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42

H;J:;HLD: HIULGUO >:GGUO

1. Ih aZf_j_gghfm jZkoh^m Q k ihfhsvx nhjfmeu

V

Q

(4.6)

Z

ih^kqblu\Zxl kj_^gb_ kdhjhklb ^\b`_gby \h \k_o k_q_gbyo ljm[hijh\h^Z, Z aZl_f kdhjhklgu_ gZihju (m^_evgZy dbg_lbq_kdZy wg_j]by) DV 22g .

2. Ih ihdZaZgbyf iv_ahf_ljh\ b agZq_gbyf kdhjhklguo gZihjh\ ih^kqblu\Zxl ihegmx m^_evgmx wg_j]bx \ k_q_gbyo

? z

p

 

DV

2

 

 

 

.

(4.7)

Ug

 

 

 

2g

 

3.Ih jZaghklyf iheguo m^_evguo wg_j]bc \ k_q_gbyo hij_^_eyxl ihl_jb wg_j]bb (gZihjZ) hlj f_`^m gbfb.

4.Ih ihdZaZgbyf iv_ahf_ljh\ gZ ko_fm ljm[hijh\h^Z, \uq_jq_ggmx gZ fbeebf_ljh\hc [mfZ]_, gZghkyl \ hij_^_e_gghf fZkrlZ[_ iv_ahf_ljbq_kdmx ebgbx.

5.Ih \uqbke_gguf agZq_gbyf iheghc m^_evghc wg_j]bb lZdbf `_ h[jZahf gZghkyl gZihjgmx ebgbx. >ey [hevr_c gZ]ey^ghklb ebgbb j_dhf_g^m_lky ihdZau\Zlv jZaguf p\_lhf.

J:;HL: 5

HIJ?>?E?GB? DHWNNBPB?GL: J:KOH>: LJM;U <?GLMJB

P_ev jZ[hlu. 1. Hiulgh_ hij_^_e_gb_ dhwnnbpb_glZ jZkoh^Z ljm[u

<_glmjb.

43

2. Ihkljh_gb_ ih hiulguf ^Zgguf ]jZnbdZ aZ\bkbfhklb jZkoh^Z \h^u

Q hl i_j_iZ^Z ihl_gpbZevguo gZihjh\ h.

H;SB? K<?>?GBY

JZkoh^ `b^dhklb, ]ZaZ beb iZjZ \ gZihjguo ljm[hijh\h^Zo ijb mklZgh\b\r_fky ^\b`_gbb gZ ijZdlbd_ qZklh baf_jyxl k ihfhsvx ki_pbZevguo km`Zxsbo mkljhckl\, gZau\Z_fuo jZkoh^hf_jZfb. Ijbgpbi bo jZ[hlu hkgh\Zg gZ baf_j_gbb i_j_iZ^Z ihl_gpbZevguo gZihjh\,

\hagbdZxsbo ba-aZ jZaghklb iehsZ^_c ljm[hijh\h^Z b kZfh]h km`Zxs_]h mkljhckl\Z. D lZdbf mkljhckl\Zf hlghkylky ^bZnjZ]fu (jbk. 5.1), khieZ

(jbk. 5.2), ljm[u <_glmjb (jbk.5.3).

Ba i_j_qbke_gguo gZb[he__ dhgkljmdlb\gh ijhkluf mkljhckl\hf y\ey_lky ^bZnjZ]fZ. H^gZdh hgZ bf__l gZb[hevr__ ]b^jZ\ebq_kdh_ khijhlb\e_gb_, qlh \uau\Z_l agZqbl_evgu_ ihl_jb gZihjZ. Djhf_ lh]h, hkljZy djhfdZ hl\_jklby ^bZnjZ]fu [ukljh bagZrb\Z_lky, qlh ijb\h^bl d baf_g_gbx dhwnnbpb_glZ jZkoh^Z. KhieZ, ohly b bf_xl emqr__ ih kjZ\g_gbx k ^bZnjZ]fhc ]b^jZ\ebq_kdb_ iZjZf_lju, aZlh [he__ keh`gu \ ba]hlh\e_gbb.

Jbk. 5.1

44

Jbk. 5.2

Jbk. 5.3

GZb[he__ kh\_jr_gghc \ hlghr_gbb ]b^jZ\ebq_kdh]h khijhlb\e_gby b hlghkbl_evgh ijhklhc \ ba]hlh\e_gbb y\ey_lky ljm[Z <_glmjb .

Ljm[Z <_glmjb, beb jZkoh^hf_j <_glmjb, khklhbl ba pbebg^jbq_kdhc \klZ\db <K d=(0,3÷ 0,5)D (D – ^bZf_lj ljm[hijh\h^Z), kh_^bg_gghc k ljm[hijh\h^hf dhgnmahjhf :< (koh^ysbfky iZljm[dhf) b ^bnnmahjhf KD (jZkoh^ysbfky iZljm[dhf) (jbk. 5.4).

45

Jbk. 5.4

>ey baf_j_gby i_j_iZ^Z ^Z\e_gby i_j_^ dhgnmahjhf b \ km`_gghc qZklb ljm[u <_glmjb mklZgZ\eb\Zxlky iv_ahf_lju beb ^bnn_j_gpbZevguc fZghf_lj.

F_`^m i_j_iZ^hf ihl_gpbZevguo gZihjh\ \ ljm[_ <_glmjb b ijhoh^ysbf q_j_a g__ jZkoh^hf kms_kl\m_l hij_^_e_ggZy nmgdpbhgZevgZy aZ\bkbfhklv, dhlhjZy fh`_l [ulv bkihevah\ZgZ ^ey hij_^_e_gby jZkoh^Z ih aZf_j_gghfm i_j_iZ^m gZihjZ.

Wlm aZ\bkbfhklv e_]dh ihemqblv bkihevamy mjZ\g_gb_ ;_jgmeeb b mjZ\g_gb_ g_jZaju\ghklb ihlhdZ. KhklZ\bf mjZ\g_gb_ ;_jgmeeb ^ey k_q_gbc

1-1 b 2-2 hlghkbl_evgh iehkdhklb kjZ\g_gby 0-0, kh\iZ^Zxs_c k ]hjbahglZevghc hkvx ljm[u, [_a mq_lZ ihl_jv gZihjZ gZ mqZkld_ f_`^m \u[jZggufb k_q_gbyfb b ijbgbfZy jZ\ghf_jguc oZjZdl_j jZkij_^_e_gby kdhjhkl_c \ \u[jZgguo k_q_gbyo

p

V 2

 

p

2

 

V

2

 

1

 

1

 

 

 

 

2

(5.1)

 

 

 

 

 

 

 

kg

2g

 

kg

2g

 

Ba mjZ\g_gby g_jZaju\ghklb ihlhdZ

V1·&1= V2&2

(5.2)

fh`gh \ujZablv kdhjhklv V2 q_j_a V1:

46

V2=V1·

Z1

mV

, ]^_ m

Z1

 

 

Z2

1

Z2

 

Lh]^Z mjZ\g_gb_ (5.1) ijbf_l \b^:

 

p

p

2

 

 

V 2

(m2 1)

 

 

1

 

 

 

 

 

 

 

1

 

(5.3)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

kg kg 2g

 

 

 

H[hagZqb\

 

 

 

p1

 

p2

 

h , mjZ\g_gb_ (5.3) aZibr_f \ lZdhf \b^_:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

kg

 

kg

 

 

 

V1=

 

 

 

2g

 

 

˜

 

h

(5.4)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

m2 1

 

 

 

L_hj_lbq_kdbc jZkoh^ q_j_a ljm[m <_glmjb fh`gh hij_^_eblv ih ke_^mxs_c aZ\bkbfhklb

QT=V1·&1=&1

2g

˜ h

(5.5)

 

 

m2 1

 

<ujZ`_gb_ &1

2g

aZ\bkbl lhevdh hl ]_hf_ljbq_kdbo jZaf_jh\

 

 

 

m2

1

 

 

jZkoh^hf_jZ.

H[hagZqbf

&1

2g

=:

(5.6)

 

 

m2 1

 

]^_ :- dhgklZglZ jZkoh^hf_jZ, lh]^Z mjZ\g_gb_ (5.5) fh`gh aZibkZlv \

lZdhf \b^_:

47

Ql = : h

(5.7)

Ijb \u\h^_ nhjfmeu (5.7) g_ [ueb mql_gu ihl_jb gZihjZ gZ lj_gb_ gZ mqZkld_ :<KD b \ebygb_ km`_gby gZ jZkij_^_e_gb_ kdhjhkl_c. Ihwlhfm

\uqbke_gguc ih nhjfme_ (5.7) jZkoh^ [m^_l g_kdhevdh

aZ\ur_g ih

kjZ\g_gbx k ^_ckl\bl_evguf jZkoh^hf.

 

>ey hij_^_e_gby ^_ckl\bl_evgh]h jZkoh^Z \\h^blky dhwnnbpb_gl

jZkoh^Z , dhlhjuc jZ\_g

hlghr_gbx ^_ckl\bl_evgh]h

jZkoh^Z Q d

l_hj_lbq_kdhfm Ql

 

 

=

Q

 

 

(5.8)

QT

 

 

 

 

HdhgqZl_evgZy nhjfmeZ ^ey hij_^_e_gby ^_ckl\bl_evgh]h jZkoh^Z

ijbf_l ke_^mxsbc \b^:

 

 

Q= A h

 

(5.9)

Dhwnnbpb_gl jZkoh^Z

ljm[u <_glmjb aZ\bkbl hl

__ jZaf_jh\,

fZl_jbZeZ b hij_^_ey_lky lZjbjh\dhc jZkoh^hf_jZ.

Ihkljhb\ gZ hkgh\Zgbb hiulguo ^Zgguo ]jZnbd aZ\bkbfhklb Q=f(h), fh`gh g_ihkj_^kl\_ggh gZoh^blv ^_ckl\bl_evguc jZkoh^ Q ih jZaghklb ihdZaZgbc iv_ahf_ljh\ h beb ^bnn_j_gpbZevgh]h fZghf_ljZ, g_ ijb[_]Zy d nhjfme_ (5.9).

G_h[oh^bfh hlf_lblv, qlh dhwnnbpb_gl jZkoh^Z [m^_l ihklhygguf ijb jZaebqguo jZkoh^Zo lhevdh \ ahg_ d\Z^jZlbqgh]h khijhlb\e_gby, dh]^Z qbkeZ Re>Reij, ]^_ Reij – ij_^_evgh_ qbkeh J_cghev^kZ, l._. gZbf_gvr__

48

agZq_gb_ qbkeZ Re ijb dhlhjhf =const. Ijb khhlghr_gbb ^bZf_ljh\ ljm[u

<_glmjb d =0,3÷ 0,5, ij_^_evgh_ qbkeh J_cghev^kZ Reij105.

D

Ijb mklZgh\d_ jZkoh^hf_jZ <_glmjb, dZd b ^jm]bo jZkoh^hf_jh\, g_h[oh^bfh bkdexqblv bkdZ`_gb_ ihlhdZ \ wlbo mkljhckl\Zo ba-aZ [ebadh jZkiheh`_gguo bklhqgbdh\ \hafms_gbc (djZgh\, \_glbe_c, km`_gbc, jZkrbj_gbc b l.^.). JZkoh^hf_j ^he`_g jZaf_sZlvky gZ ^hklZlhqghf jZkklhygbb hl bklhqgbdZ \hafms_gbc. G_h[oh^bfZy fbgbfZevgZy ^ebgZ ijyfhebg_cgh]h mqZkldZ ^h jZkoh^hf_jZ <_glmjb hij_^_ey_lky jZaf_jZfb jZkoh^hf_jZ b bklhqgbdhf \hafms_gby b fh`_l dhe_[Zlvky hl 4D ^h 50D.

FbgbfZevgZy ^ebgZ ijyfhebg_cgh]h mqZkldZ aZ jZkoh^hf_jhf jZ\gZ 5D.

HIBK:GB? HIULGHC MKL:GH<DB

JZkoh^hf_j <_glmjb mklZgh\e_g gZ ljm[hijh\h^_ i_j_f_ggh]h k_q_gby, hibkZgghf \ jZ[hl_ 4 (kf. jbk. 4.2 ).

<k_ jZaf_ju ljm[u <_glmjb ijb\_^_gu gZ jbk. 5.4

I_j_iZ^ ^Z\e_gbc \ ]hjeh\bg_ jZkoh^hf_jZ b \ _]h \oh^ghc jZkrbj_gghc qZklb baf_jy_lky ijb ihfhsb iv_ahf_ljh\ ‹1 b ‹2, kfhglbjh\Zgguo gZ sbl_ ‹ 1.

IHJY>HD IJH<?>?GBY J:;HLU

1.Ijh\_jyxl hlkmlkl\by \ha^moZ \ iv_ahf_ljZo ‹ 1, 2.

2.<dexqZxl p_gljh[_`guc gZkhk, ih^Zxsbc \h^m \ gZihjguc [Zd.

3.>Z\Zy jZaebqgh_ hldjulb_ \_glbex 2, \ ljm[hijh\h^_ mklZgZ\eb\Zxl g_kdhevdh (5-6) jZaguo jZkoh^h\ \h^u, dhlhju_ aZf_jyxl lhgdhkl_gguf lj_m]hevguf \h^hkeb\hf, jZkiheh`_gguf \ ehld_ 3.

4.Ijb ijh\_^_gbb hiulZ dZ`^uc jZa kgbfZxl ihdZaZgby iv_ahf_ljh\

1 b 2.

49

<k_ wlZiu jZ[hlu, i_j_qbke_ggu_ \ ii. 1 – 4, [he__ ih^jh[gh hibkZgu \ jZ[hl_ 4.

H;J:;HLD: HIULGUO >:GGUO

1. >ey dZ`^h]h hiulZ ih^kqblu\Zxl jZaghklb ihdZaZgbc iv_ahf_ljh\ h b khhl\_lkl\_ggh bf ih nhjfme_ (5.7) – l_hj_lbq_kdb_ jZkoh^u QT.

Ij_^\Zjbl_evgh ih nhjfme_ (5.6) gZoh^yl agZq_gb_ :.

2. >ey dZ`^h]h hiulZ ih nhjfme_ (8) ih^kqblu\Zxl agZq_gb_ dhwnnbpb_glZ jZkoh^Z ljm[u <_glmjb.

<k_ j_amevlZlu baf_j_gbc b \uqbke_gbc aZghkylky \ lZ[ebpm 5.1.

LZ[ebpZ 5.1

hiulZjGhf

 

IhdZaZgby

JZaghklvihdZaZgbc ivljh\ahf h

JZkoh^\h^u, gguc\uqbke[ a

ihllZmqjv, Q

ldZHlf jrbgu\m]eZ m]hevgh]hlj \h^hkeb\Z

Baf_j_gb_ jZkoh^Z

QJZkoh^

DhwnnbpbgljZkoh^Z

iv_ahf_ljh\

_ldZHlfmjh\gy __^ji \h^hkeb\hf

GGZihj

 

 

 

l

 

 

 

 

 

 

 

\ k_q_gbyo

 

 

 

 

D

 

 

 

 

 

 

1 b 2

 

 

 

D

 

 

 

 

 

 

p1

 

 

p2

 

 

 

 

 

 

 

 

 

 

 

Ug

 

 

Ug

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

kf

 

e/k

 

 

kf

 

e/k

 

1

2

 

3

 

4

5

 

6

7

8

9

10

3. Ih hiulguf agZq_gbyf ^_ckl\bl_evgh]h jZkoh^Z Q b jZaghklyf ihdZaZgbc iv_ahf_ljh\ h gZ fbeebf_ljh\hc [mfZ]_ \ fZkrlZ[_ kljhblky ]jZnbd aZ\bkbfhklb Q=f(h).

50

J:;HL: 6

HIJ?>?E?GB? DHWNNBPB?GL: =B>J:<EBQ?KDH=H LJ?GBY IJB ><B@?GBB @B>DHKLB < LJM;HIJH<H>?

P_ev jZ[hlu: 1.Wdki_jbf_glZevgh_ hij_^_e_gb_ dhwnnbpb_glZ ]b^jZ\ebq_kdh]h lj_gby (dhwnnbpb_gl >Zjkb O) ^ey hiulgh]h ljm[hijh\h^Z.

2.<uqbke_gb_ dhwnnbpb_glZ O ih nhjfmeZf ^ey khhl\_lkl\mxs_c h[eZklb khijhlb\e_gby b kjZ\g_gb_ _]h k hiulgufb agZq_gbyfb.

3.Ihkljh_gb_ ]jZnbdZ aZ\bkbfhklb hiulguo agZq_gbc dhwnnbpb_glZ

O hl qbkeZ J_cghev^kZ O = g(Re).

H;SB? K<?>?GBY

Ihl_jyfb gZihjZ ih ^ebg_ H^e. gZau\Z_lky qZklv m^_evghc wg_j]bb ihlhdZ `b^dhklb, dhlhjZy aZljZqb\Z_lky gZ ij_h^he_gb_ ]b^jZ\ebq_kdbo kbe lj_gby, \hagbdZxsbo, \ hkgh\ghf, \ ahg_ dhglZdlZ [hdh\hc ih\_joghklb ihlhdZ `b^dhklb k l\_j^ufb kl_gdZfb ljm[hijh\h^Z. Wlhl \b^ ihl_jv bf__l f_klh \ ijyfhebg_cguo dZgZeZo ex[hc nhjfu ihi_j_qgh]h (`b\h]h) k_q_gby, iehsZ^v dhlhjh]h g_ baf_gy_lky ih ^ebg_.

Kh]eZkgh kh\j_f_gguf \haaj_gbyf, lmj[me_glguc ihlhd khklhbl ba ih]jZgbqgh]h kehy, jZkiheh`_ggh]h g_ihkj_^kl\_ggh m kl_ghd ljm[u, b lmj[me_glgh]h y^jZ.

GZ [hdh\hc ih\_joghklb ihlhdZ, g_ihkj_^kl\_ggh khijbdZkZxs_]hky k l\_j^hc ih\_joghklvx kl_ghd ljm[u, h[jZam_lky ijbkl_gguc kehc hij_^_- e_gghc lhesbgu G =f (Re), dhlhjuc ijb fZeuo kdhjhklyo bf__l eZfbgZjgmx kljmdlmjm, Z ijb m\_ebq_gbb kdhjhklb ijbkl_gguc kehc klZgh\blky

51

lmj[me_glguf, khklhysbf ba [_kdhg_qgh]h fgh`_kl\Z fbdjh\boj_c. WlZ \boj_\Zy h[hehqdZ ihlhdZ \hagbdZ_l \ke_^kl\b_ h[l_dZgby `b^dhklvx \uklmih\ r_jhoh\Zlhklb ('), ijbkmlkl\mxsbo gZ ex[hc ih\_joghklb kl_gdb ljm[u. <j_fy kms_kl\h\Zgby fbdjh\boj_c fZeh, lZd dZd, hgb,

\aZbfh^_ckl\my ^jm] k ^jm]hf, m\_ebqb\Zxlky \ jZaf_j_ b fb]jbjmxl hl kl_gdb ljm[u d __ hkb. Ijb wlhf bo bgl_gkb\ghklv mf_gvrZ_lky, b fbdjh\boj_\h_ ^\b`_gb_ ij_h[jZam_lky \ fZdjh\boj_\h_, g_ihkj_^kl\_ggh nhjfbjmxs__ oZhlbq_kdmx kljmdlmjm lmj[me_glgh]h y^jZ ihlhdZ.

HibkZggZy \ur_ j_ZevgZy kljmdlmjZ ihlhdZ ihdZau\Z_l, qlh kbeu lj_gby b \ua\Zggu_ bfb dZkZl_evgu_ gZijy`_gby, ehdZebamxlky \ ijbkl_gghf keh_, Z lmj[me_glgh_ y^jh – wlh ljZgablguc ihlhd `b^dhklb, h[t_f dhlhjh]h khklZ\ey_l [he__ 95 ijhp_glh\ hl \k_]h h[t_fZ ihlhdZ \ dZgZe_

(ljm[_), ihqlb g_ hdZau\Z_l \ebygby gZ khijhlb\e_gb_ ^\b`_gbx `b^dhklb.

EZfbgZjguc j_`bf ^\b`_gby `b^dhklb, \ hlebqb_ hl lmj[me_glgh]h, bf__l kljh]h mihjy^hq_ggmx, kehbklmx kljmdlmjm ihlhdZ `b^dhklb, ihwlhfm aZdhgu f_oZgbdb iha\heyxl k hij_^_e_ggufb ^hims_gbyfb ihemqblv l_hj_lbq_kdb aZdhg jZkij_^_e_gby dZkZl_evguo gZijy`_gbc, aZdhg iZjZ[hebq_kdh]h jZkij_^_e_gby kdhjhkl_c \ k_q_gbb, nhjfmem jZkoh^Z `b^dhklb b aZdhg ImZa_cey ^ey hij_^_e_gby ihl_jv gZihjZ ih ^ebg_.

H[s_c nhjfmehc ^ey hij_^_e_gby ihl_jv gZihjZ ih ^ebg_ \ ljm[Zo djm]eh]h k_q_gby, dZd ijb lmj[me_glghf, lZd b ijb eZfbgZjghf j_`bfZo ^\b`_gby, y\ey_lky nhjfmeZ >Zjkb-<_ck[ZoZ

h O l V 2 , (6.1)

^e

d 2g

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