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321

1 – [ehd pbebg^jh\; 2 – gZdehggZy rZc[Z; 3 – \Ze; 4 – rlhd; 5 – ihjr_gv; 6 – mihjgh-jZkij_^_ebl_evguc ^bkd

Jbk. 31.3 :dkbZevgh-ihjrg_\hc gZkhk k gZdehgghc rZc[hc

ba[ulhqgh]h ^Z\e_gby gZ \oh^_ \ gZkhk kdhevayl ih ih\_joghklb gZdehgghc rZc[u 2, \ke_^kl\b_ q_]h kh\_jrZxl \ha\jZlgh-ihklmiZl_evgh_ ^\b`_gb_ \ jZ[hqbo dZf_jZo, ijb wlhf dZf_ju khh[sZxlky ihhq_j_^gh k ^m]hh[jZagufb hdgZfb 2, \uiheg_ggufb \ dhjimk_ 1 mihjgh-jZkij_^_ebl_evgh]h ^bkdZ

(jbk.31.4), h^gh ba dhlhjuo khh[sZ_lky kh \kZku\Zxsbf ljm[hijh\h^hf, Z ^jm]h_ k gZihjguf.

322

1 – dhjimk ^bkdZ; 2 – ^m]hh[jZagh_ hdgh Jbk. 31.4 Mihjgh-jZkij_^_ebl_evguc ^bkd

JZ[hq_c dZf_jhc \ ZdkbZevgh – ihjrg_\hf gZkhk_ k gZdehgghc rZc[hc y\ey_lky h[tzf, h]jZgbq_gguc \gmlj_gg_c ih\_joghklvx pbebg^jh\, jZkiheh`_gguo \ [ehd_ pbebg^jh\ 1, b lhjphf ihjrg_c 5

Oh^ iemg`_jh\ l hij_^_ey_lky m]ehf gZdehgZ rZc[u b jZ\_g Dtg .

JZ[hqbc h[t_f hij_^_ey_lky \ujZ`_gb_f

V0 = (ŒD2/4)Dtg z

(31.2)

]^_ D – ^bZf_lj hdjm`ghklb jZkiheh`_gby hk_c pbebg^jh\.

323

Ih^ZqZ ZdkbZevgh-ihjrg_\h]h gZkhkZ k gZdehgghc rZc[hc fh`_l baf_gylvky aZ kqzl baf_g_gby m]eZ gZdehgZ J rZc[u.

:dkbZevgh-ihjrg_\hc gZkhk k gZdehgguf pbebg^jh\uf [ehdhf (jbk.31.5) hlebqZ_lky hl gZkhkZ k gZdehgghc rZc[hc l_f, qlh hkv \jZs_gby pbebg^jh\h]h [ehdZ 3 gZdehg_gZ d hkb \jZs_gby ijb\h^gh]h \ZeZ gZ m]he D. I_j_^ZqZ fhf_glZ \jZs_gby hl \_^ms_]h \ZeZ 7 d pbebg^jh\hfm [ehdm 3 hkms_kl\ey_lky ihkj_^kl\hf dZj^ZgZ beb q_j_a rlhdb ihjrg_c. GZ jbk.31.5 ijb\_^_gZ ko_fZ gZkhkZ k gZdehgguf pbebg^jh\uf [ehdhf b [_kdZj^Zgghc k\yavx.

1 – mihjgh-jZkij_^_ebl_evguc ^bkd; 2 – \Ze; 3 – pbebg^j; 4 – ihjr_gv; 5 – rlhd; 6 – rZc[Z; 7 – \_^msbc \Ze

Jbk. 31.5 :dkbZevgh-ihjrg_\hc gZkhk k gZdehgguf pbebg^jh\uf [ehdhf

324

Hkgh\gufb we_f_glZfb gZkhkZ y\eyxlky pbebg^jh\uc [ehd (jhlhj) 3, ihjrgb 4, rlhdb 5, kh_^bgzggu_ rZjgbjgh k ihjrgyfb 4 b rZc[hc 6, dhlhjZy `_kldh k\yaZgZ k \_^msbf \Zehf 7. JZkij_^_e_gb_ `b^dhklb hkms_kl\ey_lky, dZd b \ gZkhkZo k gZdehgghc rZc[hc, ihkj_^kl\hf mihjgh-jZkij_^_ebl_evgh]h ^bkdZ 1. P_gljh\dZ pbebg^jh\h]h [ehdZ b hihjgh-jZkij_^_ebl_evgh]h ^bkdZ h[_ki_qb\Z_lky \Zehf 2. JZ[hq_c dZf_jhc \ ZdkbZevgh – ihjrg_\hf gZkhk_ k gZdehgguf pbebg^jh\uf [ehdhf y\ey_lky h[tzf, h]jZgbq_gguc \gmlj_gg_c ih\_joghklvx pbebg^jh\, jZkiheh`_gguo \ pbebg^jh\hf [ehd_ 3, b lhjphf ihjrg_c 4.

JZ[hqbc h[t_f ijb qbke_ pbebg^jh\ Z b ^bZf_lj_ D hij_^_ey_lky ih aZ\bkbfhklb

V0 = (ΠD2/4)D sinDZ

(31.3)

Ih^ZqZ ZdkbZevgh-ihjrg_\h]h gZkhkZ k gZdehgguf pbebg^jh\uf [ehdhf

fh`_l baf_gylvky aZ kqzl baf_g_gby m]eZ D gZdehgZ pbebg^jh\h]h [ehdZ.

IeZklbgqZlu_ gZkhku. JZa^_eyxlky gZ gZkhku h^ghdjZlgh]h b

^\mdjZlgh]h ^_ckl\by.

IeZklbgqZluc gZkhk h^ghdjZlgh]h ^_ckl\by (jbk.31.6) khklhbl ba

jhlhjZ 3, \ iZaZo dhlhjh]h jZaf_s_gu ieZklbgu 4, i_j_f_sZxsb_ky jZ^bZevgh b \jZsZxsb_ky \f_kl_ k jhlhjhf 3, b klZlhjZ 1. Hkv \jZs_gby jhlhjZ 3 kf_s_gZ ih hlghr_gbx d hkb kbff_ljbb klZlhjZ 1 gZ \_ebqbgm wdkp_gljbkbl_lZ E. < klZlhj_ bf_xlky hdgZ, khh[sZxsb_ky kh \kZku\Zxsbf 2 b gZ]g_lZl_evguf 5 hl\_jklbyfb, d dhlhjuf ih^kh_^bg_gu \kZku\Zxsbc b gZihjguc

ljm[hijh\h^u.

>ebgZ ^m]b i_j_fuqdb klZlhjZ f_`^m hdgZfb \kZku\Zxs_]h 2 b gZ]g_lZl_evgh]h 5 hl\_jklbc \uihegy_lky g_kdhevdh [hevr_ m]eh\h]h rZ]Z f_`^m ieZklbgZfb 2Œ/Z (Z – qbkeh ieZklbg) ^ey ij_^hl\jZs_gby i_j_l_dZgby

325

1 – klZlhj; 2 – \kZku\Zxs__ hl\_jklb_; 3 – jhlhj; 4 – ieZklbgu; 5 – gZ]g_lZl_evgh_ hl\_jklb_

Jbk. 31.6 IeZklbgqZluc gZkhk

jZ[hq_c `b^dhklb ba ahgu ih\ur_ggh]h ^Z\e_gby \ ahgm \kZku\Zgby.

JZ[hq_c dZf_jhc ieZklbgqZlh]h gZkhkZ y\ey_lky h[tzf, h]jZgbq_gguc \gmlj_gg_c ih\_joghklvx klZlhjZ 1, gZjm`ghc ih\_joghklvx jhlhjZ 3, b ^\mfy khk_^gbfb ieZklbgZfb. JZ[hqbc h[t_f jZkkfZljb\Z_fh]h gZkhkZ jZ\_g jZaghklb f_`^m h[t_fhf dhevpZ lhesbghc 2_, rbjbghc, jZ\ghc rbjbg_ jhlhjZ B, b jZ^bmkhf kj_^g_c hdjm`ghklb dhevpZ, jZ\ghc jZ^bmkm klZlhjZ R, b h[t_fhf, aZgbfZ_fuf ieZklbgZfb, l._.

326

V0 = (2ŒR /Z)2BE,

(31.4)

]^_ / – lhesbgZ ieZklbgu.

Ih^ZqZ ieZklbgqZlh]h gZkhkZ h^ghdjZlgh]h ^_ckl\by fh`_l baf_gylvky aZ kqzl baf_g_gby wdkp_gljbkbl_lZ _.

IeZklbgqZluc gZkhk ^\mdjZlgh]h ^_ckl\by khklhbl ba pbebg^jbq_kdh]h jhlhjZ 2 (jbk.31.7) k ieZklbgZfb 3, jZkiheh`_ggufb \ iZaZo jhlhjZ, b klZlhjZ 1.

1 – klZlhj; 2 – jhlhj; 3 – ieZklbgZ; 4 – \kZku\Zxs__ hdgh; 5 – gZ]g_lZl_evgh_ hdgh

Jbk. 31.7 IeZklbgqZluc gZkhk ^\mdjZlgh]h ^_ckl\by

327

< klZlhj_ bf_xlky q_luj_ hdgZ. HdgZ 4 b 5 ihiZjgh kh_^bg_gu kh \kZku\Zxsbf b gZihjguf ljm[hijh\h^Zfb. MqZkldb klZlhjgh]h dhevpZ, jZkiheh`_ggu_ f_`^m hdgZfb, hibkZgu ^m]Zfb hdjm`ghkl_c jZ^bmkZfb r1 b r2 ba p_gljZ jhlhjZ, Z mqZkldb \ ij_^_eZo hdhg \uiheg_gu \ \b^_ ieZ\guo djb\uo.

Ijb lZdhc nhjf_ ih\_joghklb klZlhjgh]h dhevpZ \_ebqbgZ h[t_fZ `b^dhklb, aZdexqzggh]h f_`^m ^\mfy khk_^gbfb ieZklbgZfb, \h \j_fy bo i_j_f_s_gby ih i_j_fuqdZf g_ baf_gy_lky. JZ[hqbc h[t_f gZkhkZ hij_^_ey_lky m^\h_gguf h[t_fhf dhevpZ, h[jZah\Zggh]h jZ^bmkZfb R1 b R2, b rbjbghc B jhlhjZ aZ \uq_lhf h[t_fZ, aZgbfZ_fh]h \u^\bgmlhc qZklvx ieZklbg. Ihwlhfm jZ[hqbc h[t_f jZ\_g:

ijb jZ^bZevghf jZkiheh`_gbb iZah\ ieZklbg \ jhlhj_

V0 = 2[Π(R12 R22) Р(R1 R2) /Z] B,

(31.5)

ijb jZkiheh`_gbb iZah\ ih^ m]ehf . d jZ^bmkm jhlhjZ

V0= 2 [ Π( R12 R22) Р((R1- R2)/ cos . )/Z ] B

(31.6)

Ih^ZqZ ieZklbgqZlh]h gZkhkZ ^\mdjZlgh]h ^_ckl\by fh`_l baf_gylvky lhevdh aZ kqzl baf_g_gby qZklhlu \jZs_gby jhlhjZ.

R_kl_j_ggu_ gZkhku. >_eylky gZ gZkhku k \g_rgbf b \gmlj_ggbf aZp_ie_gb_f.

GZkhku k \g_rgbf aZp_ie_gb_f qZs_ \k_]h \uihegyxlky \ \b^_ iZju h^bgZdh\uo dhkham[uo, r_\jhgguo beb ijyfham[uo r_kl_j_g. GZ jbk 31.8 ij_^klZ\e_gZ ko_fZ r_kl_jzggh]h gZkhkZ k dhkham[ufb r_kl_jgyfb. <_^msZy 3 b \_^hfZy 4 r_kl_jgb gZoh^ylky \ aZp_ie_gbb b mklZgh\e_gu \ dhjimk_ 2 k g_[hevrbfb aZahjZfb. Lhj_p dhjimkZ 2 aZdjul djurdhc 1.

328

1 – djurdZ dhjimkZ; 2 – dhjimk; 3 – \_^msZy r_kl_jgy; 4 – \_^hfZy r_kl_jgy

Jbk. 31.8 R_kl_j_gguc gZkhk k dhkham[ufb r_kl_jgyfb

GZ jbk.31.9 ij_^klZ\e_gZ ko_fZ r_kl_jzggh]h gZkhkZ k ijyfham[ufb r_kl_jgyfb. IZjZ h^bgZdh\uo r_kl_jzg, h^gZ ba dhlhjuo y\ey_lky \_^ms_c, Z \lhjZy- \_^hfhc , jZkiheh`_gu dhjimk_ 3. Ih h[_ klhjhgu h[eZklb aZp_ie_gby \ dhjimk_ bf_xlky ihehklb 4 b 5 , kh_^bg_ggu_ kh \kZku\Zxs_c b gZihjghc ebgbyfb. K lhjp_\uo klhjhg dhjimk aZfudZ_lky lhjp_\ufb ^bkdZfb. Ijb \jZs_gbb r_kl_j_g \h \kZku\Zxs_c ihehklb am[vy \uoh^yl ba aZp_ie_gby.

329

M\_ebq_gb_ h[t_fZ \iZ^bg f_`^m am[vyfb, dhlhju_ y\eyxlky jZ[hqbfb dZf_jZfb, h[mkeh\eb\Z_l mf_gvr_gb_ ^Z\e_gby \h \kZku\Zxs_c ihehklb b aZiheg_gb_ __ `b^dhklvx. I_j_f_s_gb_ jZ[hqbo dZf_j ijb\h^bl d aZfudZgbx dZf_ju. Dh]^Z jZ[hqb_ dZf_ju i_j_f_klylky \ ihehklv gZ]g_lZgby, am[vy r_kl_j_g \oh^yl \ aZp_ie_gb_ b \ul_kgyxl `b^dhklv \ gZihjgmx ebgbx.

AZ h^bg h[hjhl r_kl_j_g jZ[hqbc h[t_f gZkhkZ k ^\mfy h^bgZdh\ufb r_kl_jgyfb \ ij_^iheh`_gbb, qlh h[t_f am[v_\ jZ\_g h[t_fm \iZ^bg, fh`gh hij_^_eblv dZd kmffm h[tzfh\ \iZ^bg h[hbo r_kl_jzg, qlh khhl\_lkl\m_l h[t_fm dhevpZ, bf_xs_fm gZjm`guc ^bZf_lj, jZ\guc ^bZf_ljm hdjm`ghklb \uklmih\ r_kl_j_g lhesbghc, jZ\ghc \ukhl_ am[Z H, b rbjbghc, jZ\ghc rbjbg_ r_kl_jgb B. H[t_f wlh]h dhevpZ fh`gh \ujZablv dZd ijhba\_^_gb_ ^ebgu gZqZevghc hdjm`ghklb gZ iehsZ^v k_q_gby wlh]h dhevpZ, l._.

V0

= ŒDHB,

(31.7)

]^_ ^bZf_lj gZqZevghc hdjm`ghklb D = MZ b H

= 2M (M – fh^mev

aZp_ie_gby). Lh]^Z

 

V0

= 2ŒM2ZB

(31.8)

]^_ Z – qbkeh am[v_\ r_kl_j_g.

H^gZdh, ihkdhevdm m r_kl_j_g h[t_f \iZ^bg f_`^m am[vyfb g_kdhevdh [hevr_ h[t_fZ kZfbo am[v_\, lh mlhqg_ggZy nhjfmeZ ^ey hij_^_e_gby jZ[hq_]h h[t_fZ gZkhkZ bf__l \b^

V0 = 7M2ZB

(31.9)

Ih^ZqZ r_kl_jzggh]h gZkhkZ fh`_l baf_gylvky lhevdh aZ kqzl baf_g_gby qZklhlu \jZs_gby \_^hfhc r_kl_jgb.

330

1 – r_kl_jgy \_^msZy; 2 – r_kl_jgy \_^hfZy; 3 – dhjimk; 4 – ihehklv

\kZku\Zgby; 5 – ihehklv gZ]g_lZgby

Jbk. 31.9 R_kl_j_gguc gZkhk k ijyfham[ufb r_kl_jgyfb

IHJY>HD <UIHEG?GBY J:;HLU

1.Ijhba\_klb jZa[hjdm jZaguo lbih\ jhlhjguo gZkhkh\.

2.<uykgblv gZagZq_gb_ hl^_evguo we_f_glh\, \oh^ysbo \ dhgkljmdpbx

gZkhkZ.

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