, .. - .
1=2 S -.
S=0,03415 Δ/(z)
. .. , .
1)
1=1 S1 : S1=0,03415 h1/(z1)
2=2 S 2: S1=0,03415 h2/(z2)
1= 2=
2) h
1=1S1
S1=0,03415 h1/(z 1)
2=2+S2 :
S1=0,03415 h 2/(z 2)
1= 2= h
. :
=1/Ω∫ (Ω)d Ω
3 (30) .
R, Q(t), W, k, k - , h, m, m, , , z(P,T).
q(t), Q(t), (t), R(t).
- . :
Q(t)=2p×k×h×Rc2DP× (fo)/(m×c) (1)
-(Rc,t)=m×Q× (fo)/(2p×k×h) (2)
- - .
(1) (2).
Q(tn)=
, . , n - q=Dqj.
P-(R,tn)=SDPj; j=1,n (3)
P-(R,tn)=P-m/(2p×k×h)×S[Dqj× (fon-fon-1)]; j=1,n (4) foj=0=0, Dqj=0=0.
. (4) n:
P-(R,tn)=P-m/(2pkh)( -
-Dq(tn) (fon-fon-1)) (5)
q(tj)=q(tj-1)+Dq(tj) (6)
q(tn)=q(tn-1)+Dq(tn) (7)
Q(t)=Q(tn-1)+[q(tn-1)+Dq(tn)]×Dt (8)
(9)
- y(t) r×g×y(t) . - .
(R,t)-(R,t)=m/(2×p×k×h)×ln[R/R(t)]×[q(tn-1)+Dq(tn)] (10)
(10)
¢(R,t)= +r×g×y(t) (11)
P(R,t)-[ (t)+r×g×y(t)]=m/(2×p×k×h)×ln[R/R(t)]×
×[q(tn-1)+Dq(tn)] (12)
(12) (9) (5) :
-m/(2pkh)( -Dq(tn)×
× (fon-fon-1))= +
+r×g×y(n)+m/(2pkh)×ln(R/R(tn))×[q(tn-1)+Dqn] (13)
(13) - Dq(tn)
Dq(tn)=b/(2×a)-(b2/(4×a2)-c/a (14)
=m/(2×p×k×h)(Dt× (fon-fon-1)+ln[R/R(tn)])
b=Dt-m/(2×p×k×h)×Dt×q(tn-1)-ln[R/R(tn)]+
+L×m/(2×p×k×h)× (fon-fon-1)-
-m/(2×p×k×h)×Dt +
+L×m/(2×p×k×h)×ln[R/R(tn)]
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c=×L-L×m/(2×p×k×h) -
-L×m/(2×p×k×h)×q(tn-1)×ln[R/R(tn)]-d-r×g×y(tn)L
L= W-Q(tn-1)-q(tn-1)×Dt
d=( W/z-××Q(tn)/)
(14) tn: R(tn), y(tn), z(tn). . 1- :
R(1)(tn)=R(tn-1); y(1)(tn)=y(tn-1); z(1)(tn)=z(tn-1)Þq(1)(tn)Þ
ÞQ(1)(tn) ( 8)Þ (1)(tn)Þz(2)(tn)Þ
ÞQ(t)=p×[R2-R2(t)]mh(a-a)Þ
ÞR(t)=[R2-Q(1)(tn)/(p×m×h×(a-a))]0,5Þ
Þy(2)(tn)Þf[Q(1)(tn)]Þ
½(2)(tn)-(1)(tn)½£e
y(t) - .
y=max=H -
. - :½(2)(tn)-(1)(tn)½£e
4 (29) - ( ).
- -. - - .
- R q. , P(R3,t) - :
P(R,t)=P-q×m×(fo)/(2×p×k×h) (1)
fo=t/R2; h, k, n ; mb- ; P(fo) fo.
- DP=(R,t) . - QB, - t:
Q(t)=2×p×k×h×R2×D×Q(fo)/(m×) (2)
Q(fo) - fo. P(fo) Q(f) ¥ , . ¥ - - RK/R3>20, R . (1) (2), q=const D=const, , , - - H - . . , .. . . UP - R. - pR=S ( S ). , - , - , ¥ . R.
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, , , .
- , - Q=Q(t).
-.
, .. - (R3,t)@(f). . 1.
. 1. . , - - t. [0,t] Dt. =(t) . 1, . (2) , , - t, (5): Q(t)=2×p×k×h×R2/m(D0Q(fo)+D1Q(fo-fo1)+D2Q(fo-fo2)++DnQ(fo-fon)), D0, D1, D2 .. t, (tt1), (tt2) .. (. . 1):
fo=t/R2; fo-fo1=(t-t1)/R2; fo-fo2=(t-t2)/R2;
. 1 D0, D1, D2 .., Q , (5) Q(t). , , : = Q(t) (6)
- . , ..
4. - -. - - .
- - .
(t)/z()=1/[a×W-Q(t)]×[P/z×aW-××Q(t)/] (1)
Q(t) - .
Þ , - . 1949 . - -. - .
2/r2+1/r×P/r=1/c×P/t (2)
c - - ;
c=k×K/(m×m)
- .
(r,t=0)=P=const (3).
:) P(R,t)=P (4);) (/r)½r=R=0 (5).
(): ) P(R,t)- P(R,t)= DP= const (6);
) (r/r)½r=R= const (7)
q=2×p×Rk×h(P/r)½r=R/m =const
(r/r)½r=R=m q/2×p×k×h= const*
2 3,5,6, Q(t)=2×p×k×h×R2×DP× (fo) /(m×c) (8)
fo - ( , ); fo=c×t/R2; (fo) - R¥:
I0, Y0 1- 2- , 0- .
-(R,t)=m×Q× (fo) /(2×p×k×h) (9)
(fo) - - R¥:
(fo)=
I1, Y1 1- 2- , 1- .
F=p×R2R=(F/p)0,5
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