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"0:, =0?@8<5@, 4;O 4@525A8=K 7=0G5=85 ?@545;L=>9 A:>@>AB8 A>2?0405B A> A:>@>ABLN 35B5@>35==>3> 3>@5=8O (B;5=8O) 8 A>AB02;O5B V<lim = 0.005 :3/(<2A); gB - B5<?5@0BC@=K9 ?0@0<5B@ 3>@5=8O, [:3/(< 5/2A)]. ;O >F5=>G=KE @0AG5B>2 53> <>6=> ?@8=OBL :0: gB = 0.1 :3/(< 5/2A), [1].  A;CG05 1>;55 B>G=>3> @0AG5B0 @5:><5=4C5BAO 2>A?>;L7>20BLAO D>@<C;>9: ____________ _____________ ______ / 1 1 gB = 2/3m 2g(1 - "/") ( 3 "/" +1) -1 ----------- ---- (13), 1 + 3 "/" V20 345 m - :>MDD8F85=B 384@02;8G5A:>3> A>?@>B82;5=8O ?@>5<>2. 3> 7=0G5=85 3;02=K< >1@07>< 7028A8B >B :>=D83C@0F88 ?@>5<0 (:@C3;0O :204@0B=0O 8 B.4.). ;O >:>= 8 425@59, 8<5NI8E ?@O<>C3>;L=CN D>@<C, ?@8=8<05BAO m = 0.75; " 8 " - B5<?5@0BC@0 2>74CE0, 2B5:0NI53> 2 ?><5I5=85 8 B5<?5@0BC@0 ?@>4C:B>2 3>@5=8O, 2KE>4OI8E G5@57 ?@>5<K, . "0:8< >1@07>< @0AG5B ?;>I048 ?>60@0 4;O 2B>@>3> ?5@8>40 =0 7040==K9 <><5=B 2@5<5=8, t?2 , ?@>872>48BAO ?> D>@<C;5: S?2 = S?1<0E + (t?2 - t?1 <0E ) Vs?@2 (14). @5<O 2B>@>9 AB0488 @0728B8O ?>60@0 2 @568<5   @0AAG8BK205BAO ?> D>@<C;5: Dt?2 lim = (S?2 lim - S?2)/ Vs?@2 (15) . 1I55 2@5<O ?>60@0, >BAG8BK20NI55AO >B <><5=B0 53> 2>7=8:=>25=8O 8 4> 4>AB865=8O ?@545;L=>9 ?;>I048, =0E>48BAO ?> D>@<C;5: t?2 lim = t?1 <0E + Dt?2 + Dt?2 lim (16). ). 5@8>4 =0@0AB0=8O ?;>I048 ?>60@0 ?@8 ?>AB>O==>9 ?;>I048 ?>25@E=>AB8 3>@5=8O.  B5G5=85 MB>3> ?5@8>40 8=B5=A82=>ABL 3>@5=8O >?@545;O5BAO 25;8G8=>9 ?>60@=>9 =03@C7:8 8 @0728B>ABLN 55 ?>25@E=>AB8 3>@5=8O. @8 MB>< C25;8G5=85 ?;>I048 ?>60@0 ?@>8AE>48B ?@8 ?>AB>O==>9 ?;>I048 ?>25@E=>AB8 3>@5=8O 70 AG5B 2K3>@0=8O G0AB8 3>@NG53> <0B5@80;0 8, A>>B25BAB25==>, 2>2;5G5=85 2 ?@>F5AA 3>@5=8O =>2KE CG0AB:>2. "0:8< >1@07>< ?@>42865=85 ?5@54=59 :@><:8 ?;0<5=8 1C45B ?@>8AE>48BL 70 AG5B A3>@0=8O ?>60@=>9 =03@C7:8. 0AG5B ?;>I048 ?>60@0 4;O MB>3> ?5@8>40 ?@>872>48BAO ?> D>@<C;5: S?3 = S?2 lim + DS3 (17), 345 DS3 - ?@8@>AB ?;>I048 ?>60@0 70 AG5B A3>@0=8O G0AB8 ?>60@=>9 =03@C7:8 >B <5AB0 2>7=8:=>25=8O ?>60@0. 5;8G8=C DS3 <>6=> @0AAG8B0BL ?> D>@<C;5: DS3 = (t?3 -t?2 lim) (18), ?@8 CA;>288, GB> t?2 lim <t?3 < t>E2, 345 t>E2 - 2@5<O >E20B0 ?>60@>< 2A53> ?><5I5=8O @0AAG8BK205BAO ?> D>@<C;5: t>E2 = (S?>;0 - S?2 lim ) / + t?2 lim (19), 345 - A:>@>ABL 2K3>@0=8O ?>60@=>9 =03@C7:8, [:3/A], ?@8 CA;>288, GB> < Vs<0E @0AAG8BK205BAO ?> D>@<C;5: = V<lim S?2 lim ? /  (20). >42>4O 8B>3 87;>65==><C, >1I0O <5B>48:0 87<5=5=8O 2;8O=8O 307>>1<5=0 =0 @0728B85 ?;>I048 2=CB@5==53> ?>60@0 <>65B >1>1I5=0 2 2845 A;54CNI59 AE5<K:    0G0;L=K9 #AB0=>282H89AO @568< 3>@5=8O (>A=>2=0O AB048O) ?5@8>4 3>@5=85 70 AG5B 2>74CE0, ?>ABC?0NI53> 2 ?><5I5=85 (307>>1<5=)  (3>@5=85 70 5@8>4 =0@0AB0=8O ?;>I048 ?>60@0 5@8>4 =0@0AB0=8O ?;>I048 AG5B 2>74CE0 70 AG5B C25;8G5=8O ?;>I048 ?>60@0 ?@8 ?>AB>O==>9 2 >1J5<5 ?>25@E=>AB8 3>@5=8O ?;>I048 ?>25@E=>AB8 ?><5I5=8O) 3>@5=8O.   568<   568<   :B82=>5 2K3>@0=85 ?>60@-  =>9 =03@C7:8.  Dt?2 Dt?2 lim 0 t?1<0E t?2 t?2 lim t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t?1 <0E = = = 15.6 <8= 1/4 Vs<0E V<   ? V20 1/40.6600.008 3 3.766 345 V20 = 0.269 ( !/3 +  + (S - O)/8) = 0.269 ( 48/3 + 4 - 48/8) = 3.766 <3/:3. 2. ?@545;8< ?;>I04L ?>60@0 =0 <><5=B >:>=G0=8O =0G0;L=>9 AB0488 ?>60@0 ?> D>@<C;5 (7): S?1 <0E = 1/2 Vs<0E t?1 <0E = 1/2 0.6 15.6 = 4.7 <2. "0: :0: ?5@2K9 7040==K9 <><5=B 2@5<5=8 5 <8=. < t?1<0E, =0E>48< ?;>I04L ?>60@0 =0 5 <8=CB5 ?> D>@<C;5 (7): S?1 = t?1 1/2 Vs<0E = 5 1/3 0.6 = 1.5 <2. 4. ?@545;8< 7=0G5=85 ?0@0<5B@0 25=B8;OF88  ?> D>@<C;5 (2):  = F?@ ?@. = 2 2 2 = 5.66 < 5/2. 5. > D>@<C;5 (8), ?@8=8<0O 2 :0G5AB25 ?5@5E>4=>3> 7=0G5=8O $ = 0.26 :3/(<2A), >?@545;8< ?;>I04L, ?@8 :>B>@>9 ?@>87>945B 87<5=5=85 @568<0 ?>60@0: ___ ___ r2  g 1.29 5.66 9.81 S?2 = ------------- = ------------------------- = 29.3 <2. $ ? 0.26 3 6. "0: :0: 8<55B <5AB> =5@025=AB2> S?2 > S?1<0E, B> 3>@5=85 2> 2B>@>< ?5@8>45 1C45B ?@>B5:0BL 2 @568<5   4> <><5=B0, ?>:0 ?;>I04L ?>60@0 =5 4>AB83=5B 25;8G8=K S?2. > D>@<C;5 (9) @0AAG8B05< 2@5<O 2B>@>3> ?5@8>40 @0728B8O ?>60@0 4> <><5=B0 A<5=K @568<0: Dt?2 = (S?2 - S?1<0E)/Vsmax = (29.3 - 1.7) / 0.6 = 46 <8=. ! <><5=B0 2>7=8:=>25=8O ?>60@0 >:>=G0=85 MB>3> MB0?0 1C45B A>AB02;OBL 25;8G8=C: t?2 = t?1 <0E + Dt?2 = 11.3 + 46 = 57.3 <8= 0;55 ?>60@ 1C45B @072820BLAO 2 @568<5  . 7. @8=8<0O 2 :0G5AB25 gB = 0.1 :3/(< 5/2A), @0AAG8B05< <0AA>2CN A:>@>ABL 2K3>@0=8O 2 @568<5   ?> D>@<C;5 (12): V<0A  = gB  = 0.1 5.66 = 0.57 :3/A. 8. 0AAG8B05< "?@545;L=CN" ?;>I04L ?>60@0 ?> D>@<C;5 (11): V<0A  0.57 S?2 lim = ----------------- = ------------- = 38 <2. V<lim ? 0.005 3 9. ?@545;8< 2@5<O 2B>@>9 AB0488 @0728B8O ?>60@0 2 @568<5   ?> D>@<C;5 (15): Dt?2 lim = (S?2 lim - S?2)/ Vs<0E = (38 - 29.3) / 0.6 = 14.5 <8=. 10. ! <><5=B0 2>7=8:=>25=8O ?>60@0 2@5<O 4> 4>AB865=8O ?>60@>< ?@545;L=>9 ?;>I048 @0AAG8B05< ?> D>@<C;5 (16): t?2 lim = t?1 <0E + Dt?2 + Dt?2 lim = 11.3 + 46 + 14.5 = 71.8 <8=. 11. "0: :0: 2B>@>9 7040==K9 <><5=B 2@5<5=8 30 <8=. < t?2 lim >?@545;8< ?;>I04L ?>60@0 =0 30 <8=CB5 ?> D>@<C;5 (14): S?2 = S?1<0E + (t?2 - t?1 <0E ) Vs<0E = 1.7 + (30 - 11.3) 0.6 = 12.9 <2. 12. "0: :0: B@5B89 7040==K9 <><5=B 2@5<5=8 80 <8= > t?2lim, >?@545;8< ?;>I04L ?>60@0 ?> D>@<C;5 (17): S?3 = S?2 lim + DS3. ;O MB>3> @0AAG8B05< A:>@>ABL 2K3>@0=8O ?>60@=>9 =03@C7:8 ?> D>@<C;5 (20): = V<lim S?2 lim ? /  = 0.005 38 3 / 50 = 0.0076 <2/A. = 0.0076 <2/A = 0.0076 60 <2/<8= = 0.456 <2/<8=. 0B5< >?@545;8< ?@8@>AB ?;>I048 ?>60@0 70 AG5B A3>@0=8O G0AB8 ?>60@=>9 =03@C7:8 : 7040==><C <><5=BC 2@5<5=8 ?> D>@<C;5 (18): DS3 = (t?3 -t?2 lim) = 0.456 ( 80 -71.8) = 3.74 <2. !;54>20B5;L=>: S?3 = 38 + 3.74 = 41.74 <2. 13. ?@545;8< 2@5<O >E20B0 ?><5I5=8O ?> D>@<C;5 (19): t>E2 = (S?>;0 - S?2 lim ) / + t?2 lim = (50 - 41.74) / 0.456 + 71.8 = 89.9 <8=. 14. > ?>;CG5==K< 7=0G5=8O< ?>AB@>8< 3@0D8: 48=0<8:8 @>AB0 ?;>I048 ?>60@0 2> 2@5<5=8 A <><5=B0 2>7=8:=>25=8O ?>60@0 4> ?>;=>3> >E20B0 ?><5I5=8O.  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