro,

qro

pacqer

JronacrH

npH

noMorrlH

AByMepHbrx

Mero-

AOB

OCHOBaH,

B

TTaCTHOCTVI,

Ha npeA[OJIOX(eHHH

frOCTOtHcrna

rIHpKyJrf-

I{HH

BoKpyr.rronacru

BAoJrb paAHyca

fr,:

I

(r)

:

const.

I{upxyilsr\krn

BOKpyr

ironacrH

fr,

:

t

(our-

uu,)

:

2nrlrgH

fn

11,,

(32r)

@z

rAe

f,

-

qacrb

ur.rpKyJrsrlHH,

co3AaBaeMarr

xpunusHoil

upoQunx;

fo

-

I{HpI{yJIf

IIHq

BoKpyr

npoQHnrfl,,

o6ecne.rHBaeMafl

BBeAeHHeM

yrJra

ATAKH.

Ec-nu y

KopHeBoro

cerleHnfl,,ronacrH

He

BBoAHTb

yroJr araKt,

To

pac-

qerHar

qupKynsuHq

BoKpyr npoQu.na

AoJrx(Ha

6rrrn

o6ecneqeHa

3a

cqeT

yBeJIHqeHHfl

efo KpuBH3Hbi,

rocKoJlbKy

orHocHTeJIbHafl cKopocTb

noroKa.y

BryflKH

MeHbrrre,

rreM

Ha nepaQepHH

(puc.

tl2,

6).

orHoue-

HHe

f"/f,

3aBricHr

or

6srcrpoxoAHocrH

npoeKrHpyeMoro

pa6ouero

E

z-204

z2s

KOJteCa.

o6uqHo

IIpH

pacqere KopHeBoro

cerleHHs

BbIcoKoHanopHHX

pa-

6oqux

KoJIec

npuHrauaror

f"/f.,r:

0,33

+

0,5;

AJIfl

HH3KoHaIIopHbIX

f"/fr,

:

0,33.

-

Onp.1eJIHB

BxoAHbIe

H

BbIxoIHbIe

yrJIbI

H HanpaBneHge

HeBO3My-

uleHHoro

noroKa

,qIq

pacqerHblx

ceueHufi,

nepexoAflT

K

pacrleTy

npo-

Qn.rrefi

peIUeToK,

Hx

KoMnoHoBKe

u

nu6opy

ocu

noBopoTa

JIonacTLI'

S

58.

Metor

troAbeMrrbrr

efrn

B

npaKrHKe

pacrrera

oceBbrx

pa6ouux

KoJIeC

HapflAy

c

ApyrHlvlll

MeToAaMH

HaXoA;T

npHMeHeHHe

MeToA

noAbeMHbIX

qHJI'

Ha

saAaHHbIe

rrapaMeTphl

Typ6HHbI

(pacqeTHble

MoUlHoc-Ib'

Haliop

H

cunxpoHHaff

"iac-

TOTa

BpaUIeHHs)

B

CooTBeTcTBHH

c

H3JIoxeHHoft

BbIuIe

MeToAHKOfi

si'I-

6uparoi

HcxoAHbIe

flapaMerpbl

pacqerHblx

perleroK

H

orlpeAeJlflor

Tpe-

yroabggKr.t

cKop;crefi

na

sioae

r{

BbIXoAe

Hs

pa1oqero

KoJIeca"

B

xo,u,e

pacr{era

peureroK

BbrrrHcr-sror

BeJrr.qHHy

qupKyJIgIlHH

BOKpyr

Jlo[acrtt

npn 3aAaHHbIx

pacrlerHblx

rapaMerpa.l

IIpH

IIoMoIIIH

Bblpax{eHHs

(321)

H 3HaqeHr.re

Koo++I{UHeHra

noAbeMHofi

culu

rpoQHJIfl

B

peIIIerKe

cnr:'#,

B p$yJrbraTe

pacqeToB

npu

IIoMoIIIH

yKa3aHHbIX

BbIIue

3aBI{cH-

M(rcTefi

onpe,Uennrot

napaMeTpbl

npOeKTHpyeMbIx

pelxeToK:

&)^,

p^,

l,

I

u Cro.

fio

BbIuItcJIeHHbIM

sHaqeHHflM

Cup,

IIOJIb3yflcb

gKcnepHMeII-

Ta.nbHbrMH

AaHHbIMH

HCCJIeAOB

a14fl.

peIxeTOK

UpOQunefi

paS.rlruHblx

napa-

;;;p""

llli,'

pn

,

o7, noA6gpalor

peluerKH,

npoQHnH

Koropblx

o6ecne-

qHeilot

'Heo6ioAHMbIe

BeJII4TIHHbI

Co,

Ha

pacqerHblx

ceqeHuflX

nps

ruHHHMaJrbHbIx

noTepfx

SHeprHH

H

BbICOKHX

KaBHTaqI{OHHbIx

KaIIecTBax'

3rcnepuMeHraJlbHble

AaHHbIe

pe[IeToK

pa3JIHqHbIx

napaMeTpoB

oI'

paHHqeHbr,

IIO9TOMy

MOIKHO

TaK)Ke

BOCnOJIbSOBaTbCq

onbITHbIMH'qaH-

HbrMH

raccJleAoB

a'uf,

OAHH.TIHbIX

npo$I.J'efi

pa3flI'IrIHbIx

K'IIaCcoB

(npo-

Qu"rrn

BI4rl{,

NACA,

Clark_r{

Ap.).

B.nnsuHe

peu]erKH

yqllrblBaercf

npH

rroMolrlH

KO3QQnuueHra

('

oilpeAerqeMofo

no

QopMyJIe

(322)

(323)

K:

coo

-

fo

q-

f

'

xoropufi

3aBHcHr

or

rycrorbl

LI

yrJla

ycraHoBKH

pe[IerKH

-

K

:

-

f

(llt;

Fr",).

flo

Bblrl;creHHofi

BeJIHTIHHe

Cn,

^

npHHflrbIM

rlapa-

MeTpaM

peuIeTKH

onpeAeJlflioT

Ko3QQHI{HeHT

IIoAbeIYIHofi

cu'nu

OAHHoTI-

HOfO

npoQH,-rfl

Cu

:

CuelK.

Koe$QHuHeHr

BrrLs.Hr4fl,

peixeTKll

K

OnpeAelqrcT

IiO

HOMOTpaMMe

Befinuriipr..

108).

PacqerHoe

3garreHAe

Cs

nu6paHuoro

npoQHJIfl

co-

r.nacHo

xpunoft C

s

:

f

(a) o6ecneqgBaercfl

IIpH

HeKoTopoM

yIJIe

aTa'<H

c['

Aflg

BbItIHcJIeHHfl

KoToporo

nofib3ytoTcq

I\,IeToAoM

IIocJIeAoBaTeJIb.

Hbrx

npll6nttxeHHll.

226

CHasana

.noJrararcT,

HTo

pycr

:

F^

(a

:0);

no

HoMorpaMMe HaxoAsr

HyneBoe

npn6.nuxeHue

xoaQQuUHeHra

Ko

:

f

(l/t;

py"r)

H no

HeMy

BbrrrHcJflror

sin@1

:lo/nlKoa^

fi

al

(ne.nuvunoft

f"/f

saAarcrcr).

floc;re

NHTIgHY

ATAKH

gTOrO

yTOTIHflTOT

yron

yCTaHOBKU

npO+rmn

Pru""

:

p^-

d,

Be-

Kr

:

f Q/t;

ptr"r)

rr

Bbrrrr{cJrflror

BTopoe

nfH6nuxeHue

yrJra

'fa

Sln

C[s

:M

(324)

3areu

yrotlHflror

yron

ycraHoBKH

Pru",

:

:9*-q;

xoarixiruuueHr

Kz:

i

(iii;

prror)

$

onpeAeJrsror

rperbe upu6nux<eHHe

yrJra

ATAKLI:

sina"

__

*

rr r.

A.

"

tu^zu)m

B

KoHer{HoM

rrrore BbrqucJleuHrrfi

ytoJr

araK4

AoJrx(eH

6urr

paBeH

YrJY,

IrpI{

Koro-

poM

o6ecneqHBaercrr

rpe6yevoe sHaIIeHr{e

Ca

:

f

@)

r,Jrfl,

oALtHorIHoro rpoQunfl.

MeroA

noAbeMHbrx cnn 6un

ycoBep-

ureHcrBoBaH

aKaAeMHKoM f. O. flpocxypofi,

xoropufi

npeAJrox(Hil rrpr

onpeAeJIeHHH Kpr{-

BH3HbI

npoQunn

yrlurblBarb

roJIUlHHy Ilorpa-

HHrrHofo

cJroff.

floc.ne Bbr6opa

flpo$Hrefi vl

onpeAeJreHHfl

yrnoB

Lrx

ycraHoBKu

B

pacqer-

Hbrx ceqeHHsx ux co6Hpanr B

nJIaBHylo JIo-

nacTb.

S

59.

EComnosoBr{a

pemerorc

upo$n.rrefi

Fsc. I13.

I(ounononxa

pacqeTHbrx

pe[reToK

B

JIO[aCTb:

lp;lff

"

;t';3' u

",o

""*',$:ffi

Pacqer

peileroK

npoQu.rrefi npH noMotllH

KaMa,

ororHyrbrMrr npor'B Bpa-

,{ByMepHbrx

MeroAoB

Bbrrron"setcs 6ee

yuera

H,Tfi3'""f,;#3flilfi';o,ffilll

HX B3aHr\,rHoro BJr Hs Hr4 fl

.

floerouy KoMnoHoBKa

npo$n.rrefi

B

a'ionzcrb ocyqecrBlqercr HepacqerHbrM

nyreM.

Kax

no-

KagaJTr4

orrbrrHbie HcqrIeAoBaHHfl oceBbrx

pa6ouHx

KoJIec,

pa3JluqHaff

KOMIOHOBKa

OAHHX H TeX Xe

npOQu.uefi

pacqerHbrx

peueror(

npHBoAr{r

x

paauoft

Qopue

Jro[acrH

H

cyrqecrBeHHoMy orrarlr4]o

aneprerurrecKr.lx

Lr

KaBur

auuoHHbrx

xa

p

aKTep HcrHK ry

p6u

Hsr

t

28

I

. .Ilyuulae aHepro KaBr.i

-

TarIHoHHbre

xapaKTepHcrnKu

pa6ouero

r(oJreca

Aocrufalorcfl

B

ToM cJIy-

qae,

ecJrH BbrxoAHag

Kpor,lKa

JronacrH B MepHArroHaJIbHoft

npoexuHH

ro-

pHsOHTaJrbHa

UilH

HeMHOTO

HaKJTOHeHa nO HarrpaBJIeHHrc

X nepUQepr{r4,

a B nJrane

paAHaJrnHa

(puc.1l3).

PaAua"unHar

Bbrxon-Has.

KpoMKa

Jroracrn

ilpeAnorrrHTeJrbHee

TaKX(e c

rexHoJroruqecxofi

ToqKH 3peHHf.

3aAas-

IrIHcb

Qopnaofi

BbrxoAHor?

KpoMKH,

(co6upaloo)

pacqerHbre

cer{eHr.rfl

JIOTIACTH.

8*

227

,II,.nr'xaxAofi

.

p.._:;:"ofi

peuretx?,"*Q"nefi

ussecrHbl

cneAypqHe

BerrHqHHbI:

Irar

tr:Y;

rycrora

{,;,}r'

ATIHHa

xopAbl

npoSunn

Ii:

/r\

:

(+Jr

l,

u

yron

ycraHoBKn

py"r.

flpoexUnn

npo6u.neft

s nraHe

r'I H€

Me-

pHAHoHaJIsHofi

rIJIocKocrH

ollpe.{,eJlflIor

npu

lui

l,

cos

pycri

\

lni

/,

sin

py...

I

noMorrlu

3aBHcHMoCTeft

:

,325)

t

F

Puc.

114.

Teope'rnuecxufi

eepT

e)I(

r'IoIIscTH

oceBoro

pa6ouero

Ko'tleca'

IlonyueuHble

3Haq

eHuA

l*.

orxnaAblBaloT

B

MepHAHoHaJIbHofi

naoc-

pacqeT.

'

Ha TeopeTHqeCKOI{

qepTe}Ke

JIonaCTH

nOKagbIBaIOT

MepHAHOHaJIb-

HyIO

ilpOeKqHIO

H

iIJIaH

JIOIaCTH,

a

TaKX(e

pa3BepTKH

IIHJIHHApHqeCKIIX

ce.rennfi

roracTu

Ha

nrlocKocTu

(pac.

114).

Pasuepu UHJIHHApHqecKHx

ceqeHafi

ilpocTaBJIflIoT

Ha

r{epTe)Ke'

HcnoJlb3yfl

pacqeTHble

AaHHbIe

Jloracru

(cira.

npuMep

pacqera,

ra6JI

.

27).

228

T

fl

Bu6op

ocr

noBopora

Jroracrn.

Ocr noeopora

nu6upanr

raKuM

o6pa-

3oM,

'rro6H

oHa ilpoxoAHna

HeAaJreKo

or

qeHTpa

AaBJreHHs

Jrorracrlr

(pHc.

115,

a). flp" raKold

rIoJIox(eHHH

ocu rroBopora

rHApaBJrHqecKHfi

MoMeHT,

4eficrnyrcrqufi

co

cropoHbr noroKa

Ha

Jronacrb,

rpu

pagJIHq-

HIIX

yrJlax

ycraHoBKH

HMeer Mr{HHMaJrbHyro

BefiHrraHy.

3ro

no3BoJrfler

BbInoJIHH'Tb

cepBoMorop

H BTyJIKy

pa6oqero

KoJreca MHHHMaJrbHbrx pas-

MepoB.

OxoH,{areJIbHo rIoJIox(eHHe

ocH

rroBopora

eu6uparcr [ocfle

onblTHoro

o[peAeJleHr{rr

cHJIoBbrx

xapaKTepucruK MoAeJrbHoro pa6a-

qero

xoneca.

Kax

noKasbrBalor

orrbrrHbre HccJreAoBaHHfl

uo.qe.nefi

[llJ,

Puc. ll5.

K

nu6opy

ocu

noBopora Jronacru:

s

-

uepglHorrzurbgaa

rrpoexrlxt

H rrnax Jrorracrn;

6

-

ropnenoe

ceqeHue;

.

e-

nepuQepufiHoe

cesenue.

qeHrp

AaBJreHHfl

Jroracrefi

uoueHKJrarypHbrx

oceBbrx

pa6oqHx KoJrec

Ha

onTHMaJrbHoM

pex(Hr\,re

pa6oru

HaxoAr{Tcs rprrMepHo

Ha

paccrofl-

HHH

x6

:

)tll

:

0,35

-.-

0,45 or BXoAHofi

xporrrxn

JlorracrrE

(puc.

1 15,

6).

YqurHear

grr{

peKor{eHAaI{HH,

Quxclrpyror

ocb [oBopora

Jrofiacrn

cHa-

qaJla

Ha KopHeBoru cerreHHH, a 3aTe\.{ onpeAeJlflroT

ee KoopAHHaTbI

Ha

npoQnnnx

ocraJrbHbrx

pacqerHbrx

ce.reHHri

(c*.,

HailpuMep,

puc. I15, a,

fAe

yKa3aHbr

KoopAHHarhr ocH

rroBopora

at

H br Ha nepuQepufiHot'l

ceueuuu).

or"uox<un

paccroflHkrfl,

av

u by

B

rvlepHAHoHaJrbHofi

npoexuHH

It

Ha

nJraHe JroracrH

(puc.

7I5,6), ilpoBoAflr npoeKrrHH ocH

floBopora,

Koro-

pbre

oflpeAerqror

ee

rroJrox{eHue

rro

orHorr]eHuro

x

npo$1r.,-ifrr{ HZ

ocra,Tb-

HbIX

pacrlerHbrx

ceqeHHflx.

xenareJrbHo

etr6parr

ocb

noBopora

HI4x{e

rreHrpa

rflx(ecru Jrorracru. IIp" sroM MoMeHr

ueurpo6ex(Hbrx

cu.u

6yAer

HanpaBJreH fiporus

HsrH6aroqero

MoMeHTa,

Aeftcrsyrcxrero

co

cropoHbl

noroKa

Ha Jloracrr.

B

pesyJlbrare

cyMMapHoe

Hafipfl]KeHne

B

KopHe-

BOM

CeqeHHH JrO[aCTH

yMeHblrraeTcfl.

nns

o6ecn-e,reuNr

4onycxaduux

Hanpflxesufi

B ceqeHHrx

JlonacrH

BaAanrcfl

orlpeAeneusofi

lb"trqunoft

.nonacru

y

KopH fl

.v

H,a

ngpaQepuu'

Cornacuo

AaHHbIM

HoMeHKnarypHux

pa6oqHx

KoI€c

(ra6n. 23)

uaxcu'

MaJIbHafl

orHocnTejrlbHaff

ToJIITIHHa

JIo[acrH

6rn"*

:

6^^*ll

:

8

+

l2o/o

-

y

BrynKH;

6*"*

:

1,5

-+-

2'80/o

-

Ha

nepuQepuu'

Ans

yMeHbrueHufl

CTeCHeHHs

noToKa

u

yny_queHug

KaBI',ITaqHoH-

Hbrx

KaqecrB

pa6ouero

KoJreca

roJIIqHHa

Jlonacrefi

Aotx(Ha

6rttl

Mr4tlr4-

trta.nnUOft,

Ho

AOcTaTOIIHOfi

41n

O6ecneqeHgfl

ux

seO6xoArauofi

npor{HOCTI'I'

s

60.

Pacqer

pemsrorc upoonuefi

(o6paTHas salaqa)

Bnxpeaofi

11efit4

pacrleTa

pemeT6r 6ecrcOsewo

TOEI3EX

upoQxaefi

prrc.

I 16. fu4poA"""-'"";;J;Jr*:J;"iJ;-,ft"n

npo$H'reft

u

nu6op

qepg3

pa6Ouee

Ko.,'!eco

Aettcrene

CHJI

Btl3KoCTH

He

yqHTbIBaeTcs' Aony-

uleHHe

o

HeBfl3KOM

noToKe

HeilpHeMJIel\{O

npH

paccMoTpeHHH

ABHx{e-

HHs,

x(HAKocTH

HeilocpeAcTBeHHo

BAoJIb

lOnacrefi

pa6ouero

KOJIeca'

B

norpaHnqHoM

cJloe

Ha

noBepXHOcTH

JIoIIaCTU

cKopocTb

H3MeHgeT

cBOe

sHaqeHLIe

oT

IIyJIfl

Ao

KOHeqHofi

eeJgql4tibl.

Pegxoe

H3MeHeHHe

cKo-

pocTLI flBJIfleTcfl

flpHtIHHOH

Bllxpeo6pasonaHufi

s

IIorpaHHtIHoM

CJIOe'

btt"lo"uTeJlbHo,

ilofpaHgquufi

clofi

MolKHo

paccMaTpHBaTb

KaK

Buxpe-

eofi

c1ofi,

cocroftqrtfr

us

HenpepblBHo

paclpeAeJleHHblx

BHXpeft

onpe-

A*.rnoA'

""t."."i'ocr6.

BHxpenue

croil,

HMHrllpytoqqe

npoQuau

peureroK,

BbIsbIBaFoT

pa3pblBbl

HeIIpepbIBHoCTH

$yuxUufi

cKopocrl'I

H

AABJICHHg.

flonepxHocTb

JIoIIacTH

o6pasonaHa

ceMeftcTBoNi

nu:g'vtfi

ToKa

orHo-

cHTeJIbHoIo

noToKa

H

B[xpeBbIMH

IIpHcoeAI'IHeHHbI\{H

JIHHHflMH

(S

1-4-

iO).

Cna4ou"t*o*,

qro66

onpeAeJII{Tb

npoQHJIH

pelreroK'

Heo6xo-

230

AHMo

ulfrtu

Qop*y

JI

H HH

fi

,ToKa

p

$yJrbrHpyrotqero

orHocaTeJr bHoro

no-

ToKa.

Pesy"umupytoulyn

cKopocrb

orHocureflbHoro

noroKa B

Jrodofi

touxe,(e

roM

rrHcJre

H

Ha npoSu.rre)

rraoxuo

npeAcraBr4Tb

KaK cyMMy

cKo-

pocrefi

HeBo3MyrrleHHoro

noroKa @^

H

cxopocru

ilr,

unLyqr.rpoBaHHofi

BHXpSMH,

pacrroJrox(eHHbrMK

Ha nposHnnx peuerKH

(prac.

116).

OnpeAe"rraB

BeJIHqHHbT

LI HanpaBneHufl

orHocr{TeJrbHbrx

cKopocrefi

B

plcqerHbrx

ToqKax

npo$Hnrfl,

HaxoAhr

Sopuy

ero cKeJrera.

Tpe6yeuaa

Be.'tHqHHa

qvpKyJrsrruH

noxpyi npo$u.rrn

o6ecnequsa-

ercfl

rrpHHffTbrM

SaKOHOM

pacrpeleJreHHfl

nuxpelt

BAoJrb npo@ra"rrn:

(326)

rAe

t

(s)

-

noroHHar

HHTeHcHBHocrb

BHxpeBbrx

cJroeB; s

:

l+

-

6eepaeuepHafl repeMeHHafl

HHrerpHpoBaHH

s,; l_rnaHa xopAbr npoQrlax.

IIp"

pacqere pelxerKl{

npoQunefi

xoHeqsofi

roaquHbr

Heo6xoararro

SaAarbcs

BaKoHoM

pac[peAeJleH[s

oco6euuocrefi,

BKJtroqas

HcroqHHKt]-

croKu.

Cyrtlruapuoe reqeHue

HeBo3MyuleHHoro

[JrocKorrapaJrJreJrbHoro

noroKa

I{ [oroKa, BbIgBaHHoro

oco6eHnocr.flMn,

AoJIx{Ho

6url

raKHM,

qto6H

oAHa us nLrHHfr roKa

6u.na saMxHyroit

u no

cnoefi

Sopue

coorBer-

Puc'

ll7'

fpauuuuue"toT;:;,L.

""

I(oHrype

npo$H'ra

crBoBaJIa y,u,o6oo6reKaeMoMy

npoQu.rrrc.

3auxHyrylo

Jrr{HH}o roxa cyN{-

y_apHoro

noroKa

npaHnMalor

sa

KoHryp

npoQu"nr

xoHer{Holi

ro.nuluHtr.

Vcaosne

HerIpoHHIIaeMocrH

npo$r-r"rrn (pnc.

117)

cocrolrr

B rohr,

rrro

orHocHreJrbHbre

cKopocrH

KacareJrbHbr

B .uro6orl

ToqKe npoQr.let

t)n

:

un HJLH tgrur

*

aw

-

(!)n

-

0.

B

4ononHeHue

x

(326)

AoJr)KHo

raKx(e

BbrroJrHflrbcr

yc.rroBHe

+I/2

\ a(s)ds:0.

Jr.t,

_t/2

rAe

Qyuxuux

q (s)

xapaKrepusyer npuHnrufi

3aKoH

pacnpeAeJreHiis

HcrotIHHKoB-croKoB

BAoJrb cpe.4uefi

ilHHHH

npo$Hnr.

_llpnr

npnHqroM

3aKoHe

pacnpeAeJreHHs

oco6essocrefi

BAoJrb cpeA-

gefi

.n

u

g

u a np

oQua

fl Ko Heq

Ho fi ro.ituln HEi

nocJr

eIoB

aroJr bH o o n

p

eAe.,T sror

:

+I/2

P

f

:

J

r(s)ds,

_t/2

(3271

231

Qop*ty

cKeJIeTa

npoQu.rrn,

Qopr'ry

npoSu.nn

KoHeqHofi

ronqnHbl

H BbI-

qncJrrrror

cKopocrll

H

AaBJIeHHT,

Ha-KogT.yp!

npoQn'nn

peurerKn'

CVutnoctb

BHxpeBoro

Merona. 17;

281.

3aAaBIIIHcb

pacrlerublM

pex(H-

*o*

(Qi',

ni),

npHttnuaror

HcxoAHbIe

BeIHtIHHbt

peueroK

AJIfl

Bcex

pac'

qergbrx

ceuennfr,

oilpeAeJltllor

BxoAHbIe

H BbIxoAHbIe

iLpey-roJIbHI{KH

"*opo.t"fi

n

qHPKyJIflIIHIo

BoKpyr

JIonacrI'I

(o'r.

$

56'

57)'

B

pesy'rlo-

TaTe

[IepBoro

sTaIIa

pacqeToB

nolyqaoT

napaMeTpbl

peueroK

nJIOCKHX

nJIaCTHH,

Ha

KOTOpbIX

3aAaloTcs

3aKOHOM

paCnpeAeJIeHHf

nnxpefi,

IOCJIe

qero

Ilpucryraror

K

oIIpeAeJIeHHIo

Qop*lo

6ecxoHe'Iuo

ToHKI'lx

c'na6O

HcKpLIBneHHbIx

npoQu"rreft

peueror'

c*opo.r",

HrrAyrlHpyeMbre

BHxpeBbIMI,I

XOHTy.paMH

.e

Jllo6ofi

TOTIKe

c

KoopAHHaraMH

xo,

Uo

Ha

pacqeriortr

npoQn.ne

(puc' ii6)'

onpeAenfi-

rorcs

uo

QopuynaM:

thz+

uo

-

1) 1

(s)

ds

I

fl

wx-

2t

,in

2f

(xo

-()

1

(s)

ds

(328)

"hT

uo

-1)

-

cos

I

er-

rl

r,[,e

.fjy

Ao

-

KoopAugaTbil

pacqetuOfi

ToqKH

Ha

npoQHJIe;

rl,

C

-

xo-

opAHHaTI;IToqeK'BKoTopblxpacnonox(eHblBHxpH.

,II,ls

BbrrrHcreHgs

HHAyqHpYeMb

npoQu;rn

ueo6xoAuMo

3aAarbcfl

3aK

npo$ralr

H

nPHHrrb

nYTb

HH-erPH

BHXpH

pacnoJlaraloT

BAOJIb

II3BeCTH

HHq

nJlorHocrH

euxPefi

BAoJIb

npoq

y3pra:

T

(0)

-

Ao.tg+

*

Arsin0

a

42sin

2B

+.4,

sin30

+

"'

+

Ansinnl'

(32e)

BeoAsr

orHocgreJlbHylo

KoopAHHary

roqK

v

Ha

npoQu.ne

o

-

slIl2

:

-

cos

b

"

tttpux(arcT

qepes

nee

rpuroHoMeTpuqecKHe

QyuxUl'tll'

Bxo-

AfruHe

B

pnA

(329):

sin0

:{F-o2;

sin

26:2o-y'T--s!;

sin

30

:

-{T--o2

*

4o'YT--o'z;

:-

0

1/l-=osT tfT-"

0

1tr+ffi

-

{ry '

sinr-:

V'

-T-:

V'

--2

;

cos

t:

)

-T:

)'

Z,

J

ii

tt

_,,

o

af-taa

cuB

z

Y i:'

232

floc.ue ro.rrcraHosxn sHhqeHufi

"tg

+

;

sin

0;

sin 20

n

(329)

no,{yqar,or

r

(o)

-

Ao{=

*

AttlR

|

ZA,otfi

4

*

Ar(4o'z{fi2

-{1

s\

+

-.

.

(330)

CytnaapHafl

qHpr(yJrsrrHr

BoKpyr npo$u.nn

orp€.4eiturercfl

npH noMoulu

Bbrpax(eHnn

(326),

B Koropona

ds:-{sin

0dg.

floAcrasuB

B

(326)

3HaqeHHe

QyHxqH"

T

cornacHo

(329),

roryqaror

*

+.4p

sin ftO)

sin

0

d0.

HHrerpanbr rnna

I

sin

ftg sin

n0

di BbrrrucJrflror,

Ircnonrcyfl

csoficrBo

6',

op

ToroHaJrb Hocrn TpHroHoMerpHqecKux

Qyuxrur

fi

:

7E

t'

npu

k4n

\sinft0sin

n0d0:0;

un

npu

k: n

Bce

usrerpaJlbl

gToro

rurra

paBHbr

HyJrro,

ga

HcKJrroqeHHeM oAnoro,

y

Koroporo

ft

-

1. Taxuu

o6pasor'1,

ItupKyns:g:Lrfl

BoKpyr

npo$ranr

r:+(r,*

tro,)

r_

I-

Tax

xat<

As

yrpoqaercfl:

i

tf

(o

^T-0 -Ltr cinA-J-t cingAt /cineA-J-

t I lrr0r!5 t

I

irlelrrv

I

tLz ollrav

|

/rSerrruv

-T-

-r,/\

0

J

tinft0 sin

n0

d0

:

+

0

(331)

(334)

(332)

I4z

ypasrreunfl

(332)

cJleAyer,

qro

qupKyJrflqHs

BoKpyr

npoQuar

Jronacrn

co3Aaercr.

sa cqer

yrJla

araKn fo

:

f

(Ai

^

KpHBH3Hbr

npo-

Snnn

l,

:

f

(Ar).

Ocra"nrHbre

rI.reHbI

pflAa

(330)

Br-rHsFor

Ha

pacilpe-

AeJreHlre

cKopocrefi nAo.nr

npoSnaa, H€ HsMeHsfl

cl,rv{rlapHyro

qupKy-

flqul.irc.

Onpe4e.rreHue

HHAyrIHpoBaHHbrx cKopocrefi Ha

npoSu"ne

npH

aJIJII{n-

THqecKoM

3aKoHe

pacflpeAeileHuq nnxpefi.

B

cryrrae

3J;HnruqecKoro

3aKoHa xo:QQiauHeHT

Ao: 0,

H

qHpKyrsuuq

BoKp\'r

npo$rinn

co3Aa-

ercs

ro"rbKo

3a

crrer KpHBr43Hn

npoQn.rrs

(f,

-

f). ilp"

3ror,{

us

(332}

cIeAyeT,

r{To

AL

n:

:0nAz:As:

-An-

r

(o)

:#VT=o'z.

(333)

0,

errpax{eHne

(330)

llpn

rrc6ou 3aKone

pacrpeAeJleHnfl

nuxpefr

BAoJIb npotpu.nr,

e

TOM

I{I,ICflE

H 9JIJIHNTHqCCKOM,

CKOPOCTH,

HHAYIIHPOBAHHbIC

BHXPCBbIMH'

KoHrypaMH

perIIerKH B

TorIRe

c KoopAHHaraM4!_o:

Uo

HA

pacqeTl{oM

nonnbi,r)

npoQune,

orpeAeJlffIorcfi

corJlacHo

(328):

(oc-

(335)

Bbrpa-

ql

vx-

(336)

flocne

npeo6pasosaHHfi noryqalor:

*i,

r

..a-rrIf

]'r'i

\

ox

:

fr

J

\cffir,

-

l.;A5

)vG'

ao;

-1

\

ffL..-",){:

_

o",

(337)

rre

x:T@n-ni;

o:T@o_'a).

flpn HHrerp'p

ouun

ni"oono

""*0""",*

Ko'rypoB

KoopAHHarbI

tl

U

(

npUHuMalOT

BCe

gHaqeHns,

B TOM

qHCJIe

V

Xo,

Uo.

B

erOu C;yqae

11OA

uHreipa.uaMr4 Bbrpax<enufi

(328)

nonyilaercfi

HeonpeAeJleHHocrb

BH.u,a

*.

qrofibr

or

Hee

Hs6aBurbca,

HHAyttHpoBaHHyIo

cKopocrb s 4lo6ofi

U

TOtIKe

npoQu.nr

pacKJIaAbIBaIoT

Ha

ABe

cocTaBJlslolqne:

o'

(o'*;

aD

-

cxopocrb,

HHAyqHpoBaHHyIo

BHxpflMH ocHoBHoro KoH-

Typa; a"

(oi,

a'n)

-

ct<opocrb,

HHAyIrHpoBaIHyIo

BI{xplMH Bcex

Kour,v-

poB peuerxu

ga

HcKrroqeHHeM

ocHoBnoro

(pacuernoro).

flpoexuun

cxo-

pocrn,

HHAyrIHpoeaHHofi

B

pacqernofi

roqxe

o0

npoQu.na

BHxpflMH

oc-

HOBr{OrO

KOHTypa,

onpeAeJlqrcTcs

no BbIpaxeHHqM:

3

fl-

vg-

r,u,e

r

-

2tll.

Bso.ls

o6osHa.IeHus:

1

sh).

t

sinp

"Ahffi;*

-n;=

--a(o);

I

sinp

,

r

cosp

Lr-\

-U

Afrpc|sp

-r-

2i".

-"

:

a\a)t

OKO

HTIATCJIb

HO

3 AIHCbIBAIOT

:

rr,

-?I

tt

"

@

(l

-

oe)

,-.

it":

nt

) a'-iao;

(338)

.

flym

r{HrerpnpoBaHHrr

(xopaa

npoQu.rrr)

pas6unaercs

Ha ruecrb

paBHbrx

uacrefi,

u onpeAeJlfloTcs

HHAyIIHpoB^aHHbIe

cKopocTn

B ceMH

io.rxax,

0;

1;

2;3;

4; 5;

6;

(-1;

-213;

-1l3,

0;

*1/3;

*213;

+1)

(pHc.

116).

I4Hrerpa.uu

B

(338)

BbIqHcIsIor

npa IIoMoUIH

xoaQQuUtl-

eHroB

A.

HenotvrHqlqero;

TorAa

pacrlerHble

Qopuyabl

npHH}IMaIor

BHA:

--r

ai:

#rl2l0a1-

120a2

{

460at- l20ao*

210aul;

n

aI

:

#oorL2t\bL-

120b2

+

460ba

-

120b1+

210b61,

r1e

xoeQQllqueurbl

a1,

az .

. .

br, br. . .

o[peAeJIsIoT

no

CneqIiaJIbHoH

uouorpamue

(pnc.

118)

(Ha

pLIcyHKe IIpHBeAeHa

cxelvla

orpeAeneHl'is

siraxoB

xoaQQnUHeHroB

a

u b

Arq

pacqerHblx

rorleK

npo$_lila).

B

pesy.ntiare BbIIIHcJIeunfi

npu

roMoutn

Bblpax(eHufi

(335)

u

-(33B)

HaxoAffr

iIpoeKqHH

HIIAyIlHpoBaHHofi

cxopocru e

nlo6ofi

ro'Ixe

npoQuna:

Ox:

o:

+

o:;

\

oa: ai

*

ai. J

Onpe4e.neHHe HHAyqHpoBaHHbIx

cxopocrefi

Hq

npoSune

npu

HeeJI-

JrHnrHqecKoM

3aKoHe

pacrpeAeJleHns nnxpefi.

tlro6u

o6ecnetlarb

3a-

AaHHyro

rtapKyJrsuHro

BoKpyr

npoQHJrfl,

upr

efo

llpHeu.neuoii

KpHBHSHe

(i*"*

<

6

-:-

8o/o), BBoArr:

yroJr

araKr

d,.

I4seecrHo,

uro

cyl{n{apHafl

qHpKyJrsUHff

BoKpyr

npo(puJls

co3Aaercfl

3a crler

KpllBHsHu

npoSHnn'

236

+1

n

2lf

on:

nt

)

-1

Ars

sH,rHcJIeHHfl

HnAyiruposaHHofi

cKopocru

)KeHHH

(395)

pas6aeanr

Ha

ABa

HHrerpaJla,

HMeff

:

a*-

U*i

t1

a'*:#l

ffisinP

do:T,

oosinP;

-1

+1

oi

:

-H

S

fficos

P

d'o

:

-#oscosP'

ai:#J

-t'kffvreto.-

1/f,oz

tffisinPdo;

\

_H#J

vFo,ds:

)

I

('

(

I

)

ailB

,

qTo

HHTefp

B BHAY

(340)

,,

'll

vx-

234

s

I

F.

q)

E

A

o

X

q)

c)

q)

o.

o

r(

q

E

L

o

E

F

cd

(..)

r{

yrniHraKr

H

orpeAeJrsercs

npH

noMorrlH

BbrpaxeHHs

(332),

B

Koro-

poM.40

+

0.

Hee"n.nnnrurrecKufi 3aKoH

pacnpeAeneHHfl

BHxperi

rrlapoKo

npHMeHsror

rrpH

pacqeTe peueToK

oceBbrx

pa6oqHx

KoJrec, oco6eHHo

npo+Hnefi

xopHeBoro

ceqeHHfl.

3aAasue

gJrJrHnrHqecKoro

3aKoHa

npH

pacqere KopHeBoro

H cpeAHHX ceqeHHfi nonacrH

npHBeao

6u K

qpe3Mep-

Hofi

KpHBHsHe

npoQHJleft

peueroK

H

yxy,qlrreHHro

aHeprerHqecKnx H

Ka-

BHTaUHOHHbTX

XapaKTepHCTHX

pa6Oqero

KOneCa.

HegrrnnrnqecKHfi

3aKoH

pacnpeAeneHHq

BHxpefi

BAoJrb npo$Hnr

3a nHcbrBaercq

cJle.4ytoulHM

o6p a3oM:

r(o)

-

AoV-*

ArV=:T"(o)

*T,(o),

(341)

r4e

y"(o)

-

HHreHcHBHocrb

nuxpefi,

rpeAcraBnflIorrlrx

o6rexaHne

uJra-

crHHbr,

ycraHoBJleusofi

IIoA HeKoropblM

yrJIoM

araKr d,i

t,

(o)

-

HHTeH-

cHBHocrb n

n xpeft

,

rpeAcraBnsloulHx

o6rexau ne nap

a6or

H

rrecKo

ft

lyxx

n

noToKoM co

cKopocTbro

u)m, napaJIJIeJrbHbrM

ee xople.

flpu

eroM

rtHpKyJIsuHs BoKpyr npoQuna

'+/rz

+1

r-

J

1(s)ds

-

A,[

{F;f,ao+

-I

/2

-1

Cxopocru,

HHAyuHpoBaHHbr€

]e

(o)

u

T,

(o),

o6ogHa,ralor

coorBercr-

BeHHO

rrepffi

aduas;

TorAa

cyMMapHafl

HHAyuHpoBaHHafl

cKopocTb

u

:

on*

rrr.

flpoexun.rr

cKopocru

Ha

ocr

X:

ox-0ro*uxs:

{$_*do*

ftl

+/'J

Vl-o';do:f"*f,.

(342',)

(343)

(344)

237

+r +1

(

o,l/

++

, .4^ sin

(

r

lr_2,,re.-"r

sinP

do:ryJ,

Kan

H B cryqae

sJrJrHnrurrecKoro 3axoHa

pacilpeAeJleHnfl

euxpeft,

npH

3HaIIeHHsX

1:

Xo

u

e

:

Uo

noA

HHTerpaJIaMH

Bblpax(eHHfl

(343)

nonyrlaercfl

Heo[peAeJreHHocTb.

t{ro6u

lis6aerrrucfl or

Hee,

BbIqHcJIflIor

orAeJrbHo

cocraBJrflrcurae

a, u ai@,

-

u'r+

u:).

llpoexqrlu

cKopocru, HHAyIrHpoBaHHofi

sa

cqer

?"

(o) (yr.rra

araxn),

onpeAeJlfl

ror rro

Bbrpax(eHHfl

M:

7l

vx1

-

tf4o

Y

l-o

s^_

.4osinp.

oo-o

2

'

I4Hrerpaa

B

BbrpaxeHr{r{

(345)

BblqHc.llqlor

AJIfl

IIrecrH

pactlerHblx

tou"*

ip"'..

116)

nin

noMoulu

xoeffiHuHeHroB

n'

A'

HenovHslqero

A^d , '^A-. to/.\- r CDA- t QQzl^ \ /aAA\

olo:

ffit\IZba1-vuaz

+

+ou{13

-

lourr4

f

uovtzs

-T

u<r-\1r'61.

\r,zv/,

Onpe.qe.lflIoT

npoeKqgH

Ha

ocb X

CoCraB.IIflIouIHX

HHAyIIHpOBaHH6IX

cxopoireii,

eusslsielulblx

T,

(o)

(xpnnuaHofi

npoQnna)'

0'rr:#""sinP;

oi,

:

#r(210a1-

l20ar*

4604,

-

!20ao

f

2l0aul'

AnaaoruqHo

BbrqucJrsror

npoeKuuH

Ha

oct

Y cocraBJlsloulux

IIHAY'

trrapoBaHHblx

cKopocreft

:

esnsaHHux

1"

(o):

aln

:

f

cos

P;

(349)

o

AnnI

aun:

-2560t026b!-g0b2+ 460b3-

180b4

+

630b5

+

334b6h

(350)

Bbr3BaHHux

1,

(o):

ai,:-+oocosP;

aX,

:

#u*r7tlbl-

120b2+

460bs

-

120b4+

2lobb)'

(352)

llpoexuuu

pe3y,i,rbTHpyroulHx

HHAyUHpOBaHHbix

cxopocrefi

B

pac-

qeTHbIX

TOqKax

npoQH./'ifl:

ax

:

a;.

+

a';"

+

oi,

*

oi';

\

aa

:

aao

*

uk

+

us',

*

a';''

)

MapHyro

unpKynqquro

BoKpyF

npoQunx,

rroJlb3yrlcb

saBHcuMocrbto

(321).

Ii

saeucuMocrl{

or

6ucrpoxoAHocru

npoeKrHpyeMoro

pa6ouero

xo-

Jreca

saAaloTcfl OTHoIIIeHHeM

lnll:C':0+-I,0.

Ans

KopHeBoro

ce-

qeHHfl

cyqecTBeHHylo

ponb

B co3AaHI{H

IIHpKynqqHH

HrpaeT

yroJl

aTAKH,

rlogToMy Mo)KHo

npntrim C'

:0,3

+

0,6. 3aaaBtuucb

BerHtIuHoir

C',

Bblrlncrfm

fo n f.:

l':C'f

:

$t

fr:

(l-C')l

:+

,

2lc,

.

lao:A;

,.

4(l-c,)l

ttl

:

JT,l

'

sQQr.ruueHroB

As u

Ar.

'

'Onpe.qerenud

xoefr6"qve1roB

a.

s

b. KoeQQuuueHrbr

a(o)

H

b

(o)

nepecqHTaB

ee

B Mac[ITa6e

souofpaMMbl:

/"o*:

hz

(i),,",

L

tr

H

lli

(345)

(347)

(348)

(351)

(353)

Orxyla

nonyqalor:

(354)

(355)

(356)

(357)

Onpe.qeleHue

xoa$Snqneuron.As

tr

Ay

Lnn

BbITIHcJIeHHS

HHAyUH-

DOBaHHbrx

.*opocrafi

u

pacqeTHblx

TOrlKax

seo6xoAHttlo

3HaTh

xoes-

6;;;;;;;

i'ri'

a',

onpe.4^e.nnrcurrle

3aKoH

pacnpeAerleHHn

nuxpefi

BAorIb

ifo6rr"".

B"cnyuae

e.ry.rysnrHqecKoro

3aKoHa,

KofAa

uHpKyJIsuHfl

Bo-

-b'i

npoQg.rrr

co3Aaercq

rorbKo

3a

cqer

epo

KpHBH3HbI'

Ao

:

0

u

At

:

4r

:rt

flpu

HeerIJrHnrHrIecKoM

3aKoHe

P?cnp.9

eJIeHHfl

auxpeft

o6a

xoeQQu-

u".niu

Ao

H

At B BbrpaxeHunx

(34L) u

Pa\

He

panHbl

Hynrc

H

rIo'u,JIe-

)r(aT

onpeAe"neH-uro.

Aag

gTOfO

Ha

SaAaHHbIe

ycnoBHg BbIqHCJISIOT

CyM-

238

(358)

rAe l,

-

uar

HoMorpaMMbI.

BH,{HcaeHHyIo

xopAy /ro*

pas6uBalor Ha Ixecrb

paBHbIx

orp$KoB

H

orMer{anr ro.Ixu

0;

l;2; 3;

4;

5;

6,

xoropble

rocJIeAoBareJIbHo

rloMe-

IIIaIoT

B

Harraflo KoopAHHar

HoMorpaMMbI

(r4e

nuxpb

orcyrcrnyer).

3na-

qeHHfl

xoeQ$uUHeHToB

a, b

Ans,

coorBercrByloulnx

roqeK

3arIHcbIBaIor

e

ra6l.

26'.^Taw,

HanpHMeP,

Als

oilpeAe,Tenun

xoe$SHIIHeHToB

Qt,

br

/

q\

AJIfl

Bcex

pacrlerHblx

roqeK o0

Ha

xopAe

roqKy

t

l-

t/

non,t"ulalor

B

Ha-

qa.[o

KoopAHHar,

Lr s

ra6n.

26

eanucbrBaror

3HarIeHHn

au

bt

AJIfl

ToqeK

1.

2'. I

I I

,r,^ llo n 6 a\ Ilnwa'r.^rLf r.Tr

2

-rr

-J

,

-3-;

0;

it it

I

(puc. IL9, a,6,

e)'

IIp"

eroNl

B

roqKe

-

r:

er

:

0

n

b,

-

0.

Asa.uorur{Ho

rrocryrraror

AJIg

ocraJlbHblx

roqeK,

orlPg-

Aenqq

sHaKH

xoaSSnUHeHroB

no cxeMe,

IlpuBeAesuofi

Ha

pnc.

119.

B

ra6n.

26 ro.rxH

Ha Xop4e, B

KoTopbrx

onpeAeJIsIoT

HHAyqHpoBaHHbIe

239

IlocrpoeHne

npo@urcfr

KoHeqnofi

rouulunu.

B

pe3yJlbrare

pactlera

no.[vqe*rbr

6ecxoHe,{Ho

roHKHe

npoSu.rrH

pelrlerox.

flocrpoeHue

npo$H-

nefi"

xoneqsofi

roJrulHHbr

BbrfiorHqlor

HepactterHblM

[yreM,

HcnoJlb3yr

24),

nuvucJlstor

ero

KoopAHHarbI:

In,

x:irffi;

)

';:;"

D*,*

no?6

[

tso+l

U:U,ffiffio/o,

I

r.qe

/no

-

AflHHa

nPoSunn,

3aMe'

peHHafl

BAOnb

ero

cKenera;

v*

U"

-

ra6"nuquble

KoopAHHarbI

^TpH-

istoro

npoQu.nx,

z

o/o:,

E-"*

np

%

-

npHHfrT

Afl,

MaKCHMaJIbHafl

ToJIUIHH

a

pacqerHoro

npoQn.nal

8*r*

,

o/o

-

ra6nn.r

H afl

MaKcHM

aJIbHafl

To

JIUTHHa

nu6pauHoro

npo(Punn.

.[oflacrn

HgMeHlerc.fl

tlo .ttnuefiHoiwy

SaKoHy

6^^*:20/oi

rycrora

peluerKn

rpuHsra

y

ruApaBrur{ecxHfi

KnA

Ir

:0,91 (cu.

ra6;1.

or

BTyJIKH

6*"*

:

8,40/o

x

nePu$ePur'r

BTyJIKH

llt

:

1,45, ua

nePuQePuu

l,16;

22,23).

Ta|auua

25.

Pacqer

peIIIeroK

pa$ouero xo.H€ca IIJI3Q D1- l0OO *n;

H

-

|

,t;

'

ai:800

nlc;ni:Il0

o6lxa'n;

?.:O,gli2--6

Pacsetrble

BeJraqHttbl

Psc.

12l.

flocrpoeHue

npoQuar

KoHeII-

nofi roauluHu.

f

,

J

mi

tt

-

ttL:

t)r: t.

:

T6-

'

illC

Kz:

aur*"ftbgH

l(-

- nFJ

ltt

u

ln

uur-

r\2.116rrlw,

d.lv

our:

aur*

ygH

lu,

ttlc

t*f

ld \21

oz:

ei

I

+

[t

-

(rf/

]n?,

urc

lgFnr:%:az/tt-

'

wmn

I

-;

(ur,* ou")

a

Pnt

sin

p-

cos

Pt

t!)m:{ffi"-

tr

lc

@mx:

tl)ffiCOS9*,

,llc

tUmu:

A^sinP*+au

u/c

tlt

t

:2nrlz,

,u

I

t:;.t,il

116,

tt

601.gH

:

t

(u.,

-

a,,\,

nt21c

'

uL

42''

0,485

5,575

0,2

0,.319

1,904

1,275

0,261

14"38',

0,2527

0,9676

5,046

-4,883

-

1,285

l,

l5

0,87

0,507

0,582

0,097

0,804

0,1

0,0804

Koop4uHary

rpoQI4JI1.

tc

oTKJIaAbIBanT

BAoJIb

cKeJlerHofi

nUsnu

ot

BXoAHofi

KpoMKLI,

a KoopAuHary

g

-

B coorBeTcTBylolltHx

ToqKaX

t

ro

o6e

croponu

(xax

pa4lryc

oKpyxHocrn)

(pHc' 121)'

floc.ne

uocrpoeuux

np66nadfi

KoHerIHofi

roJIIrlHHbI

co6HparoT

'no-

racrb

(cu.

$

59).

Ilpnuep

pacqera .rronacrnofi

cucreM-bl

pa6ouero Kon€ca

rnna

IIJI30.

Pacqet

BhInorIHeII

Ha

llpe,qnonaraeuufi

onrnMarlbHsrfi

peir4rur

(Qf

:

800 nlc;

ni

:

ll0

o6luun)'

Ha orrTgMa;rbHoM

pe)I(HMe

npgHfrbl:

az:

I

(r):

const;

quplrynqUHq

Ha

BbIxoAe

Hg

pa6overo

KoJreca

iigMeHsloqefics

ot

Hynfl

y

BTynKIr

4o

f0,2

Ilrg,Hlu Ha nepg-

Sepnu.

flpunxro .nuaefiHoe

H3MeHeHHe K2

ot

Hyns

Ao

+0,2

(cru.

ra6.n-

25).

I

r

<Dopila

noJrocrg

H

rycrora

perueroK

3aAaHbI

6.nugxutvtll

HoMeHKJIarypHoMy

pa6o'

qeMy

Konecy [.[30/5tt

(l:

\

:

C,45; z:

6/; otto"""elbHafl

MaKcuMaJIbHafl

ToJIulHHa

zn

C':?

lo: C'f

,

u2f

c

Orsouesse

fo/f

Ann

npoQn.neft

peueroK

pacrlerHbtx

ceqenufi

npuHqro

no lssefi-

H6rr{y

saKOH}/:

y

BTynKH

To/l:0,3,

ua nepuQepuu

fo/f

:0,1.

flpuHrrble

BSJIHqHHLI

t/t

:

f

(r),

l,ll

:

f

(r);

K2:

f

Q)

rpoeKrHpyeMbrx

pemeroK

npoQu.neft

npe.4craB-

JreHbr

na

puc.

122.

Pacqer

.nonacrsoft

cgcreMbr

pa6overo KoJIeca

Bblno.rlHeH

BI{xpeBblM

MeroAoM

y,ta

Dr: 1000

il.tt

H H

:

I J,r

rrp].1-

rroMoulH

pacle]Hll^x

q]pt'ty.tt

n B

nocJleAoBareJlb-

HOCTH,

B

XOrOpOfi

arU

sOprrly.rrbr

HsJrox(eHbr

B

s

57,

60.

flanuue

pacqeTa

ocHoBHbIx

rapaMerpoB

peluerox pa'Ooieio KoJIeca

noMeuleHbl

n ta6n.

25.

242

9r

-t

-

Ao:

i

,

,lt

LT-

At:

ff

,

*lt

sin

a

:

Aol2Kwm

|

-fa,

*tzfc

0,724

0,088

1,585

0,00448

0,43

4,95

0,15

0,271

2,051

1,275

0,337

18"39'

0,3193

0,9475

3,997

-3,789

1,275

1,23

0,813

0,45

0,554

0,0922

0,804

0,15

0,1205

0,6835

0,139

1,57

0,0107

Pacserdbrc

ceqeEsf,

0,375

4,32

0,1

o,2Q7

2,252

1,275

o,387

2lo9'

o,3608

o,9327

3,53

III

-3,296

1,275

l,3l

Q,762

o,393

o,515

o,0859

o,804

o,2

o,168

o,643

o,199

1,595

q0les

IV

0,32

3,68

0,05

o,l2l

2,521

1,275

0,542

28"27',

0,4764

0,8792

2,682

-2,359

1,275

1,385

0,722

0,385

0,464

0,0774

0,804

0,25

0,2005

0,6035

0,276

I,65

0,0486

0,265

3,05

0

2,9

1,275

0,796

3go3l,

0,6227

0,7824

2,046

-1,6

1,275

1,46

0,685

0,277

0,403

0,0672

0,804

0,3

0,241

0,563

0,381

1,775

0,0852

243

Барлит В.В. Гидравлические турбины

Подождите немного. Документ загружается.