Click here to load reader

Zbirka zadataka izzs

  • View
    282

  • Download
    10

Embed Size (px)

DESCRIPTION

Rasprostiranje poremecaja

Text of Zbirka zadataka izzs

  • 1

    - -

    2014

  • 2

    1. 1. =1 cm2, . - , , C(z=0)=100 g/cm3 C(z=10 cm)=0 g/cm3, D =10-5 cm2/s. . .

    1

    10cm - 0cm10 0z

    C z C zCq A Az

    ' 'D D

    -5 -40 -100-10 1 10 g/s

    10 .

    "+" , z-. , , . 2. , , D a) ) ? 2 ) , . . x t . , , 2 /x t D .

  • 3

    ) , , . x t 2 /x t D . 3. h= 40 cm . 1 20 cmh . . 1.1.

    1.1

    t [s] [cm] 1. 86400 3,0 2. 345600 6,0

    : ) D ; ) . 3 a) .

    2 ts D ,

    2

    2tsD .

    , 1.1,

    22 -9 211

    1

    0,03= = 5,2 10 m /s,

    2 2 86400ts D

    22 -9 222

    2

    0,06= = 5,2 10 m /s.

    2 2 345600ts D

    D =5,210-5 m2/s. ) je L=40 cm. 4s 95% , 4L s .

    4 4 2 ts D = 40 cm,

    22 59

    0,1 = = = 9,61 10 s

    2 2 5,2 10t s D .

  • 4

    4. - CO2, m = 0,1 g, (t = 0) , =5 cmr . - CO2

    1 ppm C =50 cm x , ) ) .

    : = 1,23 kg/m3 ; = 1000 kg/m3; D= 1,7110-5 cm2/s; D = 0,14 cm2/s. 4 )

    9 36

    1ppm,

    1,23 1,23 10 g/cm .10

    a

    C

    C

    r

    x y z x y zC C C C C C Cv v v St x y z x x y y z z

    D D D .

    0x y zv v v . , .

    .C const - 0C Cy z

    .

    , 0S . , x -.

    2

    2

    C Ct x

    D.

    2

    exp44

    m xCtA tp

    DD.

    1 ppm C 50 cmx

    2

    9 322 2

    50cm0,11,23 10 g/cm exp4 0,14cm /s5cm 4 0,14cm /s

    gttp p

    ,

    4 3

    9 9,599 10 4,464 101,23 10 exptt

    ,

  • 5

    354,464 10exp 0,128 10 t

    t

    . (1)

    (1) . . (1) 1y t , (1) 2y t . 350 500 st (1), 1y t

    2y t . 1y t 2y t . 1 1y t y t , 420 st . (1)

    , C = 1 ppm x = 50 cm t = 432 s.

    )

    6 36

    1ppm,

    1000 1 10 g/cm .10

    C

    C

    r

    ),

    2

    exp44

    m xCtA tp

    DD.

    1 ppm C 50 cmx

    2

    6 35 22 5 2

    50cm0,1g1 10 g/cm exp4 1,71 10 cm /s5cm 4 1,71 10 cm /s ttp p

    ,

    2 76 8,69 10 3,655 101 10 exp

    tt

    ,

    743,655 10exp 0,115 10 t

    t

    . (2)

  • 6

    (2) . . (2) 1y t , (2) 2y t . 7 70,5 10 2 10 st (2), 1y t

    2y t . 1y t 2y t . 1 1y t y t , 71,12 10 st . (2)

    , C = 1 ppm x = 50 cm 71,12 10 st .

    5. . je o 1 kgm . , D = 0,01 m2/s. , . , 1 mh 5 mb . a) ) , ) )

    5 ) . , 2s . 2 = 50 m,

    2 2 50t D ,

  • 7

    2 250 50

    31250 s=8,68 h8 8 0,01

    t D.

    )

    x y z x y zC C C C C C Cv v v St x y z x x y y z z

    D D D .

    . 0x y zv v v . , .

    0C Cy z

    .

    x-. , . 0S .

    2

    2

    C Ct x

    D . , ,

    2

    , exp44

    m xC x ttA tp

    DD. (1)

    , )

    2

    2

    22 , 31250 exp

    24mC x t s

    A ts

    ssp

    D

    1 exp -2

    5 1 4 3,14 0,01 31250

    -4 3 3= 4,3 10 kg/m =0,43 g/m . ) (x = -50 m) .

    50 , 0d C x m tdt

    . . (1) , t . t 50 mx , 1.1.

  • 8

    1.1 50 mx 1, max 0,97C g/m3 t = 120 000 s.

    2.

    6. , a 10 cm2 , 1 2 20 cm/sv v . 1 9mg/lC ,

    2 0 mg/lC . , . , 3C ( )

    6 , 2.1, 1, 2 3, , .

    / 0C n . ,

    d d d .nCC V Cv n A A S

    t n

    D

  • 9

    2.1

    / 0t ,

    d 0C vt .

    ,

    dnCD An

    =0 .

    o1 1 1 1 1 1 1 1 1 1cos , cos180v n v n v n v n v n , o2 2 2 2 2 2 2 2 2 2cos , cos180v n v n v n v n v n , o3 3 3 3 3 3 3 3 3 3cos , cos 0v n v n v n v n v n .

    1 1 1 1 2 2 2 2 3 3 3 3

    C dvn A C v n A C v n A C v n A .

    1 1 1 2 2 2 3 3 3 0v A C v A C v A C . (1)

    1 1 2 2 3 30 v A v A v A (2) (1) (2)

    6

    61 1 1 2 2 23

    1 1 2 2

    0,2 0,1 9 10 0,2 0,1 0 4,5 10 kg/L=4,5 mg/L0,2 0,1 0,2 0,1

    v AC v A CCv A v A

    .

    7. 21 10cm . , 5 g/sS . 1 10 cm/sv , .

  • 10

    7 , 2.2, 1 2 , . / 0C n .

    2.2

    ,

    d d d .nCC V Cv n A A S

    t n

    D

    / 0t ,

    d 0C vt .

    ,

    dnCD An

    =0.

    o1 1 1 1 1 1 1 1 1 1cos , cos180v n v n v n v n v n , o2 2 2 2 2 2 2 2 2 2cos , cos180v n v n v n v n v n .

    1 1 1 1 2 2 2 2

    C dvn A C v n A C v n A .

    1 1 1 2 2 2 0v A C v A C S , 1 0C ,

    2 2 2 0v A C S . (1)

    1 1 2 20 v A v A (2) 1 2A A 1 2v v .

  • 11

    (1) (2),

    3 32 42 2 1 1

    0,005 50 kg/m 50 mg/cm0,1 10 10

    S SCv A v A

    .

    8. 21 2 20 cmA ,

    o1 10 Ct o2 20 Ct . 3A .

    , : . : tr r p pc c t .

    8

    d d dnCC V Cv n A A S

    t n D

    ,

    3J/mpC c Tr ,

    : - [kg/m3]; pc - [J/kgK];

    T - [ K ].

    d d dpp p nc T

    c T V c Tv n A A St n

    rr r

    D .

    2.3

    0t

    ,

    d 0C Vt .

    ,

    / 0T n , .

    d 0nC An

    D , 2.3. , , . =0S .

    o1 1 1 1 1 1 1 1 1 1cos , cos180v n v n v n v n v n , o2 2 2 2 2 2 2 2 2 2cos , cos180v n v n v n v n v n ,

  • 12

    o3 3 3 3 3 3 3 3 3 3cos , cos0v n v n v n v n v n .

    1 1 2 2 3 3

    dp p p pc Tv n A c Tv A c Tv A c Tv Ar r r r .

    1 1 1 2 2 2 3 3 30 p p pc T v A c T v A c T v Ar r r . (1) ,

    1 1 2 2Q v A v A . (2)

    1 1 2 2 3 3Q v A v A v A . (3) (1), (2) (3)

    1 1 1 21 1 1 2 2 23 1 23 3 1 1

    1 288,15 K2 2

    v A T Tv AT v A TT T Tv A v A

    ,

    . o

    3 15 Ct .

    9. , 0x . (x > 0) 2800 W/mSH . oT , /T x x > 0. h=1 m, b=10 m v=1 m/s.

    20,1 m /sD . 4200 J/kgKpc , 31000 kg/m .

    : tr r p pc c t . 9

    x . pC c Tr

    d d dpp p n Sc T

    c T V c Tv n A A H xbt n

    rr r

    D . (1)

  • 13

    0t ,

    d 0pc T Vtr .

    o1 1 1 1 1 1 1 1 1 1cos , cos180v n v n v n v n v n , o2 2 2 2 2 2 2 2 2 2cos , cos180v n v n v n v n v n ,

    1 2

    dp p pc Tv n A c vbhT c vbhTr r r .

    Tx

    n . +, -.

    2 1

    dn p pC T TA c bh c bhn x x

    r r D D D . ( ) 2J/smSH , ,

    2J/msS

    H ,

    JsS

    H xb .

    (1)

    2 12 1

    0 p p ST Tc vbh T T c bh H xbx x

    r r

    D . (2)

    T x

    2 1 /T T T x x ,

    2 1

    T T T xx x x x

    ,

    2

    20 p ST Tc h xb v H xbx x

    r

    D .

    xb , 2

    20 p ST Tc h v Hx x

    r

    D . (3)

    . x

    T Tv vx x

    ,

  • 14

    2

    2 2

    T Tx x

    D D ,

    T x . ,

    v xPe D

    .

    1Pe , 2

    2

    T Tvx x

    D, .

    1Pe , 2

    2

    T Tvx x

    D, .

    x , , ?

    1v xPe D

    ,

    0,1 0,1 m1

    xv

    D .

    , 100 m 1 km. 1 mx , . (3)

    0 p STc hv Hx

    r . (4)

    o o

    4800 C C2 10 0,21000 4200 1 1 m km

    S

    p

    HTx c hvr

    .

    pC c Tr

    .p x p y p z p

    x p y p z p

    c T v c T v c T v c Tt x y z

    c T c T c T Sx x y y z z

    r r r r

    r r r

    D D D

    (5)

    f tr , , , ,f x y z tr . 0y zv v .

    , ,x y z f x y z D D D D . ,

    ,t f y z , . 0T Ty z

    .

    2J/smSH . , h

  • 15

    2J/m

    sSH

    ,

    3J/ms

    SHSh

    .

    , (5) 2

    2S

    pHT T Tc v