calculations for ground water contamination process

1. Scanned by CamScanner
M a s s Tra n s p o r t in S a tu ra te d M e d ia 6 7
(im u M w a te r tlo w
S O W C
FIG U R E 2 1 1 Plu m e re s u ıtin g fr o m the c o n tin
u o u 5 in je c tio n o f a łra c e r in ło a t w i m e n
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H yd ro g e o lo g y,
3 rd e d (u p p e r sa d d ıe R iv e r,
N e w Je rs e y P re n tic e H a ll,
ın c ,
19 9 4 1
S te a dy s la te c o n d itio n s a re o b ta i. E d . H e n tim e a p p ro a c h e s i. ñ n ity T h e re fo re
e q u a tio ° 2 30 is i. Te g ra ıe d lr o m 0 to n m e re s u lt is
w h e r e
K o
= th e m o d ifie d B e s s e ll fu n c tio n o f th e s e c o n d k in d a n d z e r o o r d e r (v a lu e s
a r e ta b u la te d in A p p e n d ix B )
Q = th e r a te th a t th e c o n ta m in a n t is in je c te d
b = th e th ic k n e s s o f th e a q u ife r o v e r w h ic h th e c o n ta m in a n t is in je c te d
EX A M p LE A w a s te liq u id c o n ta in in g flu o r id e a t a c o n c e n tr a tio n o f 133 m w w a s p u m p e d in to
p R O B LEM a s h a llo w d is p o s a l p it lo c a te d a b o v e a th in ı7 5 m th ic k (t w i m e n s r o n a l ) a q u ik r
a t a r a te o f 3 66 m
3
/d a y fo r m a n y y e a r s T h e a v e r a ge lin e a r v e l t y o f th e
g r o u n d w a te r w a s 0 187 m /d a y A s s ıim e th a t th e tT a n s v e rs e d is p e rs io n is 10 % o f th e
ıo n g itu d in a l d is p e rs io n If th e d is p o s a l p it is a q ç u m e d to b e a t a lo c a tio n o f x o
- O
a n d yo
- O ,
w h a t w o u ld th e c o n c e n tr a tio n o f flu o r id e be in a m o n ito r in g w e u
k )c a te d a t x - 123 m a n d y - 16 m ? A s s u m e th a t th e O u o r id e is n o n r e a c tiv e a n d
n o n a d s o r b e d b y th e a q u ife r
1 F irs t th e v a lu e o f a L m u s t be c a ıc u la te d u s in g e q tıa tio n 2 8 2
a - 0 83 ((lo g (U )1 4 14
L is e q u a l to x x o o r 123 m
a L
- 0 8 3((1o g(123))
U 14
a L
= 4 9 ı9 m
2 N e x t th e v a lu e o f D L a n d D r m u s t b e fo u n d
D L
= V .
(ıし
D L
- 0 187 m /d a x 4 9 19 m - 0 9 20 m
z
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D T
= 0 10 D L
D T
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2
lda
th e v aria błe s a re the n in se rte d in to e qu a tio n 2 30a
q = 133 m gíし
Q = 3 66 m
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m g/L
C =
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o f 13 52 T he v a lu e lis te d a bo v e ,
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c o m p u ta tio n a lp r o gr a m w a s g e n e r a te d by a . a th e m X
tio n °' " h in fin ity A s th is
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3. Scanned by CamScanner
M a s s Tra n s p o rt in S a tu ra te d M e d ıa 6 9
w ith
V
2
X
2
4 D L
2
'
4 D L
D T
T h e in te gr a lin th e a b o v e e q u a tio n w a s s o lv e d by H a n tu s h (1956)T h is s o lu tio n is
w ith tD a n d B a s d e fin e d a b o v e
It s h o u ld b e n o te d th a t in e ffe c t tD
is a d im e n s io n le s s fo r ırr o f tim e T h e v a lu e s
o f W ttD ,
B ]c a n b e fo tın d in H a n tu s h (1956) a n d a lim ite d s e r ie s is ta b u la te d in A p
p e n d ix C In w e ll h y d r a u lic s th is is k n o w n a s th e le a k y w e ll fu n c tio n ,
W [u ,
/ lb]
EX A M PLE A u n d e r g r o u n d ta n k w h ic h fo r m e r ly łie ld b e n z e n e b u t n o w h o ld s w a te r is le a k in g
p R O B LEM a t a r a te o f 1 93 m
3
/ye a r H o w e v e r ,
th e w a te r s till c o n ta in s s o m e b e n z e n e a t a
c o n c e n tr a tio n o f 12 ,
95 0 p g/し T h e gr o u n d w a te r w h ic h flo w s b e n e a th th e le a k in g
ta n k g o e s d ir e c tly n o r th A d r in k in g w a te r s u p p ly w e ll is lo c a te d a t a s p o t th a t c a n
b e lo c a te d b y g o in g 12 3 5 m d u e n o r th o f th e le a k in g ta n k a n d th e n 7 2 m d u e e a s t
A s s u m e th a t th e a v e r a g e lin e a r v e lo c ity o f th e g r o u n d w a te r is 0 2 3 5 m /d a y a n d th e
lo n gitu d in a l d isp e r s iv ity is 12 m a n d tłie la te r a l d is p e r s iv ity is 1 2 m a n d th e a q u ife r
th ic k n e s s is 1 00 m W n a t w o u ld th e b e n e z e n e c o n c e n tr a tio n b e a fte r 2 0 0 y e a r s ?
T h is is a n e x a m p le o f a c o n tin u o u s le a k a g e in to a tw o d im e n s io n a l flo w fie ld
e q u a tio n 2 3 1
1 T he v a lu e s o f D L a n d D T m u st b e ca lc u la d fr o m e q u a tio n s 2 1 1a a n d 2 1 1b .
W e w ill ign o r e th e e ffe c tiv e ıjiff,]l i. n c o e ffic ie n t a s it is s o m u c h sm a lle r th a n
dispersiity
D L
- a L v .
- 12 m x 0 235 m /d a y - 2 82 m
2
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D T
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2
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2 T h e v a lu e o f B m u s t b e c a lc u la te d
l
A

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3 Th e n e x t ste p is to fin d tD C o n v e r t tim e in ye a rs to tim e in d a ys by m u ltip
365 d a ys p e r ye a r
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4 0 n e m u st n o w fin d W TO ,
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W to ,
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W ttD ,
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5 26]= 0 0 019
5 T he v a lu e s a r e th e n s u bs titu te d in to E q u a tio n 2 3 1 T h e r a te o f le a k a g e ,
Q ,
is c o nv e r te d in to c u b ic m e te r s p e r d a y by d iv id in g by 3 65 T ire a q u ife r th ic k n e s s is 1 00 m
Q = 1 93 m
3
/y e a r /365 d a /ye a r -
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3
ld a
C (į , y ,
t) = 0 0 06 1e x p (5 16)[0 00 79]lt g/L
C (x , y ,
1) = 0 006 1 x 174 X 0 00 79 lt g/L
C (x , y ,
t) = 0 00 84 lt g/L
2 8 8 Slu g In ie c fio n in ıo a U n ifo r m Tw o D im e n s io n a lFlo w Fie ıd
If a s lu g o f c o n ta m in a tio n is in je c te d o v e r th e ń ıllth ic k n e s s o f a tw o d im e n s io n a l u n i
fo i n r flo w fie ld in a s h o r t p e r io d o f tim e ,
it w illm o v e in th e d ir e c tio n o f flo w a n d s p r e a g

5. Scanned by CamScanner
M a s s Tra n s p o rt in So hJra fe d M e d ia 7 1
y (c m )
In itia l po in t in je c tio n
:X
= ı
t
5 10
D is ta n c e x fro m
in je c tio n po in t (c m )
FIG U R E 2 12 ın ie c łio n o fa s lu g o Fa tra c e r in to a łwimensional flo w fie ld s ho w n a f thre e
tim e in c re m e n ts Ex p e rim e n ta ıre s u ıts fro m J Be a r,
JOUrnol o fG e o p hy s ic o ıRe s e a rc h 6 6 ,
n o 8
(19 6 1):2 4 5 5 6 7 C o py rig ht by the A m e ric a n G e o p hys ic a lU n io n
w ith thn e T his r e s u lt is i끄u s tr a te d b y F ig u r e 2 12 a n d r e p r e s e n ts th e pattern o f c o n ta
m in a tio n a t th r e e in c r e m e n ts th a t r e s u lt Ir o m a o n e tim e s p ill F rgu r e 2 12 is b a s e d o n
th e r e s u lts o f a la bo r a to ry e x p e rim e n t c o n d u c te d b y B e a r (1961) F ig u re 2 13 s h o w s th e
s p r e a d o f a p lu m e o f c h lo rid e th a t w a s in je c te d in to a n a q u ife r a s a p a r t o f a la rge s c a le
fie ld te s t (M a c k a y e t a l 1986) T h e p lu m e th a t r e su lte d fr o m th e fie ld te s t is m o r e
c o m p le x th a n th e la b o r a to ry p lu m e d u e to th e h e te r o g e n e itie s e n c o u n te r e d in th e r e a l
w o r ld a n d th e fa c t th e p iu m e m a y n o t b e fo llo w in g th e d iffu s io n a lm o d e lo f d is p e r s io n
D e Jo s s e lin D e Jo n g (1958)d e r iv e d a s o lu tio n to th is p r o b le m o n th e b a s is o f a
s ta tis tic a ltr e a tm e n t o f la te r a la n d tr a n s v e r s e d is p e r s iv itie s B e a r (196 1)la te r verified
it e x p e r im e n ta lly If a tr a c e r w ith c o n c e n tr a tio n C o
is in je c te d in to a tw o d im e n s io n
a l flo w fie ld o v e r a n a r e a A a t a p o in t (x o , } o),
th e c o n c e n tra tio n a t a p o in t (x , y ),
a t
tim e t a fte r th e in je c tio n is
C (x , y ,
t) =
4 r rt (D L
D r Y/2
e x p
EX A M pLE A ta n k tr u c k w h ic h is c a r ry in g w a te r c o n ta in in g 127 5 m Y L o f d is s o lv e d b e n z e n e
p R O B Į EM o v e r tu r n s a n d s p ills a v o lu m e o f w a te r s u ffic ie n t to s a tu r a te a th in a q u ife r o v e r a n
a r e a o f 5 n ı
2
T he a q u ife r c o n ta in s gr o u n d w a te r flo w in g w ith a n a v e r a ge lin e a r
v e lo c ity o f 0 4 5 m /d a y A s su m e th a t th e v a lu e s o f D L a n d o f D T a r e 2 1 m
2
/d a y a n d
0 2 1 m
2
/d a y r e s p e c tħtlly
T he re is a n e a r by priv a te w e lla t a s e a s o n a lc o tta ge If th e c e n te r o fth e sp illis a t lo
c a tio n x o
- O a n d yo
- O,
th e n th e lo c a ń o n o f th e w e llis x - 72 m a n d y - 5 5 m Æ e o w n
e rs o f th e priv a te w e ll a r e a w a y fo r th e s e a s o n a n d w illn o t ret urn fo r a n o th e r 200 d a ys
1f th e r e is n o d e gr a d a tio n o r r e ta r d a tio n o f th e b e n z e n e a s it m o v e s th r o u gh th e a q u ife r ,
w ha t w illth e c o n c e n tra tio n o f b e m e n e b e in th e p riv a te w e llw h e n th e o w n e r s return
T h e c o r r e c t e q u a tio n to u s e is 2 32 fo r a s lu g in je c tio n o f c o n ta m in a tio n in to a
tw o d im e n s io n a l a q u ife r

6. Scanned by CamScanner
C ha pte r Tw o
r
r
462 da ys
647 days
:
C
y
FIG U RE 2 13 Ve rtic a lly a v e ra g e d c hïo riđe
c o n c e n tra tio n a t 1 da y,
85 da ys ,
4 62 da ys,
a n d 6 4 7 da ys a fte r the in je c tio n o fa slug into
a s ha ııo w a q u ife r So u rc e D M M a c ka
y et
a l W a te r Re s o u rc e s Re s e a rc h 2 2,
n o 13
(19 8 6 ):2 0 17 2 9 C o pyr ig ht by the A m e ri
c a n G e o p hys ic a ıU n io n
C °
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e x p l

7. Scanned by CamScanner
M o s s Tra n s p o r t in S a h Jra te d M e d ia 7 3
C = 3 82 e x p (0 3 7 2 ) - 3 82 x 0 6 8 92 = 2 6 3 m g L 1
T h e m a x im u m c o n c e n tr a tio n o f a c o n ta m in a n t fr o m a s lu g in je c tio n is fo u n d in
th e c e n te r o f th e p lu m e ,
o r th e c e n te r o fm a s x If th e flo w is in th e d ir e c tio n o f th e x
a x i a n d th e s p ill w a s a t lo c a tio n x o
- O a n d } o
- O ,
th e c e n te r o f m a s s o f a c o n s e r v
a tiv e s u b s ta n c e a t a n y tim e t s in c e th e s p ill w ill b e a t a lo c a tio n w h e r e x -
v J a n d y
- 0 If w e s u b s titu te th e s e v a lu e s in to e q u a tio n 2 32 ,
w e o b ta in
C o A
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T h e d is tr ib u tio n o f c o n ta m in a tio n in th e p lu m e w ill fo llo w a n o r m a l o r G a u s s
ia n d is tr ib u tio n F T o m e q u a ń o n s 2 12 a a iıd 2 12 b th e s ta n d a r d d e v ia tio n o f th e d is
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p
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99 7 p e r c e n t o f th e m a s s o f c o n ta m in a tio n w illb e c o n ta in e d w ith
in a n a r e a r e p r e s e n te d b y th r e e s ta n d a r d d e v ia tio n s a w a y fr o m th e c e n te r o f m a s s
o f th e p lu m e T hu s th e p lu m e c a n b e defined b y th e lo c a tio n o f th e c e n te r o f m a s s ,
3 [T
×
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EX A M P LE A tr u c k c a r r y in g d ilu te b r in e w ith 2 13 0 m g/L c h lo r id e fr o m th e c le a n u p o f a p o n dPR O B LEM c o n ta in in g w a s te fr o m a p r o d u c in g o il w e ll overturns a n d s p ills th e d ilu te b r in eo v e r a n a r e a o f 455 s q u a r e fe e t T h e u n d e r ly in g th in a q u ife r h a s a n a v e r a g e lin e a r
g r o u n d w a te r v e lo c ity o f 1 2 3 fu d a y W U e r e w o u ld th e c e n te r o f m a s s o f th e p lu m eb e in 133 d a y s ,
w h a t w o u ld th e m a x im u m c o n c e n tr a tio n b e a n d h o w fa r b e y o n da n d to th e s id e o f th e c e n te r o f m a s s w o u ld th e p lţ ım e s p r e a d ?
1 T he p lu m e w o u ld b e a d v e c te d b y th e flo w in g gr o u n d w a te r s o th a t th e c e n te r o fï n a s s w o u ld b e a t x -
v x
t
X - 1 2 3 ft/d a X 133 d a - 164 fe e t
2 T he m a x im u m c o n c e n tr a tio n a t th e c e n te r o fm a s s c a n b e fo u n d fr o m e q u a tio n 2 32 a
C . .
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C o A
4 t
a W e n e e d to fin d th e v a lu e s o f D L a n d D t T h is c a n b e d o n e u s in g e q u a tio n s2 11a a n d 2 1 1b b u t,
fir s t w e n e e d to u s E X o . 2 82 to e s tim a te o ĹL
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C ho pb r Tw o
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0,
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2 4 ı4
e 5 66 ft X 1,
23 ftda
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da
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W e c a n a ssu m e D T
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2
da
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2130m gL '
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4 x IT x 1 3 3 d a ft2d a 1 × 6 696 ft2d a I
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3 T he siz e o f the plu m e c a n b e d e te rm in e d fro m th e s ta n d a r d d e v ia tio n s
(T
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T h e le a d in g e d ge o f th e plu m e is 3[T
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fe e t a h e a d o f th e c e n te r o f m a s s o r 129
fe e t a n d th e plu m e h a d s p r e a d o u t 3
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o r 40 8 fe e t
2 9 Effe c ts o fTra n sv e rse D is pe rs io n
T he r a tio o f lo n gitu d in a lto tr a n s v e r s e d is p e r s iv ity (c TL /c ľ T iin a n a q u ife r is a n im p o r
ta n t c o n tr o l o v e r th e s h a p e o f a c o n ta m in a n t p lu m e in tw o d im e n s io n a l m a s s tr a n s
P o r t T h e lo w e r th e r a tio ,
the br o a d e r th e s h a p e o f th e r e s u ltin g p lu m e w ill b e F ig u r e
2 14 sh o w s v a r io u s tw o d im e n s io n a ls h a p e s o f a c o n ta m in a n t p lu m e ,
w h e r e th e o n ıyfa c to r v a r ie d w a s th e r a tio o f lo n gitu d in a l to tr a n s v e r s e d is p e r s iv ity T M s íu u s tr a te s
th e fa c t th a t it is im p o r ta n t to h a v e s o m e k n o w le d g e o f th e tr a n s v e r s e d is p e r s iv ity in
a d d itio n to th e lo n gitu d is a ld is p e r s iv ity T h e r e is a p a u c ity o f d a ta in th e ıite r a tu r e o n
th e r e la tio n s h ip s o f lo n gitu d in a lto tr a n s v e r s e d is p e r s iv 让他s F T o m th e fe w fie ld s tu d
ie s a v a ila b le ,
CtL " LT " in th e r a n ge o f 6 to 2 0 iA nd e r s o n 197 9 ,
K lo tz e t a l 1 98 0 ) ï n a d i l
d itio n ,
d is p e r s iv ity r a tio s b a s e d o n fie ld s tu d ie s a r e b a s e d o n fittin g th e d iffu s iu i国团团図
m o d e l o f d is p e r s io n to c a s e s w h e r e it m ig h t n o t b e a p p lic a b le

9. Scanned by CamScanner
Ex A M pLE A so ilc o lu m n is 40 c m lo n g It is se t u p s o th a t d e io n iz e d w a te r ís flo w in g ıiìro uÈpRo BLEM a t a n a v e r a ge lin e a r v e lo c ity o f 1 35 × 10 2
c m s
1
.
M e flu id s o u r c e is c ha n y c d 1o n e w ith a c hlo ride c o n c e n tra tio n o f 300 m gL 1
A fte r 500 s e c o n d s, tj tíc o n c e n tr a tio n o f c hlo r id e w a s 48 m gL 1
a n d a fte r 4 000 s e c o n d s ,
l2 ,
it W :m gL 1
W Ĥ a t is the disp e rs iv ity o f th e sa n d in th e s o il c o lu m n ?
ı1re n u m be r o fp o re v o lm e s a t a giv e n tim e c a n b e c a lc u la te d fro m E q u a tio n ) 1
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1 35 X 10 2
C m s
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X 4 000 5 /4 0 c m =
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C /C o is 48/3 00 , W h ic h e q u a ls 0 16 W ith a p o r e v o lu m e o f 0 17
A t t2 ,
C /C o is 2 52/3 0 0 , W h ic h e q u a ls 0 8 4 W ith a p o r e v o lu m e o f 1 3 2s in c e c /c o a t tl is c o n v e n ie n tly e q u a l to o 16 ,
th e n (u ry lu ì/2
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FıG U R E 2 9 D im e n s io n le s s typ e c u r v e s
T
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5 8 C o p y rig ht b A m e ric a n G e o p hys ic a lU n io n
Re s e a rc h 16 , n o (19 80 ):14 5
fo r the c o n tin u o u s in je c tio n o fa tra c e r in to a o n e di
to th e r a te o f tr a n s p o r t b y h y d r o d y n a m ic d is p e r s io n F o r p e c le t n u m b e r 1,
th e fix e d
s te p ħın c tio n a n d th e c o n tin u o u s in je c tio n fu n c tio n giv e qu ite d iffe r e n t r e s u lts,
w h e r e
m id w a y b e tw e e n th e o th e r tw o T h is figu r e s u gg e s ts th a t fo r p e c le t n u m b e r s te s s th a n
a b o u t 10 ,
th e e x a c t s o lu tio n s n e e d to b e c o n s id e r e d ,
w h e r e a s fo r p e c le t n u m be r sg r e a te r th a n 10 ,
th e a p p r o x im a te s o lu tio n is p r o b a b ly a c c e p ta b le ,
e sp e c ia lly a s th eP e c le t n u m b e r a p p r o a c h e s 100 T his P e c le t n u m b e r in c r e a s e s w ith flo w p a th le n gtha s a d v e c tiv e tr a n sp o r t b e c o m e s m o r e d o m in a n t o v e r d is p e r s iv e tr a n sp o r t T h u s fo rm a s s tr a n s p o r t n e a r th e in le t b o u n d a r y it is im p o r ta n t to u s e th e c o rr e c t e q u a tio n ,
b u ta s o n e g o e s a w a y fr o m th e in le t b o u n d a r % it is le s s im p o r ta n t th a t th e c o rr e c t fo r m
o f th e e q u a tio n is e m p lo y e d
EX A M P LE
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P ic k le s a r e m a d e in la r g e w o o d e n v a ts A t th e H a p p y G h e r k in Ħc k le F a c to ry o n e
o f th e v a ts h a s b e e n le a k in g b r in e d ir e c tly in to th e w a te r ta b le T he c o n c e n tr a tio n
o f c h lo r id e ín th e b r in e is 157 5 m g L 1
T h e flo w in th e a q u ife r th a t r e c e iv e s th e
b r in e is e s s e n tia lly o n e d im e n s io n a l a n d h a s th e fo llo w in g c h a r a c te r is tic s
H y d r a u lic c o n d u c tiv ity - 2 93 X 10 4
m s
1
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E ffe c tiv e p o r o s ity - 0 2 59
T h e e s tim a te d e ffe c tiv e d iffu s io n c o e ffic ie n t fo r c h lo r id e ís 2 X 10 9
m
2
s
]
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ta n c e 12 5 m fr o m th e le a k in g v a t 0 50 ye a r s a fte r th e le a k b e g a n
W e w ill a p p ly e q u a tio n 2 2 5 to th is p r o b le m N o te th a t th is is a n a pp r o x im a te
s o lu tio n a s th e s e c o n d te rm o f e q u a tio n 2 2 3 h a s b e e n d r o p p e d
c =
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n z s
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M a s s Tra n s p o rt in Sa ïu ra b d M e d ia 6 5
C = 7 87 5e r fc
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C = 7 87 5 e r fc (0 08 16 )m g /L
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8 5 Third Bo u n da r y C o n diño n
A s o ıu tio n fo r E q u a tio n 2 18 fo r th e fo llo w in g b o u n d a ry c o n d itio n w a s giv e n b y v a n
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O ) = O In itia lc o n d itio n
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th e c o n c e n tr a tio n
g r a d ie n t w ill s till b e fin ite U n d e r th e s e c o n d itio n s th e s o lu tio n to E q u a tio n 2 18 is
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E q u a tio n 2 2 5 ,
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If a s lu g o f c o n ta m in a tio n is in s ta n ta n e o u s ly in je c te d in to a u n ifo r m ,
o n e d im e n s io n a l
flo w fie ld ,
it w illp a s s th r o u gh th e a q u ife r a s a p u ls e w ith a p e a k c o n c e n tr a tio n ,
C . a x ,
a t s o m e tim e a fte r in je c tio n ,
im a x
T h e s o lu tio n to E q u a tio n 2 18 u n d e r th e s e c o n d itio n s
(S a u ty 19 80 )is in d im e n s io n le s s fo r m
C R (tR ,
P e ) = . . ( (1 tR Y (2 2 8 )
w ith
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EX A M P LE
P R O B LEM
A s s u m e a D o f 1 X 10 9
m
2
/s e c a n d a n m o f 0 5 ,
to giv e a D *
o f 5 × 10 ıo
m
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F in d th e v a lu e o f th e c o n c e n tr a tio n r a tio .
C ,
/C o ,
a t a d is ta n c e o f 5 m a fte r 10 0 y r
o f d iffu s io n
1 C o n v e r t 10 0 y r to s e c o n d s
10 0 y r X 36 5 d a /y r x 144 0 m in /d a X 60 s e c /m in - 3 15 X 109
s e c
2 In s e r t v a lu e s in to E q u a tio n 2 5
C t _ e r fc
5
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m
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/s e c X 3 15 X 109
s e e p 5
3 S o lv e
Q _ e r fc
(į _ e r fc 1 99 = 0 0 05
c o
2 5 1 )

15. Scanned by CamScanner
EX A M PLE D is s o lv e d n itr a te in a c o n c e n tr a tio n o f 18 0 m glL is b e in g a d v e c te d w ith flo w in g
PRO B LEM gr o u n d w a te ľ a t a v e lo c ity o f 0 33 1 m /d a y in a n a q u ife r w ith a p o r o s ity o f 0 2 2 5
G r o u n d w a te r fr o m th e a q u ife r d is c h a rg e s in to a s tr e a m W n a t is th e m a s s flu x o f
n itr a te in to th e s tr e a m if th e a q u ife r is 1 80 m th ic k a n d 123 m w id e w h e r e it
d is c h a r ge s in to th e s tr e a m ?
F r o m E q u a tio n 2 7 th e o n e d im e n s io n a l m a s s flu x is
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F o r c o n s is te n t u n its th e c o n c e n tr a tio n s h o u ld b e in g m /m
3
C = 18 0 m g/L X 1/10 00 g m /m g X 1000 L /m
3

16. Scanned by CamScanner
■自自由
5 2 Chapr Tw o
C - 18 0 g m /m
3
T h e o n e d im e n s io n a lm a s s flu x is
F ,
= 0 3 3 1 m /d a X 0 2 2 5 X 18 0 g m /m
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= 1 34 gm /d a m
2
T h e flu x in to th e s tr e a 】x ıis th e o n e d im e n s io n a l m a s s flu x tim e s th e c r o ss se c
tio n a l a r e a w h e r e th e a q u ife r d is c h a r g e s in to th e s tr e a m
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2
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