Physical interpretation
consider
a
.
flow of fluid .
The flow of the fluid
velocity
Consider
is
described
by its
vection field.
an
imaginary volume of the shape of
parallelopiped placed inside the flow of fluid .
Sides
of the volume
are x
,
.
64 and E
T
I
-X
Fluid
flowing inside ABCD per unit time
F
.
OSABAD
.
,
(n +
,
7,
2)0y0z5
Va (n + *
-
+ , z)0y07
,
Gua(n) +38
=
Fluid
flowing outside
↑ (x -
=
=
Net
Va
-
1
,
-
eva
7)
(n -
G Va(x
flow
,
of
,
.
,
y, +)
EFGH
per
0802(5)
y,
unit time ,
.
z)0y87
+ 30%
fluid ,
onwyz
similarly for
quoyz
other
two
and
set of surfaces ,
OzRy
Not fluid
per
unit
passing through
time
,
per unit
the
parallelopiped
volume ,
a
If
E ~
.
30
F ECO
.
,
,
net fluid
net
fluid
coming outsource
coming
.
Physical interpretation of carl
in
:
.
Sink .
Carli
Let's define a rector
#
En
Ay
is
Az
[An]-y]
+
*
.
=
I
z
I
1As
=
using operator
a
e[@r]
measure
"cods around
"
.
of how much the
The point in question
.
rector
(x y 07)
,
↑3 (
+
>
&
+ 0x, y +
r
circulation :
(1) Quen
·
+
=>
=
07)
[ (3)
·
(a(1)on +
·
-
Ca(3)*x
Cy(4)0y
.
-
.
56(4) +Eaton
-en)
circulation
Es
.
-
=
by
(en) + () 07 tes)
on
Call) Ou + Cy(e)0y
(2)
+
by a
per unit area
.
=
(e)
cy(4)0Y